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Sample records for continuum hartree-fock-bogoliubov theory

  1. Extended Hartree-Fock-Bogoliubov theory for degenerate Bose systems

    International Nuclear Information System (INIS)

    Tommasini, Paolo; Passos, E J V de; Pires, M O C; Piza, A F R de Toledo

    2005-01-01

    An extension of the Hartree-Fock-Bogoliubov (HFB) theory of degenerate Bose systems in which the coupling between one and two quasi-particles is taken into account is developed. The excitation operators are written as linear combinations of one and two HFB quasi-particles. Excitation energies and quasi-particle amplitudes are given by generalized Bogoliubov equations. The excitation spectrum has two branches. The first one is a discrete branch which is gapless and has a phonon character at large wavelength and, contrarily to HFB, is always stable. This branch is detached from a second, continuum branch whose threshold, at fixed total momentum, coincides with the two quasi-particle threshold of the HFB theory. The gap between the two branches at P = 0 is twice the HFB gap, which thus provides for the relevant energy scale. Numerical results for a specific case are given

  2. Hartree-Fock-Bogoliubov approximation for finite systems

    International Nuclear Information System (INIS)

    Bulgac, A.

    1980-08-01

    The features of the spectrum of the Hartree-Fock-Bogoliubov equations are examined. Special attention is paid to the asymptotic behaviours of the single quasiparticle wave functions (s.qp.w.fs.), matter density distribution and density of the pair condensate. It is shown that, due to the coupling between hole and particle, the sufficiently deeply bound hole states acquire a width and consequently have to be treated as continuum states. The proper normalization of the s.qp.w.fs. is discussed. (author)

  3. Instability of the cranked Hartree-Fock-Bogoliubov field in backbending region

    International Nuclear Information System (INIS)

    Horibata, Takatoshi; Onishi, Naoki.

    1982-01-01

    The stability condition of the cranked Hartree-Fock-Bogoliubov field is examined explicitly by solving the eigenvalue equation for the second order variation of the energy, which is reduced to an algebraic equation through a coupled dispersion formula. We confirm that the Hartree-Fock-Bogoliubov field is unstable in the backbending region of an irregular rotational band, even though the frequency of the softest random phase approximation mode always has a positive value. We investigate properties of the softest mode in detail. (author)

  4. Application of the gradient method to Hartree-Fock-Bogoliubov theory

    International Nuclear Information System (INIS)

    Robledo, L. M.; Bertsch, G. F.

    2011-01-01

    A computer code is presented for solving the equations of the Hartree-Fock-Bogoliubov (HFB) theory by the gradient method, motivated by the need for efficient and robust codes to calculate the configurations required by extensions of the HFB theory, such as the generator coordinate method. The code is organized with a separation between the parts that are specific to the details of the Hamiltonian and the parts that are generic to the gradient method. This permits total flexibility in choosing the symmetries to be imposed on the HFB solutions. The code solves for both even and odd particle-number ground states, with the choice determined by the input data stream. Application is made to the nuclei in the sd shell using the universal sd-shell interaction B (USDB) shell-model Hamiltonian.

  5. Relativistic Hartree-Bogoliubov description of thorium and uranium isotopes

    International Nuclear Information System (INIS)

    Naz, Tabassum; Ahmad, Shakeb

    2016-01-01

    The relativistic Hartree-Bogoliubov (RHB) theory is a relativistic extension of the Hartree-Fock- Bogoliubov theory. It is a unified description of mean-field and pairing correlations and successfully describe the various phenomenon of nuclear structure. In the present work, RHB is applied to study the thorium and uranium isotopes

  6. Hartree-Fock-Bogoliubov model: a theoretical and numerical perspective

    International Nuclear Information System (INIS)

    Paul, S.

    2012-01-01

    This work is devoted to the theoretical and numerical study of Hartree-Fock-Bogoliubov (HFB) theory for attractive quantum systems, which is one of the main methods in nuclear physics. We first present the model and its main properties, and then explain how to get numerical solutions. We prove some convergence results, in particular for the simple fixed point algorithm (sometimes called Roothaan). We show that it converges, or oscillates between two states, none of them being a solution. This generalizes to the HFB case previous results of Cances and Le Bris for the simpler Hartree-Fock model in the repulsive case. Following these authors, we also propose a relaxed constraint algorithm for which convergence is guaranteed. In the last part of the thesis, we illustrate the behavior of these algorithms by some numerical experiments. We first consider a system where the particles only interact through the Newton potential. Our numerical results show that the pairing matrix never vanishes, a fact that has not yet been proved rigorously. We then study a very simplified model for protons and neutrons in a nucleus. (author)

  7. The Hartree-Fock seniority approximation

    International Nuclear Information System (INIS)

    Gomez, J.M.G.; Prieto, C.

    1986-01-01

    A new self-consistent method is used to take into account the mean-field and the pairing correlations in nuclei at the same time. We call it the Hartree-Fock seniority approximation, because the long-range and short-range correlations are treated in the frameworks of Hartree-Fock theory and the seniority scheme. The method is developed in detail for a minimum-seniority variational wave function in the coordinate representation for an effective interaction of the Skyrme type. An advantage of the present approach over the Hartree-Fock-Bogoliubov theory is the exact conservation of angular momentum and particle number. Furthermore, the computational effort required in the Hartree-Fock seniority approximation is similar to that ofthe pure Hartree-Fock picture. Some numerical calculations for Ca isotopes are presented. (orig.)

  8. Extreme exotic calcium lambda hypernuclei in the relativistic continuum Hartree-Bogoliubov theory

    International Nuclear Information System (INIS)

    Lv Hongfeng

    2008-01-01

    Exotic calcium lambda hypernuclei properties with the neutron number of 20-400 by a step of 20 are discussed by employing the relativistic continuum Hartree-Bogoliubov theory with a zero range pairing interaction. The Bethe-Weizsaecker mass formula of a multi-strange system and the Woods-Saxon-type potential of lambda need to be modified for exotic calcium hypernuclei with unusual number of neutrons and lambdas. The possible neutron and lambda limits of exotic Ca lambda hypernuclei are also investigated. (authors)

  9. Relativistic Hartree-Bogoliubov description of the halo nuclei

    Energy Technology Data Exchange (ETDEWEB)

    Meng, J.; Ring, P. [Universitaet Muenchen, Garching (Germany)

    1996-12-31

    Here the authors report the development of the relativistic Hartree-Bogoliubov theory in coordinate space. Pairing correlations are taken into account by both density dependent force of zero range and finite range Gogny force. As a primary application the relativistic HB theory is used to describe the chain of Lithium isotopes reaching from {sup 6}Li to {sup 11}Li. In contrast to earlier investigations within a relativistic mean field theory and a density dependent Hartree Fock theory, where the halo in {sup 11}Li could only be reproduced by an artificial shift of the 1p{sub 1/2} level close to the continuum limit, the halo is now reproduced in a self-consistent way without further modifications using the scattering of Cooper pairs to the 2s{sub 1/2} level in the continuum. Excellent agreement with recent experimental data is observed.

  10. Equivalence of classical spins and Hartree-Fock-Bogoliubov approximation of the Fermionic Anharmonic Oscillator

    International Nuclear Information System (INIS)

    Thomaz, M.T.; Toledo Piza, A.F.R. de

    1994-01-01

    We show that the Hartree-Fock-Bogoliubov (alias Gaussian) approximation of the initial condition problem of the Fermionic Anharmonic Oscillator i equivalent to a bosonic Hamiltonian system of two classical spin. (author)

  11. The Gogny-Hartree-Fock-Bogoliubov nuclear-mass model

    Energy Technology Data Exchange (ETDEWEB)

    Goriely, S. [Universite Libre de Bruxelles, Institut d' Astronomie et d' Astrophysique, CP-226, Brussels (Belgium); Hilaire, S.; Girod, M.; Peru, S. [CEA, DAM, DIF, Arpajon (France)

    2016-07-15

    We present the Gogny-Hartree-Fock-Bogoliubov model which reproduces nuclear masses with an accuracy comparable with the best mass formulas. In contrast to the Skyrme-HFB nuclear-mass models, an explicit and self-consistent account of all the quadrupole correlation energies is included within the 5D collective Hamiltonian approach. The final rms deviation with respect to the 2353 measured masses is 789 keV in the 2012 atomic mass evaluation. In addition, the D1M Gogny force is shown to predict nuclear and neutron matter properties in agreement with microscopic calculations based on realistic two- and three-body forces. The D1M properties and its predictions of various observables are compared with those of D1S and D1N. (orig.)

  12. A constrained Hartree-Fock-Bogoliubov equation derived from the double variational method

    International Nuclear Information System (INIS)

    Onishi, Naoki; Horibata, Takatoshi.

    1980-01-01

    The double variational method is applied to the intrinsic state of the generalized BCS wave function. A constrained Hartree-Fock-Bogoliubov equation is derived explicitly in the form of an eigenvalue equation. A method of obtaining approximate overlap and energy overlap integrals is proposed. This will help development of numerical calculations of the angular momentum projection method, especially for general intrinsic wave functions without any symmetry restrictions. (author)

  13. Uniform in N global well-posedness of the time-dependent Hartree-Fock-Bogoliubov equations in R^{1+1}

    Science.gov (United States)

    Chong, Jacky Jia Wei

    2018-04-01

    We prove the global well-posedness of the time-dependent Hartree-Fock-Bogoliubov (TDHFB) equations in R^{1+1} with two-body interaction potential of the form N^{-1}v_N(x) = N^{β -1} v(N^β x) where v≥0 is a sufficiently regular radial function, i.e., v \\in L^1(R)\\cap C^∞ (R) . In particular, using methods of dispersive PDEs similar to the ones used in Grillakis and Machedon (Commun Partial Differ Equ 42:24-67, 2017), we are able to show for any scaling parameter β >0 the TDHFB equations are globally well-posed in some Strichartz-type spaces independent of N, cf. (Bach et al. in The time-dependent Hartree-Fock-Bogoliubov equations for Bosons, 2016. arXiv:1602.05171).

  14. On the solution of the Hartree-Fock-Bogoliubov equations by the conjugate gradient method

    International Nuclear Information System (INIS)

    Egido, J.L.; Robledo, L.M.

    1995-01-01

    The conjugate gradient method is formulated in the Hilbert space for density and non-density dependent Hamiltonians. We apply it to the solution of the Hartree-Fock-Bogoliubov equations with constraints. As a numerical application we show calculations with the finite range density dependent Gogny force. The number of iterations required to reach convergence is reduced by a factor of three to four as compared with the standard gradient method. (orig.)

  15. Generalized Hartree-Fock-Bogoliubov approach in the description of many-body systems

    International Nuclear Information System (INIS)

    Janssen, D.

    1979-01-01

    The quantum mechanical equation for a group of states connected by large probabilities of transitions to each other, i.e. possessing common internal structure, is found. No phenomenological assumptions about the vibrational or rotational character of these states have been used. The equations obtained here can be understood as a direct generalization of the Hartree-Fock-Bogoliubov equation, this scheme including not only the ground state, but some excited states as well. The question of normalization of the density matrix in the generalized space has been solved and the additional solutions of the problem have been excluded. (author)

  16. Semiclassical approximation to time-dependent Hartree--Fock theory

    International Nuclear Information System (INIS)

    Dworzecka, M.; Poggioli, R.

    1976-01-01

    Working within a time-dependent Hartree-Fock framework, one develops a semiclassical approximation appropriate for large systems. It is demonstrated that the standard semiclassical approach, the Thomas-Fermi approximation, is inconsistent with Hartree-Fock theory when the basic two-body interaction is short-ranged (as in nuclear systems, for example). However, by introducing a simple extension of the Thomas-Fermi approximation, one overcomes this problem. One also discusses the infinite nuclear matter problem and point out that time-dependent Hartree-Fock theory yields collective modes of the zero sound variety instead of ordinary hydrodynamic (first) sound. One thus emphasizes that one should be extremely circumspect when attempting to cast the equations of motion of time-dependent Hartree-Fock theory into a hydrodynamic-like form

  17. Time-dependent--S-matrix Hartree-Fock theory of complex reactions

    International Nuclear Information System (INIS)

    Griffin, J.J.; Lichtner, P.C.; Dworzecka, M.

    1980-01-01

    Some limitations of the conventional time-dependent Hartree-Fock method for describing complex reactions are noted, and one particular ubiquitous defect is discussed in detail: the post-breakup spurious cross channel correlations which arise whenever several asymptotic reaction channels must be simultaneously described by a single determinant. A reformulated time-dependent--S-matrix Hartree-Fock theory is proposed, which obviates this difficulty. Axiomatic requirements minimal to assure that the time-dependent--S-matrix Hartree-Fock theory represents an unambiguous and physically interpretable asymptotic reaction theory are utilized to prescribe conditions upon the definition of acceptable asymptotic channels. That definition, in turn, defines the physical range of the time-dependent--S-matrix Hartree-Fock theory to encompass the collisions of mathematically well-defined ''time-dependent Hartree-Fock droplets.'' The physical properties of these objects then circumscribe the content of the Hartree-Fock single determinantal description. If their periodic vibrations occur for continuous ranges of energy then the resulting ''classical'' time-dependent Hartree-Fock droplets are seen to be intrinsically dissipative, and the single determinantal description of their collisions reduces to a ''trajectory'' theory which can describe the masses and relative motions of the fragments but can provide no information about specific asymptotic excited states beyond their constants of motion, or the average properties of the limit, if it exists, of their equilibrization process. If, on the other hand, the periodic vibrations of the time-dependent Hartree-Fock droplets are discrete in energy, then the time-dependent--S-matrix Hartree-Fock theory can describe asymptotically the time-average properties of the whole spectrum of such periodic vibrations

  18. Linearized Jastrow-style fluctuations on spin-projected Hartree-Fock

    International Nuclear Information System (INIS)

    Henderson, Thomas M.; Scuseria, Gustavo E.

    2013-01-01

    The accurate and efficient description of strong electronic correlations remains an important objective in electronic structure theory. Projected Hartree-Fock theory, where symmetries of the Hamiltonian are deliberately broken and projectively restored, all with a mean-field computational scaling, shows considerable promise in this regard. However, the method is neither size extensive nor size consistent; in other words, the correlation energy per particle beyond broken-symmetry mean field vanishes in the thermodynamic limit, and the dissociation limit of a molecule is not the sum of the fragment energies. These two problems are closely related. Recently, Neuscamman [Phys. Rev. Lett. 109, 203001 (2012)] has proposed a method to cure the lack of size consistency in the context of the antisymmetrized geminal power wave function (equivalent to number-projected Hartree-Fock-Bogoliubov) by using a Jastrow-type correlator in Hilbert space. Here, we apply the basic idea in the context of projected Hartree-Fock theory, linearizing the correlator for computational simplicity but extending it to include spin fluctuations. Results are presented for the Hubbard Hamiltonian and for some simple molecular systems

  19. Projection after variation in the finite-temperature Hartree-Fock-Bogoliubov approximation

    Science.gov (United States)

    Fanto, P.

    2017-11-01

    The finite-temperature Hartree-Fock-Bogoliubov (HFB) approximation often breaks symmetries of the underlying many-body Hamiltonian. Restricting the calculation of the HFB partition function to a subspace with good quantum numbers through projection after variation restores some of the correlations lost in breaking these symmetries, although effects of the broken symmetries such as sharp kinks at phase transitions remain. However, the most general projection after variation formula in the finite-temperature HFB approximation is limited by a sign ambiguity. Here, I extend the Pfaffian formula for the many-body traces of HFB density operators introduced by Robledo [L. M. Robledo, Phys. Rev. C. 79, 021302(R) (2009), 10.1103/PhysRevC.79.021302] to eliminate this sign ambiguity and evaluate the more complicated many-body traces required in projection after variation in the most general HFB case. The method is validated through a proof-of-principle calculation of the particle-number-projected HFB thermal energy in a simple model.

  20. Adaptive multi-resolution 3D Hartree-Fock-Bogoliubov solver for nuclear structure

    Science.gov (United States)

    Pei, J. C.; Fann, G. I.; Harrison, R. J.; Nazarewicz, W.; Shi, Yue; Thornton, S.

    2014-08-01

    Background: Complex many-body systems, such as triaxial and reflection-asymmetric nuclei, weakly bound halo states, cluster configurations, nuclear fragments produced in heavy-ion fusion reactions, cold Fermi gases, and pasta phases in neutron star crust, are all characterized by large sizes and complex topologies in which many geometrical symmetries characteristic of ground-state configurations are broken. A tool of choice to study such complex forms of matter is an adaptive multi-resolution wavelet analysis. This method has generated much excitement since it provides a common framework linking many diversified methodologies across different fields, including signal processing, data compression, harmonic analysis and operator theory, fractals, and quantum field theory. Purpose: To describe complex superfluid many-fermion systems, we introduce an adaptive pseudospectral method for solving self-consistent equations of nuclear density functional theory in three dimensions, without symmetry restrictions. Methods: The numerical method is based on the multi-resolution and computational harmonic analysis techniques with a multi-wavelet basis. The application of state-of-the-art parallel programming techniques include sophisticated object-oriented templates which parse the high-level code into distributed parallel tasks with a multi-thread task queue scheduler for each multi-core node. The internode communications are asynchronous. The algorithm is variational and is capable of solving coupled complex-geometric systems of equations adaptively, with functional and boundary constraints, in a finite spatial domain of very large size, limited by existing parallel computer memory. For smooth functions, user-defined finite precision is guaranteed. Results: The new adaptive multi-resolution Hartree-Fock-Bogoliubov (HFB) solver madness-hfb is benchmarked against a two-dimensional coordinate-space solver hfb-ax that is based on the B-spline technique and a three-dimensional solver

  1. Hartree-Fock theory for the equilibrium shape of light nuclei; Theorie Hartree-Fock de la forme d'equilibre des noyaux legers

    Energy Technology Data Exchange (ETDEWEB)

    Ripka, G [Commissariat a l' Energie Atomique, 91 - Saclay (France). Centre d' Etudes Nucleaires

    1968-09-01

    Most of the content of this thesis is published in english in Advances In Nuclear Physics, Vol. 1 (Editors: Baranger and Vogt - Plenum Press). The Hartree- Fock equations are derived. The expansions of the orbits and the possible symmetries of the Hartree-Fock field are discussed. Wavefunctions of even-even N = Z nuclei are given for 12 {<=} A {<=} 40. The role of the monopole, quadrupole and exchange components of the force are discussed. The multiplicity of the solutions and the effect of the spin-orbit interaction are discussed. Exact angular momentum projection is used to generate rotational bands. The validity of the adiabatic rotational model in light nuclei is discussed. Hartree-Fock calculations are extended to include major-shell mixing in order to obtain quadrupole deformations without the use of effective charge. The incompressibility, of nuclei is discussed and the compatibility between the Hartree-Fock solutions, the Mottelson model of quadrupole deformations and the SU3 states of J.P. Elliott and M. Moshinsky is established. (author) [French] La theorie de Hartree-Fock est appliquee au calcul des fonctions d'onde des noyaux legers deformes. Les equations de Hartree-Fock, les symetries permises et le choix du developpement des orbites sont discutes. Les fonctions d'onde des noyaux pair-pairs N = Z (12 {<=} A {<=} 40) sont tabulees. Les contributions des composantes monopolaires et quadrupolaires ainsi que des termes d'echange de la force nucleon-nucleon sont discutees. La methode de projection de moment cinetique est utilisee pour engendrer les bandes de rotation. La validite du modele rotationnel adiabatique est discutee. Les calculs de Hartree-Fock qui tiennent compte du melange de plusieurs couches majeures dans chaque orbite sont appliques au calcul des deformations quadrupolaires sans l'utilisation de charge effective. L'incompressibilite des noyaux et la compatibilite des fonctions d'onde de Hartree- Fock avec les fonctions d'onde SU3 de J

  2. Hartree-Fock theory for the equilibrium shape of light nuclei; Theorie Hartree-Fock de la forme d'equilibre des noyaux legers

    Energy Technology Data Exchange (ETDEWEB)

    Ripka, G. [Commissariat a l' Energie Atomique, 91 - Saclay (France). Centre d' Etudes Nucleaires

    1968-09-01

    Most of the content of this thesis is published in english in Advances In Nuclear Physics, Vol. 1 (Editors: Baranger and Vogt - Plenum Press). The Hartree- Fock equations are derived. The expansions of the orbits and the possible symmetries of the Hartree-Fock field are discussed. Wavefunctions of even-even N = Z nuclei are given for 12 {<=} A {<=} 40. The role of the monopole, quadrupole and exchange components of the force are discussed. The multiplicity of the solutions and the effect of the spin-orbit interaction are discussed. Exact angular momentum projection is used to generate rotational bands. The validity of the adiabatic rotational model in light nuclei is discussed. Hartree-Fock calculations are extended to include major-shell mixing in order to obtain quadrupole deformations without the use of effective charge. The incompressibility, of nuclei is discussed and the compatibility between the Hartree-Fock solutions, the Mottelson model of quadrupole deformations and the SU3 states of J.P. Elliott and M. Moshinsky is established. (author) [French] La theorie de Hartree-Fock est appliquee au calcul des fonctions d'onde des noyaux legers deformes. Les equations de Hartree-Fock, les symetries permises et le choix du developpement des orbites sont discutes. Les fonctions d'onde des noyaux pair-pairs N = Z (12 {<=} A {<=} 40) sont tabulees. Les contributions des composantes monopolaires et quadrupolaires ainsi que des termes d'echange de la force nucleon-nucleon sont discutees. La methode de projection de moment cinetique est utilisee pour engendrer les bandes de rotation. La validite du modele rotationnel adiabatique est discutee. Les calculs de Hartree-Fock qui tiennent compte du melange de plusieurs couches majeures dans chaque orbite sont appliques au calcul des deformations quadrupolaires sans l'utilisation de charge effective. L'incompressibilite des noyaux et la compatibilite des fonctions d'onde de Hartree- Fock avec les

  3. A study of self-consistent Hartree-Fock plus Bardeen-Cooper-Schrieffer calculations with finite-range interactions

    Science.gov (United States)

    Anguiano, M.; Lallena, A. M.; Co', G.; De Donno, V.

    2014-02-01

    In this work we test the validity of a Hartree-Fock plus Bardeen-Cooper-Schrieffer model in which a finite-range interaction is used in the two steps of the calculation by comparing the results obtained to those found in fully self-consistent Hartree-Fock-Bogoliubov calculations using the same interaction. Specifically, we consider the Gogny-type D1S and D1M forces. We study a wide range of spherical nuclei, far from the stability line, in various regions of the nuclear chart, from oxygen to tin isotopes. We calculate various quantities related to the ground state properties of these nuclei, such as binding energies, radii, charge and density distributions, and elastic electron scattering cross sections. The pairing effects are studied by direct comparison with the Hartree-Fock results. Despite its relative simplicity, in most cases, our model provides results very close to those of the Hartree-Fock-Bogoliubov calculations, and it reproduces the empirical evidence of pairing effects rather well in the nuclei investigated.

  4. Excess Charge for Pseudo-relativistic Atoms in Hartree-Fock Theory

    DEFF Research Database (Denmark)

    Dall'Acqua, Anna; Solovej, Jan Philip

    2010-01-01

    We prove within the Hartree-Fock theory of pseudo-relativistic atoms that the maximal negative ionization charge and the ionization energy of an atom remain bounded independently of the nuclear charge $Z$ and the fine structure constant $\\alpha$ as long as $Z\\alpha$ is bounded.......We prove within the Hartree-Fock theory of pseudo-relativistic atoms that the maximal negative ionization charge and the ionization energy of an atom remain bounded independently of the nuclear charge $Z$ and the fine structure constant $\\alpha$ as long as $Z\\alpha$ is bounded....

  5. Functionals Hartree-Fock equations in the Schrodinger representation of quantum field theory

    International Nuclear Information System (INIS)

    Gamboa, J.

    1989-08-01

    Hartree-Fock equations for a scalar field theory in the Schrodinger representation are derived. It is shown that renormalization of the total energy in the functional Schrodinger equation is enterely contained in the eigenvalues of the Hartree-Fock hamiltonian. (A.C.A.S.) [pt

  6. Variational derivation of a time-dependent Hartree-Fock Hamiltonian

    International Nuclear Information System (INIS)

    Lichtner, P.C.; Griffin, J.J.; Schultheis, H.; Schultheis, R.; Volkov, A.B.

    1979-01-01

    The variational derivation of the time-dependent Hartree-Fock equation is reviewed. When norm-violating variations are included, a unique time-dependent Hartree-Fock Hamiltonian, which differs from that customarily used in time-dependent Hartree-Fock analyses, is implied. This variationally ''true'' Hartree-Fock Hamiltonian has the same expectation value as the exact Hamiltonian, equal to the average energy of the system. Since this quantity remains constant under time-dependent Hartree-Fock time evolution, we suggest the label ''constant '' for this form of time-dependent Hartree-Fock theory

  7. Global solutions of restricted open-shell Hartree-Fock theory from semidefinite programming with applications to strongly correlated quantum systems.

    Science.gov (United States)

    Veeraraghavan, Srikant; Mazziotti, David A

    2014-03-28

    We present a density matrix approach for computing global solutions of restricted open-shell Hartree-Fock theory, based on semidefinite programming (SDP), that gives upper and lower bounds on the Hartree-Fock energy of quantum systems. While wave function approaches to Hartree-Fock theory yield an upper bound to the Hartree-Fock energy, we derive a semidefinite relaxation of Hartree-Fock theory that yields a rigorous lower bound on the Hartree-Fock energy. We also develop an upper-bound algorithm in which Hartree-Fock theory is cast as a SDP with a nonconvex constraint on the rank of the matrix variable. Equality of the upper- and lower-bound energies guarantees that the computed solution is the globally optimal solution of Hartree-Fock theory. The work extends a previously presented method for closed-shell systems [S. Veeraraghavan and D. A. Mazziotti, Phys. Rev. A 89, 010502-R (2014)]. For strongly correlated systems the SDP approach provides an alternative to the locally optimized Hartree-Fock energies and densities with a certificate of global optimality. Applications are made to the potential energy curves of C2, CN, Cr2, and NO2.

  8. Extension of Hartree-Fock theory including tensor correlation in nuclear matter

    Science.gov (United States)

    Hu, Jinniu; Toki, Hiroshi; Ogawa, Yoko

    2013-10-01

    We study the properties of nuclear matter in the extension of Hartree-Fock theory including tensor correlation using a realistic nucleon-nucleon (NN) interaction. The nuclear wave function consists of the Hartree-Fock and two-particle-two-hole (2p-2h) states, following the concept of the tensor-optimized shell model (TOSM) for light nuclei. The short range repulsion and strong tensor force of realistic NN interaction provide high momentum components, which are taken into account in a many-body framework by introducing 2p-2h states. Single particle states are determined by the variational principle of the total energy with respect to 2p-2h amplitudes and Hartree-Fock (HF) single-particle states. The resulting differential equation is almost identical with that of Brueckner-Hartree-Fock (BHF) theory by taking two-body scattering terms only. We calculate the equation of state (EOS) of nuclear matter in this framework with the Bonn potential as a realistic NN interaction. We found similar results to BHF theory with slightly repulsive effects in the total energy. The relativistic effect is discussed for the EOSs of nuclear matter in both non-relativistic and relativistic frameworks. The momentum distribution has large components at high momenta due to 2p-2h excitations. We also obtain the EOSs of pure neutron matter, where the tensor effect is small in the iso-vector channel.

  9. The Strutinsky method and its foundation from the Hartree-Fock-Bogoliubov approximation at finite temperature

    International Nuclear Information System (INIS)

    Brack, M.

    1981-01-01

    Strutinsky's shell-correction method is investigated in the framework of the microscopial Hartree-Fock-Bogoliubov method at finite temperature HFBT. Applying the Strutinsky energy averaging consistently to the normal and abnormal density matrices and to the entropy, we define a self-consistently average HFBT system as the solution of a variational problem. From the latter we derive the generalized Strutinsky energy theorem and the explicit expressions for the shell correction of a statistically excited system of BCS quasiparticles. Using numerical results of HF calculations, we demonstrate the convergence of the Strutinsky expansion and estimate the validity of the partical shell-correction approach. We also discuss the close connections of the Strutinsky energy averaging with semiclassical expansions and their usefulness for solving the average nuclear self-consistency problem. In particular we argue that the Hohenberg-Kohn theorem should hold for the averaged HFBT system and we thus provide a justification of the use of semiclassical density functionals. (orig.)

  10. Extension of the multiconfiguration Hartree-Fock program for continuum functions

    International Nuclear Information System (INIS)

    Fischer, C.F.; Saha, H.P.

    1984-01-01

    The wave function of an outer electron coupled to a core, possibly with correlation included in the core, is similar to a multiconfiguration Hartree-Fock (MCHF) wavefunction, except that the radial function of the electron is a continuum function, and different numerical procedures are required for determining it. Only a single continuum function is allowed, and the orbitals defining the wave function of the core and bound channels are assumed to be fixed. The coefficients in the expansion of the wave function of the core are also fixed and are the result of a bound state calculation for the core. Under these assumptions, the equation for the radial wave function of the electron is solved iteratively. The asymptotic phase shift is evaluated. In order to test the accuracy of the procedure, calculations were performed for the scattering of electrons by neutral hydrogen. Some results of a photo-ionization calculation are compared, and for an electron transition in nitrogen

  11. Time dependent resonating Hartree-Bogoliubov theory

    International Nuclear Information System (INIS)

    Nishiyama, Seiya; Fukutome, Hideo.

    1989-01-01

    Very recently, we have developed a theory of excitations in superconducting Fermion systems with large quantum fluctuations that can be described by resonance of time dependent non-orthogonal Hartree-Bogoliubov (HB) wave functions with different correlation structures. We have derived a new kind of variation equation called the time dependent Resonating HB equation, in order to determine both the time dependent Resonating HB wave functions and coefficients of a superposition of the HB wave functions. Further we have got a new approximation for excitations from time dependent small fluctuations of the Resonating HB ground state, i.e., the Resonating HB RPA. The Res HB RPA equation is represented in a given single particle basis. It, however, has drawbacks that the constraints for the Res HB RPA amplitudes are not taken into account and the equation contains equations which are not independent. We shall derive another form of the Res HB RPA equation eliminating these drawbacks. The Res HB RPA gives a unified description of the vibrons and resonons and their interactions. (author)

  12. Multiconfiguration Hartree-Fock calculations for complex atoms

    International Nuclear Information System (INIS)

    Fischer, C.F.

    1984-01-01

    The Hartree-Fock method has become a standard in atomic structure theory. Simpler methods are often compared with it when accessing their reliability or worth and the notion of correlation, which intuitively may be thought of as the correction needed to account for the fact that electrons do not move independently in a central field, is defined with respect to the Hartree-Fock method rather than some other independent-particle model. In fact, in an earlier article in this series, Fricke (Progress in Atomic Spectroscopy, Part A, Plenum Press (1978)), states, ''The so-called HF method is the basis of all good atomic calculations.'' In some sense, the Hartree-Fock method is the best method. The author briefly reviews its properties here. 67 references, 2 figures

  13. Damping of monopole vibrations in time dependent Hartree-Fock theory

    International Nuclear Information System (INIS)

    Vautherin, D.; Stringari, S.

    1979-01-01

    Monopole vibrations in oxygen-16 and calcium-40 have been investigated in time-dependent Hartree-Fock theory. The characteristic damping time obtained is tau approximately 1.5x10 -22 sec. This value is in good agreement with the width of the monopole mode calculated in the random phase approximation

  14. Spatial and Spin Symmetry Breaking in Semidefinite-Programming-Based Hartree-Fock Theory.

    Science.gov (United States)

    Nascimento, Daniel R; DePrince, A Eugene

    2018-05-08

    The Hartree-Fock problem was recently recast as a semidefinite optimization over the space of rank-constrained two-body reduced-density matrices (RDMs) [ Phys. Rev. A 2014 , 89 , 010502(R) ]. This formulation of the problem transfers the nonconvexity of the Hartree-Fock energy functional to the rank constraint on the two-body RDM. We consider an equivalent optimization over the space of positive semidefinite one-electron RDMs (1-RDMs) that retains the nonconvexity of the Hartree-Fock energy expression. The optimized 1-RDM satisfies ensemble N-representability conditions, and ensemble spin-state conditions may be imposed as well. The spin-state conditions place additional linear and nonlinear constraints on the 1-RDM. We apply this RDM-based approach to several molecular systems and explore its spatial (point group) and spin ( Ŝ 2 and Ŝ 3 ) symmetry breaking properties. When imposing Ŝ 2 and Ŝ 3 symmetry but relaxing point group symmetry, the procedure often locates spatial-symmetry-broken solutions that are difficult to identify using standard algorithms. For example, the RDM-based approach yields a smooth, spatial-symmetry-broken potential energy curve for the well-known Be-H 2 insertion pathway. We also demonstrate numerically that, upon relaxation of Ŝ 2 and Ŝ 3 symmetry constraints, the RDM-based approach is equivalent to real-valued generalized Hartree-Fock theory.

  15. New algorithm for Hartree-Fock variational equation

    International Nuclear Information System (INIS)

    Iwasawa, K.; Sakata, F.; Hashimoto, Y.; Terasaki, J.

    1994-08-01

    Aiming at microscopically understanding the shape-coexistence phenomena, a new algorithm for obtaining many self-consistent Hartree-Fock states is developed. In contrast with the conventional numerical method of solving the constrained Hartree-Fock equation which gives the most energetically favorable state under a given constrained condition, it can find many high-lying Hartree-Fock states as well as many continuous constraint Hartree-Fock solutions by dictating their configurations through some reference state. Numerical calculation is performed by using the Skyrme III. (author)

  16. Derivative discontinuity with localized Hartree-Fock potential

    Energy Technology Data Exchange (ETDEWEB)

    Nazarov, V. U. [Research Center for Applied Sciences, Academia Sinica, Taipei 11529, Taiwan (China); Vignale, G. [Department of Physics, University of Missouri-Columbia, Columbia, Missouri 65211 (United States)

    2015-08-14

    The localized Hartree-Fock potential has proven to be a computationally efficient alternative to the optimized effective potential, preserving the numerical accuracy of the latter and respecting the exact properties of being self-interaction free and having the correct −1/r asymptotics. In this paper we extend the localized Hartree-Fock potential to fractional particle numbers and observe that it yields derivative discontinuities in the energy as required by the exact theory. The discontinuities are numerically close to those of the computationally more demanding Hartree-Fock method. Our potential enjoys a “direct-energy” property, whereby the energy of the system is given by the sum of the single-particle eigenvalues multiplied by the corresponding occupation numbers. The discontinuities c{sub ↑} and c{sub ↓} of the spin-components of the potential at integer particle numbers N{sub ↑} and N{sub ↓} satisfy the condition c{sub ↑}N{sub ↑} + c{sub ↓}N{sub ↓} = 0. Thus, joining the family of effective potentials which support a derivative discontinuity, but being considerably easier to implement, the localized Hartree-Fock potential becomes a powerful tool in the broad area of applications in which the fundamental gap is an issue.

  17. Cranked relativistic Hartree-Bogoliubov theory: formalism and application to the superdeformed bands in the A∼190 region

    International Nuclear Information System (INIS)

    Afanasjev, A.V.; Ring, P.; Koenig, J.

    2000-01-01

    Cranked relativistic Hartree-Bogoliubov theory without and with approximate particle number projection by means of the Lipkin-Nogami method is presented in detail as an extension of relativistic mean field theory with pairing correlations to the rotating frame. Pairing correlations are taken into account by a finite range two-body force of Gogny type. The applicability of this theory to the description of rotating nuclei is studied in detail on the example of superdeformed bands in even-even nuclei of the A∼190 mass region. Different aspects such as the importance of pairing and particle number projection, the dependence of the results on the parametrization of the RMF Lagrangian and Gogny force, etc., are investigated in detail. It is shown that without any adjustment of new parameters the best description of experimental data is obtained by using the well established parameter sets NL1 for the Lagrangian and D1S for the pairing force. Contrary to previous studies at spin zero it is found that the increase of the strength of the Gogny force is not necessary in the framework of relativistic Hartree-Bogoliubov theory provided that particle number projection is performed

  18. Spin contamination analogy, Kramers pairs symmetry and spin density representations at the 2-component unrestricted Hartree-Fock level of theory

    KAUST Repository

    Bučinský , Luká š; Malček, Michal; Biskupič, Stanislav; Jayatilaka, Dylan; Bü chel, Gabriel E.; Arion, Vladimir B.

    2015-01-01

    "Kramers pairs symmetry breaking" is evaluated at the 2-component (2c) Kramers unrestricted and/or general complex Hartree-Fock (GCHF) level of theory, and its analogy with "spin contamination" at the 1-component (1c) unrestricted Hartree-Fock (UHF

  19. An adiabatic time-dependent Hartree-Fock theory of collective motion in finite systems

    International Nuclear Information System (INIS)

    Baranger, M.; Veneroni, M.

    1977-11-01

    It is shown how to derive the parameters of a phenomenological collective model from a microscopic theory. The microscopic theory is Hartree-Fock, and one starts from the time-dependent Hartree-Fock equation. To this, the adiabatic approximation is added, and the energy in powers of an adiabatic parameter is expanded, which results in a collective kinetic energy quadratic in the velocities, with coefficients depending on the coordinates, as in the phenomenological models. The adiabatic equations of motion are derived in different ways and their analogy with classical mechanics is stressed. The role of the adiabatic hypothesis and its range of validity, are analyzed in detail. It assumes slow motion, but not small amplitude, and is therefore suitable for large-amplitude collective motion. The RPA is obtained as the limiting case where the amplitude is also small. The translational mass is correctly given and the moment of inertia under rotation is that of Thouless and Valatin

  20. The time dependent Hartree-Fock-theory for collective nuclear motions

    International Nuclear Information System (INIS)

    Goeke, K.

    1976-11-01

    The time-dependent Hartree-Fock theory (TDHF) approximately solves the Schroedinger equation by a variational method in the space of the time-dependent Slater determinants. As the TDHF wave function, similar to the exact solution has the property of being determined completely for all times by the nucleon-nucleon interaction and by assuming initial conditions. TDHF is expected to describe collective motion of nuclei with large amplitudes, too. The subject of this paper is to formulate the TDHF theory and its adiabatic limiting case (ATDHF) suited for setting up a collective Schroedinger equation, to investigate the relations with other theories, and to show the applicability for solving practical problems. (orig./WL) [de

  1. Theories of the nuclear ground state beyond Hartree-Fock

    International Nuclear Information System (INIS)

    Gogny, D.

    1979-01-01

    Intensive efforts have been invested toward defining a microscopic approach, simple enough to render feasible systematic calculations of nuclear structure and of the some time sufficiently rich in information as to serve for updating traditional microscopic approaches to the collective excitations. Our starting point is the mean field approximation with density dependent effective forces. To describe the collective excitations we use the two well known extensions based on the H.F. theory namely the random phase approximation and the adiabatic approximation to the time dependent Hartree-Fock theory. The purpose of this paper is to show what sort of calculations can be effectively carried out in the frame of such fully self consistent approaches. (KBE) 891 KBE/KBE 892 ARA

  2. Hartree--Fock density matrix equation

    International Nuclear Information System (INIS)

    Cohen, L.; Frishberg, C.

    1976-01-01

    An equation for the Hartree--Fock density matrix is discussed and the possibility of solving this equation directly for the density matrix instead of solving the Hartree--Fock equation for orbitals is considered. Toward that end the density matrix is expanded in a finite basis to obtain the matrix representative equation. The closed shell case is considered. Two numerical schemes are developed and applied to a number of examples. One example is given where the standard orbital method does not converge while the method presented here does

  3. Basic and heavy ion scattering in time dependent Hartree-Fock Theory

    International Nuclear Information System (INIS)

    Weiss, M.S.

    1984-01-01

    Time Dependent Hartree-Fock theory, TDHF, is the most sophisticated, microscopic approach to nuclear dynamics yet practiced. Although it is far from a description of nature it does allow us to examine multiply interactive many-body systems semi quantum mechanically and to visualize otherwise covert processes. Some of the properties of the TDHF equations are stated leaving the interested reader to one of several excellent review articles for the derivations. Some of the applications to the collision of heavy ions are briefly described

  4. On the problem of representability and the Bogolyubov-Hartree-Fock theory

    Energy Technology Data Exchange (ETDEWEB)

    Knoerr, Hans Konrad

    2013-11-22

    The general topic of this thesis is an approximation of the ground state energy for many-particle quantum systems. In particular the Bogolyubov-Hartree-Fock theory and the representability of one- and two-particle density matrices are studied. After an introductory chapter we specify some basic notation of many-body quantum mechanics in Chapter 2. In Chapter 3 we consider boson, as well as fermion systems. We first tackle the question of representability for bosons, i.e., the question which conditions a one- and a two-particle operator must satisfy to ensure that they are the one- and the two-particle density matrix of a state. For a particle number-conserving system, the representability conditions up to second order for bosons are well-known and called admissibility, P-, and G-conditions. Since, however, most physical systems consisting of bosons are not particle number-conserving, we give an alternative for such systems: Generalizing the two-particle density matrix, we observe that the representability conditions up to second order hold if and only if this generalized two-particle density matrix is positive semi-definite and the one- and the two-particle density matrices fulfill trace class and symmetry conditions. Moreover, we study the Bogolyubov-Hartree-Fock energy of boson and fermion systems. We generalize Lieb's variational principle which in its original formulation holds for purely repulsive particle interactions for fermions only. Our second main result is the following: for bosons, as well as for fermions the infimum of the energy for a variation over pure quasifree states coincides with the one for a variation over all quasifree states under the assumption that the Hamiltonian is bounded below. In the last section of Chapter 3 we specify the relation between centered quasifree states and their corresponding generalized one-particle density matrix, which finds an application in the variational process in the Bogolyubov-Hartree-Fock theory. It is

  5. On the problem of representability and the Bogolyubov-Hartree-Fock theory

    International Nuclear Information System (INIS)

    Knoerr, Hans Konrad

    2013-01-01

    The general topic of this thesis is an approximation of the ground state energy for many-particle quantum systems. In particular the Bogolyubov-Hartree-Fock theory and the representability of one- and two-particle density matrices are studied. After an introductory chapter we specify some basic notation of many-body quantum mechanics in Chapter 2. In Chapter 3 we consider boson, as well as fermion systems. We first tackle the question of representability for bosons, i.e., the question which conditions a one- and a two-particle operator must satisfy to ensure that they are the one- and the two-particle density matrix of a state. For a particle number-conserving system, the representability conditions up to second order for bosons are well-known and called admissibility, P-, and G-conditions. Since, however, most physical systems consisting of bosons are not particle number-conserving, we give an alternative for such systems: Generalizing the two-particle density matrix, we observe that the representability conditions up to second order hold if and only if this generalized two-particle density matrix is positive semi-definite and the one- and the two-particle density matrices fulfill trace class and symmetry conditions. Moreover, we study the Bogolyubov-Hartree-Fock energy of boson and fermion systems. We generalize Lieb's variational principle which in its original formulation holds for purely repulsive particle interactions for fermions only. Our second main result is the following: for bosons, as well as for fermions the infimum of the energy for a variation over pure quasifree states coincides with the one for a variation over all quasifree states under the assumption that the Hamiltonian is bounded below. In the last section of Chapter 3 we specify the relation between centered quasifree states and their corresponding generalized one-particle density matrix, which finds an application in the variational process in the Bogolyubov-Hartree-Fock theory. It is

  6. Hartree-Fock (HF) method and density functional theory calculations of Methanol to Gasoline (MTG) reaction

    International Nuclear Information System (INIS)

    Seddigi, Z.S.

    2004-01-01

    We found interesting results regarding some thermodynamical parameters (Delta H, Delta G and Delta S of the MTG Reaction and FTIR Spectra of methanol and dimethylether, using the Hartree-Fock method and Density Functional Theory (DFT) calculations at different computational levels. It is the aim of this paper to highlight these results. The GAUSSIAN 98 program was used to carry out the LCAO-MO-SCF calculations at the following levels: RHF/3-21g, RHF/6-31g and DFT/B3LYP/d95**. Calculations at the restricted Hartree-Fock levels (FHR/3-22 g and RHF/6-31g) were performed since they are expensive as other levels (DFT/B3LYP/d95**. In case of the HF method, working with larger basis set (6-31g) has improved the values slightly, which is as expected. We have noticed that performing calculations at higher levels (DFT/B3LY/D95**) than the Hartree-Fock method does not dramatically improve the situation. Indeed RHF is a reasonable approximation for many single gas phase molecular calculations. HF calculations at relatively small basis sets are adequate. The theoretical vibrational spectra of both methanol and dimethylether were compared with experimental results. (author)

  7. Hartree-Fock-Bogolyubov Calculations

    International Nuclear Information System (INIS)

    Wolter, H.H.

    1970-01-01

    The author discusses in which way and to what extent pairing correlations affect the nuclear wave function. He finds that for many nuclei in the pf-shell the Hartree-Fock approximation is not valid. (author)

  8. The Hartree-Fock approximation applied to nuclear structure problems

    International Nuclear Information System (INIS)

    Oliveira, D.R. de.

    1972-01-01

    The Hartree-Fock indepedent-particle state basis is firstly constructed, whose wave functions are expressed as linear combinations of states of a Known basis. The coefficients of these combinations are reals e from themselves the Hartree-Fock density matrix is defined. The symmetries which characterize the system in study are embedded in these coefficients and in the density matrix. The formalism is applied to the Ne 20 , Si 28 and Ar 36 nuclei whose lowest Hartree-Fock energies are obtained admitting that theirs wave functions having axial symmetry. Once known the Hartree-Fock wave function, states are projected from it with well-defined total angular momentum using the Peierls and Yoccoz method. From these wave functions energy levels of the ground band are calculated as well as the electric quadrupole transition probabilities among these levels. (L.C.) [pt

  9. Multiconfiguration hartree-fock theory for pseudorelativistic systems: The time-dependent case

    KAUST Repository

    Hajaiej, Hichem

    2014-03-01

    In [Setting and analysis of the multi-configuration time-dependent Hartree-Fock equations, Arch. Ration. Mech. Anal. 198 (2010) 273-330] the third author has studied in collaboration with Bardos, Catto and Mauser the nonrelativistic multiconfiguration time-dependent Hartree-Fock system of equations arising in the modeling of molecular dynamics. In this paper, we extend the previous work to the case of pseudorelativistic atoms. We show the existence and the uniqueness of global-in-time solution to the underlying system under technical assumptions on the energy of the initial data and the charge of the nucleus. Moreover, we prove that the result can be extended to the case of neutron stars when the number of electrons is less than a critical number N cr. © 2014 World Scientific Publishing Company.

  10. Stability of the Hartree-Fock model with temperature

    OpenAIRE

    Dolbeault, Jean; Felmer, Patricio; Lewin, Mathieu

    2008-01-01

    This paper is devoted to the Hartree-Fock model with temperature in the euclidean space. For large classes of free energy functionals, minimizers are obtained as long as the total charge of the system does not exceed a threshold which depends on the temperature. The usual Hartree-Fock model is recovered in the zero temperature limit. An orbital stability result for the Cauchy problem is deduced from the variational approach.

  11. Time-dependent Hartree-Fock dynamics and phase transition in Lipkin-Meshkov-Glick model

    International Nuclear Information System (INIS)

    Kan, K.; Lichtner, P.C.; Dworzecka, M.; Griffin, J.J.

    1980-01-01

    The time-dependent Hartree-Fock solutions of the two-level Lipkin-Meshkov-Glick model are studied by transforming the time-dependent Hartree-Fock equations into Hamilton's canonical form and analyzing the qualitative structure of the Hartree-Fock energy surface in the phase space. It is shown that as the interaction strength increases these time-dependent Hartree-Fock solutions undergo a qualitative change associated with the ground state phase transition previously studied in terms of coherent states. For two-body interactions stronger than the critical value, two types of time-dependent Hartree-Fock solutions (the ''librations'' and ''rotations'' in Hamilton's mechanics) exist simultaneously, while for weaker interactions only the rotations persist. It is also shown that the coherent states with the maximum total pseudospin value are determinants, so that time-dependent Hartree-Fock analysis is equivalent to the coherent state method

  12. SU(3) versus deformed Hartree-Fock state

    International Nuclear Information System (INIS)

    Johnson, Calvin W.; Stetcu, Ionel; Draayer, J.P.

    2002-01-01

    Deformation is fundamental to understanding nuclear structure. We compare two ways to efficiently realize deformation for many-fermion wave functions, the leading SU(3) irreducible representation and the angular-momentum-projected Hartree-Fock state. In the absence of single-particle spin-orbit splitting the two are nearly identical. With realistic forces, however, the difference between the two is nontrivial, with the angular-momentum-projected Hartree-Fock state better approximating an 'exact' wave function calculated in the fully interacting shell model. The difference is driven almost entirely by the single-particle spin-orbit splitting

  13. Microscopic optical model potential based on Brueckner-Hartree-Fock theory

    International Nuclear Information System (INIS)

    Li Lulu; Zhao Enguang; Zhou Shangui; Li Zenghua; Zuo Wei; Bonaccorso, Angela; Lonbardo, Umberto

    2010-01-01

    The optical model is one of the most important models in the study of nuclear reactions. In the optical model, the elastic channel is considered to be dominant and the contributions of all other absorption channels are described by introducing an imaginary potential, Koning and Delaroche obtained empirically the so-called KDR optical potentials based on a best-fitting of massive experimental data on nucleon-nucleus scattering reactions. The volume part is found to be dominant in the real component of the OMP at low energies. Using the Bruckner-Hartree-Fock theory with Bonn B potential plus self consistent three body force, the nucleon-nucleus optical potential is studied in this thesis. In the Bruckner theory, the on-shell self energy, is corresponding to the depth of the volume part of the optical model potential (OMP) for nucleon-nucleus scattering. Using Bruckner-Hartree-Fock theory, the nucleon on-shell self energy is calculated based on Hughenoltz-Van Hove (HVH) theorem. The microscopic optical potentials thus obtained agree well with the volume part of the KDR potentials. Furthermore, the isospin splitting in the volume part of the OMP is also reproduced satisfactorily. The isospin effect in the volume part of the OMP is directly related to the isospin splitting of the effective mass of the nucleon. According to our results, the isospin splitting of neutron to proton effective mass is such that the neutron effective mass increases with isospin, whereas the proton effective mass decreases. The isovector potential U n (E) - U p (E) vanishes at energy E ≈ 200 MeV and then changes sign indicating a possible inversion in the effective mass isospin spitting. We also calculated from the Bruckner theory the imaginary part of the OMP, and the microscopic calculations predict that the isospin splitting exists also in the imaginary OMP whereas the empirical KDR potentials do not show this feature. The shape of the real component of the nucleon-nucleus OMP is

  14. Dispersion correction derived from first principles for density functional theory and Hartree-Fock theory.

    Science.gov (United States)

    Guidez, Emilie B; Gordon, Mark S

    2015-03-12

    The modeling of dispersion interactions in density functional theory (DFT) is commonly performed using an energy correction that involves empirically fitted parameters for all atom pairs of the system investigated. In this study, the first-principles-derived dispersion energy from the effective fragment potential (EFP) method is implemented for the density functional theory (DFT-D(EFP)) and Hartree-Fock (HF-D(EFP)) energies. Overall, DFT-D(EFP) performs similarly to the semiempirical DFT-D corrections for the test cases investigated in this work. HF-D(EFP) tends to underestimate binding energies and overestimate intermolecular equilibrium distances, relative to coupled cluster theory, most likely due to incomplete accounting for electron correlation. Overall, this first-principles dispersion correction yields results that are in good agreement with coupled-cluster calculations at a low computational cost.

  15. Properties of nuclear and neutron matter in a relativistic Hartree-Fock theory

    International Nuclear Information System (INIS)

    Horowitz, C.J.; Serot, B.D.

    1983-01-01

    Relativistic-Hartree-Fock (HF) equations are derived for an infinite system of mesons and baryons in the framework of a renormalizable relativistic quantum field theory. The derivation is based on a diagrammatic approach and Dyson's equation for the baryon propagator. The result is a set of coupled, nonlinear integral equations for the baryon self-energy with a self-consistency condition on the single-particle spectrum. The HF equations are solved for nuclear and neutron matter in the Walecka model, which contains neutral scalar and vector mesons. After renormalizing model parameters to reproduce nuclear matter saturation properties, HF results at low to moderate densities are similar to those in the mean-field (Hartree) approximation. Self-consistent exchange corrections to the Hartree equation of state become negligible at high densities. Rho- and pi-meson exchanges are incorporated using a renormalizable gauge-theory model. A chiral transformation of the lagrangian is used to replace the pseudoscalar πN coupling with a pseudovector coupling, for which one-pion exchange is a reasonable first approximation. This transformation maintains the model's renormalizability so that corrections may be evaluated. Pion exchange has a small effect on the HF results of the Walecka model and brings HF results in closer in closer agreement with the mean-field theory. The diagrammatic techniques used here retain the mesonic degrees of freedom and are simple enough to be extended to more refined self-consistent approximations. (orig.)

  16. Second-Order Moller-Plesset Perturbation Theory for Molecular Dirac-Hartree-Fock Wave Functions

    Science.gov (United States)

    Dyall, Kenneth G.; Arnold, James O. (Technical Monitor)

    1994-01-01

    Moller-Plesset perturbation theory is developed to second order for a selection of Kramers restricted Dirac-Hartree-Fock closed and open-shell reference wave functions. The open-shell wave functions considered are limited to those with no more than two electrons in open shells, but include the case of a two-configuration SCF reference. Denominator shifts are included in the style of Davidson's OPT2 method. An implementation which uses unordered integrals with labels is presented, and results are given for a few test cases.

  17. Hartree-Fock states in the thermodynamic limit

    International Nuclear Information System (INIS)

    Aguilera-Navarro, V.C.; Llano, M. de; Peltier, S.; Plastino, A.

    1976-01-01

    Two infinite families of two-parameter generalized Overhauser orbitals are introduced and shown to explicitly satisfy, for occupied states, the self-consistent Hartree-Fock equations in the thermodynamic limit. For an attractive delta interaction, they give lower Hartree-Fock energy than the usual plane-wave solutions, even for relatively weak coupling and/or low density. The limiting members (possessing an infinite number of harmonics) of both families appear to tend to a 'classical static lattice' state. The related density profiles and energy expressions are calculated as functions of the two new parameters. A direct-variation with respect to these parameters was done numerically and results are presented graphically. (Author) [pt

  18. Hartree--Fock time-dependent problem

    Energy Technology Data Exchange (ETDEWEB)

    Bove, A; Fano, G [Bologna Univ. (Italy). Istituto di Fisica; Istituto Nazionale di Fisica Nucleare, Bologna (Italy)); Da Prato, G [Rome Univ. (Italy). Istituto di Matematica

    1976-06-01

    A previous result is generalized. An existence and uniqueness theorem is proved for the Hartree--Fock time-dependent problem in the case of a finite Fermi system interacting via a two body potential which is supposed to be dominated by the kinetic energy part of the one-particle Hamiltonian.

  19. Testing the multi-configuration time-dependent Hartree-Fock method

    International Nuclear Information System (INIS)

    Zanghellini, Juergen; Kitzler, Markus; Brabec, Thomas; Scrinzi, Armin

    2004-01-01

    We test the multi-configuration time-dependent Hartree-Fock method as a new approach towards the numerical calculation of dynamical processes in multi-electron systems using the harmonic quantum dot and one-dimensional helium in strong laser pulses as models. We find rapid convergence for quantities such as ground-state population, correlation coefficient and single ionization towards the exact results. The method converges, where the time-dependent Hartree-Fock method fails qualitatively

  20. Fock exchange in meson theories of nuclei

    International Nuclear Information System (INIS)

    Bolsterli, M.

    1986-01-01

    The Fock exchange term in meson field theories of nuclear systems is shown to arise from a two-loop ground-state self-energy diagram. Evaluation of this diagram gives the relativistic or semirelativistic analog of the Fock exchange energy; it differs from the nucleon-nucleon Fock energy in including retardation effects. In finite meson-field theories of nuclear systems, the variational nature of the meson-field analog of the Hartree-Fock energy functional can be further elucidated. 4 refs

  1. Semiclassical expansions of the nuclear relativistic Hartree-Fock theory

    International Nuclear Information System (INIS)

    Weigel, M.K.; Haddad, S.

    1991-01-01

    Semiclassical expansions for Green functions, self-energy, phase-space density and density are given and discussed. The many-body problem was treated in the relativistic Hartree-Fock approximation with a Lagrangian with a standard OBE potential structure including the possibility of space-dependent couplings. The expansions are obtained by formulating the many-body problem in the mixed position-momentum (Wigner) representation and application of the (h/2π)-Wigner-Kirkwood expansion scheme. The resulting self-consistency problems for the zeroth and second order are formulated in three versions. (author)

  2. Adiabatic time-dependent Hartree-Fock theory of collective motion in finite systems

    International Nuclear Information System (INIS)

    Baranger, M.; Veneroni, M.

    1978-01-01

    We show how to derive the parameters of a phenomenological collective model from a microscopic theory. The microscopic theory is Hartree-Fock, and we start from the time-dependent Hartree-Fock equation. To this we add the adiabatic approximation, which results in a collective kinetic energy quadratic in the velocities, with coefficients depending on the coordinates, as in the phenomenological models. The crucial step is the decomposition of the single-particle density matrix p in the form exp(i/sub chi/) rho/sub omicron/exp(-i/sub chi/), where rho/sub omicron/ represents a time-even Slater determinant and plays the role of coordinate. Then chi plays the role of momentum, and the adiabatic assumption is that chi is small. The energy is expanded in powers of chi, the zeroth-order being the collective potential energy. The analogy with classical mechanics is stressed and studied. The same adiabatic equations of motion are derived in three different ways (directly, from the Lagrangian, from the Hamiltonian), thus proving the consistency of the theory. The dynamical equation is not necessary for writing the energy or for the subsequent quantization which leads to a Schroedinger equation, but it must be used to check the validity of various approximation schemes, particularly to reduce the problem to a few degrees of freedom. The role of the adiabatic hypothesis, its definition, and range of validity, are analyzed in great detail. It assumes slow motion, but not small amplitude, and is therefore suitable for large-amplitude collective motion. The RPA is obtained as the limiting case where the amplitude is also small. The translational mass is correctly given, and the moment of inertia under rotation is that of Thouless and Valatin. For a quadrupole two-body force, the Baranger-Kumar formalism is recovered. The self-consistency brings additional terms to the Inglis cranking formula. Comparison is also made with generator coordinate methods

  3. Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

    Directory of Open Access Journals (Sweden)

    Thomas Gomez

    2018-04-01

    Full Text Available Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods. Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numerical complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. This technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.

  4. Giant resonances in the deformed continuum

    International Nuclear Information System (INIS)

    Nakatsukasa, T.; Yabana, K.

    2004-01-01

    Giant resonances in the continuum for deformed nuclei are studied with the time-dependent Hartree-Fock (TDHF) theory in real time and real space. The continuum effect is effectively taken into account by introducing a complex Absorbing Boundary Condition (ABC). (orig.)

  5. An introduction to the adiabatic time-dependent Hartree-Fock method

    International Nuclear Information System (INIS)

    Giannoni, M.J.

    1984-05-01

    The aim of the adiabatic time-dependent Hartree-Fock method is to investigate the microscopic foundations of the phenomenological collective models. We briefly review the general formulation, which consists in deriving a Bohr-like Hamiltonian from a mean field theory, and discuss the limiting case where only a few collective variables participate to the motion. Some applications to soft nuclei and heavy ion collisions are presented

  6. The total Hartree-Fock energy-eigenvalue sum relationship in atoms

    International Nuclear Information System (INIS)

    Sen, K.D.

    1979-01-01

    Using the well known relationships for the isoelectronic changes in the total Hartree-Fock energy, nucleus-electron attraction energy and electron-electron repulsion energy in atoms a simple polynomial expansion in Z is obtained for the sum of the eigenvalues which can be used to calculate the total Hartree-Fock energy. Numerical results are presented for 2-10 electron series to show that the present relationship is a better approximation than the other available energy-eigenvalue relationships. (author)

  7. Computational Nuclear Physics and Post Hartree-Fock Methods

    Energy Technology Data Exchange (ETDEWEB)

    Lietz, Justin [Michigan State University; Sam, Novario [Michigan State University; Hjorth-Jensen, M. [University of Oslo, Norway; Hagen, Gaute [ORNL; Jansen, Gustav R. [ORNL

    2017-05-01

    We present a computational approach to infinite nuclear matter employing Hartree-Fock theory, many-body perturbation theory and coupled cluster theory. These lectures are closely linked with those of chapters 9, 10 and 11 and serve as input for the correlation functions employed in Monte Carlo calculations in chapter 9, the in-medium similarity renormalization group theory of dense fermionic systems of chapter 10 and the Green's function approach in chapter 11. We provide extensive code examples and benchmark calculations, allowing thereby an eventual reader to start writing her/his own codes. We start with an object-oriented serial code and end with discussions on strategies for porting the code to present and planned high-performance computing facilities.

  8. Improvement of one-nucleon removal and total reaction cross sections in the Liège intranuclear-cascade model using Hartree-Fock-Bogoliubov calculations

    Science.gov (United States)

    Rodríguez-Sánchez, Jose Luis; David, Jean-Christophe; Mancusi, Davide; Boudard, Alain; Cugnon, Joseph; Leray, Sylvie

    2017-11-01

    The prediction of one-nucleon-removal cross sections by the Liège intranuclear-cascade model has been improved using a refined description of the matter and energy densities in the nuclear surface. Hartree-Fock-Bogoliubov calculations with the Skyrme interaction are used to obtain a more realistic description of the radial-density distributions of protons and neutrons, as well as the excitation-energy uncorrelation at the nuclear surface due to quantum effects and short-range correlations. The results are compared with experimental data covering a large range of nuclei, from carbon to uranium, and projectile kinetic energies. We find that the new approach is in good agreement with experimental data of one-nucleon-removal cross sections covering a broad range in nuclei and energies. The new ingredients also improve the description of total reaction cross sections induced by protons at low energies, the production cross sections of heaviest residues close to the projectile, and the triple-differential cross sections for one-proton removal. However, other observables such as quadruple-differential cross sections of coincident protons do not present any sizable sensitivity to the new approach. Finally, the model is also tested for light-ion-induced reactions. It is shown that the new parameters can give a reasonable description of the nucleus-nucleus total reaction cross sections at high energies.

  9. Time Dependent Hartree Fock Equation: Gateway to Nonequilibrium Plasmas

    International Nuclear Information System (INIS)

    Dufty, James W.

    2007-01-01

    This is the Final Technical Report for DE-FG02-2ER54677 award 'Time Dependent Hartree Fock Equation - Gateway to Nonequilibrium Plasmas'. Research has focused on the nonequilibrium dynamics of electrons in the presence of ions, both via basic quantum theory and via semi-classical molecular dynamics (MD) simulation. In addition, fundamental notions of dissipative dynamics have been explored for models of grains and dust, and for scalar fields (temperature) in turbulent edge plasmas. The specific topics addressed were Quantum Kinetic Theory for Metallic Clusters, Semi-classical MD Simulation of Plasmas , and Effects of Dissipative Dynamics.

  10. Parallel scalability of Hartree-Fock calculations

    Science.gov (United States)

    Chow, Edmond; Liu, Xing; Smelyanskiy, Mikhail; Hammond, Jeff R.

    2015-03-01

    Quantum chemistry is increasingly performed using large cluster computers consisting of multiple interconnected nodes. For a fixed molecular problem, the efficiency of a calculation usually decreases as more nodes are used, due to the cost of communication between the nodes. This paper empirically investigates the parallel scalability of Hartree-Fock calculations. The construction of the Fock matrix and the density matrix calculation are analyzed separately. For the former, we use a parallelization of Fock matrix construction based on a static partitioning of work followed by a work stealing phase. For the latter, we use density matrix purification from the linear scaling methods literature, but without using sparsity. When using large numbers of nodes for moderately sized problems, density matrix computations are network-bandwidth bound, making purification methods potentially faster than eigendecomposition methods.

  11. Density Functional Theory versus the Hartree-Fock Method: Comparative Assessment

    International Nuclear Information System (INIS)

    Amusia, M.Ya.; Shaginyan, V.R.; Msezane, A.Z.

    2003-01-01

    We compare two different approaches to investigations of many-electron systems. The first is the Hartree-Fock (HF) method and the second is the Density Functional Theory (DFT). Overview of the main features and peculiar properties of the HF method are presented. A way to realize the HF method within the Kohn-Sham (KS) approach of the DFT is discussed. We show that this is impossible without including a specific correlation energy, which is defined by the difference between the sum of the kinetic and exchange energies of a system considered within KS and HF, respectively. It is the nonlocal exchange potential entering the HF equations that generates this correlation energy. We show that the total correlation energy of a finite electron system, which has to include this correlation energy, cannot be obtained from considerations of uniform electron systems. The single-particle excitation spectrum of many-electron systems is related to the eigenvalues of the corresponding KS equations. We demonstrate that this spectrum does not coincide in general with the eigenvalues of KS or HF equations

  12. Density Functional Theory versus the Hartree-Fock Method: Comparative Assessment

    Energy Technology Data Exchange (ETDEWEB)

    Amusia, M.Ya.; Shaginyan, V.R. [The Hebrew University, Jerusalem (Israel); Msezane, A.Z. [Clark Atlanta Univ., Atlanta, GA (United States). Center for Theoretical Studies of Physical Systems

    2003-12-01

    We compare two different approaches to investigations of many-electron systems. The first is the Hartree-Fock (HF) method and the second is the Density Functional Theory (DFT). Overview of the main features and peculiar properties of the HF method are presented. A way to realize the HF method within the Kohn-Sham (KS) approach of the DFT is discussed. We show that this is impossible without including a specific correlation energy, which is defined by the difference between the sum of the kinetic and exchange energies of a system considered within KS and HF, respectively. It is the nonlocal exchange potential entering the HF equations that generates this correlation energy. We show that the total correlation energy of a finite electron system, which has to include this correlation energy, cannot be obtained from considerations of uniform electron systems. The single-particle excitation spectrum of many-electron systems is related to the eigenvalues of the corresponding KS equations. We demonstrate that this spectrum does not coincide in general with the eigenvalues of KS or HF equations.

  13. Study on formalism of Griffin-Wheeler-Hartree-Fock equations and a propose for its variational discretization; Estudo sobre o formalismo das equacoes Griffin-Wheeler-Hartree-Fock e uma proposta para sua discretizacao variacional

    Energy Technology Data Exchange (ETDEWEB)

    Barbosa, Rugles Cesar

    2002-07-01

    The present thesis is divided into two parts. The first part describes the many kind of the formalisms of the Generator Coordinate Hartree-Fock method (GCHFM) and second part describes the computational aspect applied to the GCHFM formalism in its discreet form. The major aim of this work is the development of an alternative method to non-linear parameters optimization (basis set) and later uses these optimized parameters to adjust the weight function into GCHFM method. The study of the weight function when N {yields} {infinity} (or for large N), where N represents the number of mesh, is important since the GCHFM theory in its continuous form depend on understanding of such behavior. In this thesis, a detailed study is carried out about the methodologies of the self-consistent solution of the GCHFM and some methodology aspects of non-linear parameters optimization. This work shows that the Generator Coordinate Hartree-Fock method is general and it has as particular case the Hartree-Fock Roothaan method. Some possible variations or combinations around of the characteristics of the GCHFM and a comparison with conventional SCF procedure are reported in this thesis. The piecewise weight function method developed in this work shows to be very good for collective parameter optimizations of the Generator Coordinate (GC). The GCHFM calculations are necessary restrict (GCM-RHF), especially when the calculated value energies approach of its numerical values or Hartree-Fock limit. In the optimization methods of state functions for atomic electronic systems is very common the application of the gradient method and its efficacy is not contested. However, the method describes above allow us to obtain results as good as the gradient method. The basis set generated using the piecewise weight function method for Gaussian type function were used in the Restrict Hartree-Fock (RHF) calculations to obtain the total energies for some atomic electronic systems, such as neutron atoms and

  14. Efficient, approximate and parallel Hartree-Fock and hybrid DFT calculations. A 'chain-of-spheres' algorithm for the Hartree-Fock exchange

    International Nuclear Information System (INIS)

    Neese, Frank; Wennmohs, Frank; Hansen, Andreas; Becker, Ute

    2009-01-01

    In this paper, the possibility is explored to speed up Hartree-Fock and hybrid density functional calculations by forming the Coulomb and exchange parts of the Fock matrix by different approximations. For the Coulomb part the previously introduced Split-RI-J variant (F. Neese, J. Comput. Chem. 24 (2003) 1740) of the well-known 'density fitting' approximation is used. The exchange part is formed by semi-numerical integration techniques that are closely related to Friesner's pioneering pseudo-spectral approach. Our potentially linear scaling realization of this algorithm is called the 'chain-of-spheres exchange' (COSX). A combination of semi-numerical integration and density fitting is also proposed. Both Split-RI-J and COSX scale very well with the highest angular momentum in the basis sets. It is shown that for extended basis sets speed-ups of up to two orders of magnitude compared to traditional implementations can be obtained in this way. Total energies are reproduced with an average error of <0.3 kcal/mol as determined from extended test calculations with various basis sets on a set of 26 molecules with 20-200 atoms and up to 2000 basis functions. Reaction energies agree to within 0.2 kcal/mol (Hartree-Fock) or 0.05 kcal/mol (hybrid DFT) with the canonical values. The COSX algorithm parallelizes with a speedup of 8.6 observed for 10 processes. Minimum energy geometries differ by less than 0.3 pm in the bond distances and 0.5 deg. in the bond angels from their canonical values. These developments enable highly efficient and accurate self-consistent field calculations including nonlocal Hartree-Fock exchange for large molecules. In combination with the RI-MP2 method and large basis sets, second-order many body perturbation energies can be obtained for medium sized molecules with unprecedented efficiency. The algorithms are implemented into the ORCA electronic structure system

  15. Accuracy of the Hartree-Fock and local density approximations for electron densities: a study for light atoms

    International Nuclear Information System (INIS)

    Almbladh, C.-O.; Ekenberg, U.; Pedroza, A.C.

    1983-01-01

    The authors compare the electron densities and Hartree potentials in the local density and the Hartree-Fock approximations to the corresponding quantities obtained from more accurate correlated wavefunctions. The comparison is made for a number of two-electron atoms, Li, and for Be. The Hartree-Fock approximation is more accurate than the local density approximation within the 1s shell and for the spin polarization in Li, while the local density approximation is slightly better than the Hartree-Fock approximation for charge densities in the 2s shell. The inaccuracy of the Hartree-Fock and local density approximations to the Hartree potential is substantially smaller than the inaccuracy of the local density approximation to the ground-state exchange-correlation potential. (Auth.)

  16. Hartree-Fock description of superdeformed states

    International Nuclear Information System (INIS)

    Dobaczewski, J.; Meyer, J.

    1991-10-01

    The discovery of superdeformation has been preceded by theoretical predictions made in Nilsson-Strutinsky calculations and a description of the phenomenon still constitutes an exciting challenge to the theory of nuclear collective motion. In particular, a determination of electromagnetic transition rates requires a knowledge of microscopic collective wave functions, which can be achieved by using the Hartree-Fock (HF) theory and the generator coordinate method (GCM). In this study we present results of our calculations concerning the properties and superdeformed states in the mercury region. Using the GCM, we diagonalize the microscopic two-body hamiltonian within the basis set of constrained HF+BCS wave functions. The GCM provides values for the energy of the ground and excited states including the shape isomer which take into account the effect of correlations in the collective degree of freedom. The GCM will also allow us to discuss the qualitative modifications of the shape isomeric stability as induced by changes in pairing correlations

  17. Toward a muon-specific electronic structure theory: effective electronic Hartree-Fock equations for muonic molecules.

    Science.gov (United States)

    Rayka, Milad; Goli, Mohammad; Shahbazian, Shant

    2018-02-07

    An effective set of Hartree-Fock (HF) equations are derived for electrons of muonic systems, i.e., molecules containing a positively charged muon, conceiving the muon as a quantum oscillator, which are completely equivalent to the usual two-component HF equations used to derive stationary states of the muonic molecules. In these effective equations, a non-Coulombic potential is added to the orthodox coulomb and exchange potential energy terms, which describes the interaction of the muon and the electrons effectively and is optimized during the self-consistent field cycles. While in the two-component HF equations a muon is treated as a quantum particle, in the effective HF equations it is absorbed into the effective potential and practically transformed into an effective potential field experienced by electrons. The explicit form of the effective potential depends on the nature of muon's vibrations and is derivable from the basis set used to expand the muonic spatial orbital. The resulting effective Hartree-Fock equations are implemented computationally and used successfully, as a proof of concept, in a series of muonic molecules containing all atoms from the second and third rows of the Periodic Table. To solve the algebraic version of the equations muon-specific Gaussian basis sets are designed for both muon and surrounding electrons and it is demonstrated that the optimized exponents are quite distinct from those derived for the hydrogen isotopes. The developed effective HF theory is quite general and in principle can be used for any muonic system while it is the starting point for a general effective electronic structure theory that incorporates various types of quantum correlations into the muonic systems beyond the HF equations.

  18. Constant resolution of time-dependent Hartree--Fock phase ambiguity

    International Nuclear Information System (INIS)

    Lichtner, P.C.; Griffin, J.J.; Schultheis, H.; Schultheis, R.; Volkov, A.B.

    1978-01-01

    The customary time-dependent Hartree--Fock problem is shown to be ambiguous up to an arbitrary function of time additive to H/sub HF/, and, consequently, up to an arbitrary time-dependent phase for the solution, PHI(t). The ''constant'' (H)'' phase is proposed as the best resolution of this ambiguity. It leads to the following attractive features: (a) the time-dependent Hartree--Fock (TDHF) Hamiltonian, H/sub HF/, becomes a quantity whose expectation value is equal to the average energy and, hence, constant in time; (b) eigenstates described exactly by determinants, have time-dependent Hartree--Fock solutions identical with the exact time-dependent solutions; (c) among all possible TDHF solutions this choice minimizes the norm of the quantity (H--i dirac constant delta/delta t) operating on the ket PHI, and guarantees optimal time evolution over an infinitesimal period; (d) this choice corresponds both to the stationary value of the absolute difference between (H) and (i dirac constant delta/delta t) and simultaneously to its absolute minimal value with respect to choice of the time-dependent phase. The source of the ambiguity is discussed. It lies in the time-dependent generalization of the freedom to transform unitarily among the single-particle states of a determinant at the (physically irrelevant for stationary states) cost of altering only a factor of unit magnitude

  19. Structure of single-particle nuclear densities from Hartree-Fock theory and model independent analysis

    International Nuclear Information System (INIS)

    Starodubskij, V.E.; Shaginyan, V.R.

    1979-01-01

    Friar-Negele method is applied to determine the static densities of neutrons and nuclear matter from the fast proton-nuclei elastic scattering data. This model-independent analysis (MIA) has been carried out for 28 Si, sup(32,34)S, sup(40,42,44,48)Ca, 48 Ti, sup(58,60)Ni, 90 Zr, 208 Pb nuclei. The binding energies, rms radii, densities and scattering cross sections of 1 GeV-proton are calculated in the framework of the Hartree-Fock theory (HF) with Skyrme's interaction. The HF and MIA densities and cross sections have been compared to draw a conclusion on the quality of the HF densities. Calculation of the cross sections has included the spin-orbit interaction with parameters taken from the polarization data

  20. On the relation between the Hartree-Fock and Kohn-Sham approaches

    Energy Technology Data Exchange (ETDEWEB)

    Amusia, M.Ya. [Racah Institute of Physics, Hebrew University, 91904 Jerusalem (Israel); A.F. Ioffe Physical-Technical Institute, 194021 St. Petersburg (Russian Federation); Msezane, A.Z. [CTSPS, Clark Atlanta University, Atlanta, GA 30314 (United States); Shaginyan, V.R. [CTSPS, Clark Atlanta University, Atlanta, GA 30314 (United States); Petersburg Nuclear Physics Institute, 188300 Gatchina (Russian Federation)]. E-mail: vrshag@thd.pnpi.spb.ru; Sokolovski, D. [Queen' s University of Belfast, Belfast BT7 1NN (United Kingdom)

    2004-09-13

    We show that the Hartree-Fock (HF) results cannot be reproduced within the framework of Kohn-Sham (KS) theory because the single-particle densities of finite systems obtained within the HF calculations are not v-representable, i.e., do not correspond to any ground state of a N non-interacting electron systems in a local external potential. For this reason, the KS theory, which finds a minimum on a different subset of all densities, can overestimate the ground state energy, as compared to the HF result. The discrepancy between the two approaches provides no grounds to assume that either the KS theory or the density functional theory suffers from internal contradictions.

  1. On the relation between the Hartree-Fock and Kohn-Sham approaches

    International Nuclear Information System (INIS)

    Amusia, M.Ya.; Msezane, A.Z.; Shaginyan, V.R.; Sokolovski, D.

    2004-01-01

    We show that the Hartree-Fock (HF) results cannot be reproduced within the framework of Kohn-Sham (KS) theory because the single-particle densities of finite systems obtained within the HF calculations are not v-representable, i.e., do not correspond to any ground state of a N non-interacting electron systems in a local external potential. For this reason, the KS theory, which finds a minimum on a different subset of all densities, can overestimate the ground state energy, as compared to the HF result. The discrepancy between the two approaches provides no grounds to assume that either the KS theory or the density functional theory suffers from internal contradictions

  2. Relativistic Hartree-Fock theory. Part I: density-dependent effective Lagrangians

    Energy Technology Data Exchange (ETDEWEB)

    LongWen Hui [School of Physics, Peking University, 100871 Beijing (China)]|[CNRS-IN2P3, UMR 8608, F-91406 Orsay Cedex (France)]|[Univ Paris-Sud, F-91405 Orsay (France); Giai, Nguyen Van [CNRS-IN2P3, UMR 8608, F-91406 Orsay Cedex (France)]|[Univ Paris-Sud, F-91405 Orsay (France); Meng, Jie [School of Physics, Peking University, 100871 Beijing (China)]|[Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing (China)]|[Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator, 730000 Lanzhou (China)

    2006-10-15

    Effective Lagrangians suitable for a relativistic Hartree-Fock description of nuclear systems are presented. They include the 4 effective mesons {sigma}, {omega}, {rho} and {pi} with density-dependent meson-nucleon couplings. The criteria for determining the model parameters are the reproduction of the binding energies in a number of selected nuclei, and the bulk properties of nuclear matter (saturation point, compression modulus, symmetry energy). An excellent description of nuclear binding energies and radii is achieved for a range of nuclei encompassing light and heavy systems. The predictions of the present approach compare favorably with those of existing relativistic mean field models, with the advantage of incorporating the effects of pion-nucleon coupling. (authors)

  3. Spin contamination analogy, Kramers pairs symmetry and spin density representations at the 2-component unrestricted Hartree-Fock level of theory

    KAUST Repository

    Bučinský, Lukáš

    2015-05-11

    "Kramers pairs symmetry breaking" is evaluated at the 2-component (2c) Kramers unrestricted and/or general complex Hartree-Fock (GCHF) level of theory, and its analogy with "spin contamination" at the 1-component (1c) unrestricted Hartree-Fock (UHF) level of theory is emphasized. The GCHF "Kramers pairs symmetry breaking" evaluation is using the square of overlaps between the set of occupied spinorbitals with the projected set of Kramers pairs. In the same fashion, overlaps between α and β orbitals are used in the evaluation of "spin contamination" at the UHF level of theory. In this manner, UHF Š2 expectation value is made formally extended to the GCHF case. The directly evaluated GCHF expectation value of the Š2 operator is considered for completeness. It is found that the 2c GCHF Kramers pairs symmetry breaking has a very similar extent in comparison to the 1c UHF spin contamination. Thus higher excited states contributions to the 1c and 2c unrestricted wave functions of open shell systems have almost the same extent and physical consequences. Moreover, it is formally shown that a single determinant wave function in the restricted open shell Kramers case has the expectation value of K2 operator equal to the negative number of open shell electrons, while the eigenvalue of K2 for the series of simple systems (H, He, He*-triplet, Li and Li*-quartet) are found to be equal to minus the square of the number of open shell electrons. The concept of unpaired electron density is extended to the GCHF regime and compared to UHF and restricted open shell Hartree-Fock spin density. The "collinear" and "noncollinear" analogs of spin density at the GCHF level of theory are considered as well. Spin contamination and/or Kramers pairs symmetry breaking, spin populations and spin densities are considered for H2O+, Cl, HCl+, phenoxyl radical (C6H5O) as well as for Cu, Cu2+, Fe and the [OsCl5(1H-pyrazole)]- anion. The 1c and 2c unpaired electron density representation is found

  4. Hartree-Fock calculations of nuclear masses

    International Nuclear Information System (INIS)

    Quentin, P.

    1976-01-01

    Hartree-Fock calculations pertaining to the determination of nuclear binding energies throughout the whole chart of nuclides are reviewed. Such an approach is compared with other methods. Main techniques in use are shortly presented. Advantages and drawbacks of these calculations are also discussed with a special emphasis on the extrapolation towards nuclei far from the stability valley. Finally, a discussion of some selected results from light to superheavy nuclei, is given [fr

  5. Study on formalism of Griffin-Wheeler-Hartree-Fock equations and a propose for its variational discretization

    International Nuclear Information System (INIS)

    Barbosa, Rugles Cesar

    2002-01-01

    The present thesis is divided into two parts. The first part describes the many kind of the formalisms of the Generator Coordinate Hartree-Fock method (GCHFM) and second part describes the computational aspect applied to the GCHFM formalism in its discreet form. The major aim of this work is the development of an alternative method to non-linear parameters optimization (basis set) and later uses these optimized parameters to adjust the weight function into GCHFM method. The study of the weight function when N → ∞ (or for large N), where N represents the number of mesh, is important since the GCHFM theory in its continuous form depend on understanding of such behavior. In this thesis, a detailed study is carried out about the methodologies of the self-consistent solution of the GCHFM and some methodology aspects of non-linear parameters optimization. This work shows that the Generator Coordinate Hartree-Fock method is general and it has as particular case the Hartree-Fock Roothaan method. Some possible variations or combinations around of the characteristics of the GCHFM and a comparison with conventional SCF procedure are reported in this thesis. The piecewise weight function method developed in this work shows to be very good for collective parameter optimizations of the Generator Coordinate (GC). The GCHFM calculations are necessary restrict (GCM-RHF), especially when the calculated value energies approach of its numerical values or Hartree-Fock limit. In the optimization methods of state functions for atomic electronic systems is very common the application of the gradient method and its efficacy is not contested. However, the method describes above allow us to obtain results as good as the gradient method. The basis set generated using the piecewise weight function method for Gaussian type function were used in the Restrict Hartree-Fock (RHF) calculations to obtain the total energies for some atomic electronic systems, such as neutron atoms and ions in

  6. Nuclear Hartree-Fock approximation testing and other related approximations

    International Nuclear Information System (INIS)

    Cohenca, J.M.

    1970-01-01

    Hartree-Fock, and Tamm-Dancoff approximations are tested for angular momentum of even-even nuclei. Wave functions, energy levels and momenta are comparatively evaluated. Quadripole interactions are studied following the Elliott model. Results are applied to Ne 20 [pt

  7. Relativistic hadrodynamics with field-strength dependent coupling of the scalar fields in Hartree and Hartree-Fock approximation

    International Nuclear Information System (INIS)

    Lindner, J.

    1992-09-01

    In this thesis in the framework of our model of the field-strength dependent coupling the properties of infinitely extended, homogeneous, static, spin- and isospin-saturated nuclear matter are studied. Thereby we use the Hartree-Mean-Field and the Hartree-Fock approximation, whereby the influence of the antiparticle states in the Fermi sea is neglected. In chapter 2 the Lagrangian density basing to our model is fixed. Starting from the Walecka model we modify in the Lagrangian density the Linear coupling of the scalar field to the scalar density as follows g S φanti ψψ→g S f(φ) anti ψψ. In chapter 3 we fix three different functions f(φ). For these three cases and for the Walecka model with f(φ)=φ nuclear-matter calculations are performed. In chapter 4 for the Hartree-Fock calculations, but also very especially regarding the molecular-dynamics calculations, the properties of the Dirac spinors in the plane-wave representation are intensively studied. (orig.)

  8. Generalized Hartree-Fock method for electron-atom scattering

    International Nuclear Information System (INIS)

    Rosenberg, L.

    1997-01-01

    In the widely used Hartree-Fock procedure for atomic structure calculations, trial functions in the form of linear combinations of Slater determinants are constructed and the Rayleigh-Ritz minimum principle is applied to determine the best in that class. A generalization of this approach, applicable to low-energy electron-atom scattering, is developed here. The method is based on a unique decomposition of the scattering wave function into open- and closed-channel components, so chosen that an approximation to the closed-channel component may be obtained by adopting it as a trial function in a minimum principle, whose rigor can be maintained even when the target wave functions are imprecisely known. Given a closed-channel trial function, the full scattering function may be determined from the solution of an effective one-body Schroedinger equation. Alternatively, in a generalized Hartree-Fock approach, the minimum principle leads to coupled integrodifferential equations to be satisfied by the basis functions appearing in a Slater-determinant representation of the closed-channel wave function; it also provides a procedure for optimizing the choice of nonlinear parameters in a variational determination of these basis functions. Inclusion of additional Slater determinants in the closed-channel trial function allows for systematic improvement of that function, as well as the calculated scattering parameters, with the possibility of spurious singularities avoided. Electron-electron correlations can be important in accounting for long-range forces and resonances. These correlation effects can be included explicitly by suitable choice of one component of the closed-channel wave function; the remaining component may then be determined by the generalized Hartree-Fock procedure. As a simple test, the method is applied to s-wave scattering of positrons by hydrogen. copyright 1997 The American Physical Society

  9. Temperature effects on nuclear pseudospin symmetry in the Dirac-Hartree-Bogoliubov formalism

    OpenAIRE

    Lisboa, R.; Alberto, P.; Carlson, B. V.; Malheiro, M.

    2017-01-01

    We present finite temperature Dirac-Hartree-Bogoliubov (FTDHB) calculations for the tin isotope chain to study the dependence of pseudospin on the nuclear temperature. In the FTDHB calculation, the density dependence of the self-consistent relativistic mean fields, the pairing, and the vapor phase that takes into account the unbound nucleon states are considered self-consistently. The mean field potentials obtained in the FTDHB calculations are fit by Woods-Saxon (WS) potentials to examine ho...

  10. How good are Hartree-Fock charge densities

    International Nuclear Information System (INIS)

    Campi, X.

    1975-01-01

    The principle characteristics of Hartree-Fock charge densities (mean square radius, surface thickness, quantum fluctuation) calculated using different effective interactions are discussed in terms of their nuclear matter properties (Fermi momentum, effective mass, incompressibility). A comparison with the experimental charge distributions is made. Differences between the charge densities of neighbouring nuclei (isotope and isotone shifts) are also considered and the main factors governing these effects are discussed [fr

  11. Cluster modeling of solid state defects and adsorbates: Beyond the Hartree-Fock level

    International Nuclear Information System (INIS)

    Kunz, A.B.

    1990-01-01

    The use of finite clusters of atoms to represent the physically interesting portion of a condensed matter system has been an accepted technique for the past two decades. Physical systems have been studied in this way using both density functional and Hartree-Fock methodologies, as well as a variety of empirical or semiempirical techniques. In this article, the author concentrates on the Hartree-Fock based methods. The attempt here is to construct a theoretical basis for the inclusion of correlation corrections in such an approach, as well as a strategy by which the limits of a finite cluster may be transcended in such a study. The initial appeal will be to a modeling approach, but methods to convert the model to a self-contained theory will be described. It will be seen for the case of diffusion of large ions in solids that such an approach is quite useful. A further study of the case of adsorption of rare gas atoms on simple metals will demonstrate the value of inclusion of electron correlation

  12. Time-dependent Hartree-Fock studies of the dynamical fusion threshold

    Directory of Open Access Journals (Sweden)

    Nakatsukasa Takashi

    2012-12-01

    Full Text Available A microscopic description of dynamical fusion threshold in heavy ion collisions is performed in the framework of time-dependent Hartree-Fock (TDHF theory using Skyrme energy density functional (EDF. TDHF fusion threshold is in a better agreement with experimental fusion barrier. We find that the onset of extra push lies at the effective fissility 33, which is consistent with the prediction of Swiatecki’s macroscopic model. The extra push energy in our TDHF simulation is systematically smaller than the prediction in macroscopic model. The important dynamical effects and the way to fit the parameter might be responsible for the different results.

  13. Hartree-Fock-Bogolubov approximation in the models with general four-fermion interaction

    International Nuclear Information System (INIS)

    Bogolubov, N.N. Jr.; Soldatov, A.V.

    1995-12-01

    The foundation of this work was established by the lectures of Prof. N.N. Bogolubov (senior) written in the beginning of 1990. We should like to develop some of his ideas connected with Hartree-Fock-Bogolubov method and to show how this approximation works in connection with general equations for Green's functions with source terms for sufficiently general model Hamiltonian of four-fermion interaction type and how, for example, to get some results of superconductivity theory by means of this method. (author). 5 refs

  14. The Hartree-Fock seniority method and its foundation

    International Nuclear Information System (INIS)

    Gomez, J.M.G.; Prieto, C.

    1987-01-01

    The seniority scheme is discussed in the framewok of quasi-spin formalism. It is shown that the ground-state wave function of the seniority scheme can be determined self-consistently from a set of Hartree-Fock seniority equations derived from the variational prinicple. The method takes into account the mean-field and the pairing correlations in nuclei at the same time. Angular momentum and particle number are exactly conserved. (author)

  15. General multi-configuration Hartree--Fock program: MCHF77

    International Nuclear Information System (INIS)

    Fischer, C.F.

    1977-11-01

    This technical report contains a listing of a general program for multi-configuration Hartree--Fock (MCHF) calculations, including its documentation. Several examples are given showing how the program may be used. Typical output for several cases is also presented. This program has been tested over an extended period of time for a large variety of cases. This program is written for the IBM 360 or 370 in double-precision arithmetic

  16. The positronium and the dipositronium in a Hartree-Fock approximation of quantum electrodynamics

    DEFF Research Database (Denmark)

    Sok, Jérémy Vithya

    2016-01-01

    The Bogoliubov-Dirac-Fock (BDF) model is a no-photon approximation of quantum electrodynamics. It allows to study relativistic electrons in interaction with the Dirac sea. A state is fully characterized by its one-body density matrix, an infinite rank non-negative projector. We prove the existence...

  17. Contribution to the projected Hartree-Fock method and microscopic theory of coupling between rotation bands

    International Nuclear Information System (INIS)

    Brut, F.

    1982-01-01

    The spectroscopy of odd-A nuclei, in the 1p and 2s-1d shells, is studied in the framework of the projected Hartree-Fock method and by the generator coordinate method. The nuclear effective interactions of Cohen and Kurath, on the one hand, and of Kuo or Preedom-Wildenthal, on the other hand, are used. The binding energies, the nuclear spectra, the static moments and the electromagnetic transitions obtained by these two approaches are compared to the same quantities given by a complete diagonalization in the shell model basis. This study of light nuclei gives some possibilities to put in order the energy levels by coupled rotational bands. In the microscopic approach, thus we find all the elements of the unified model of Bohr and Mottelson. To give evidence of such a relation, the functions of the angle β, in the integrals of the projection method of Peierls and Yoccoz, for a Slater determinant, are developed in the vicinity of the bounds β = O and β = π. The microscopic coefficients are evaluated in the Hartree-Fock approximation, using the particle-hole formalism. Calculations are made for 20 Ne and 21 Ne and the resulting microscopic coefficients are compared with the corresponding terms of the unified model of Bohr and Mottelson [fr

  18. Vibrational spectroscopic investigation of p-, m- and o-nitrobenzonitrile by using Hartree-Fock and density functional theory

    Science.gov (United States)

    Sert, Y.; Ucun, F.

    2013-08-01

    In the present work, the theoretical vibrational spectra of p-, m- and o-nitrobenzonitrile molecules have been analyzed. The harmonic vibrational frequencies and geometric parameters (bond lengths and bond angles) of these molecules have been calculated using ab initio Hartree-Fock and density functional theory methods with 6-311++G(d,p) basis set by Gaussian 03 W, for the first time. Assignments of the vibrational frequencies have been performed by potential energy distribution by using VEDA 4 program. The optimized geometric parameters and harmonic vibrational frequencies have been compared with the corresponding experimental data and seen to be in a good agreement with each other. Also, the highest occupied molecular orbital and lowest unoccupied molecular orbital energies have been obtained.

  19. A finite difference Hartree-Fock program for atoms and diatomic molecules

    Science.gov (United States)

    Kobus, Jacek

    2013-03-01

    The newest version of the two-dimensional finite difference Hartree-Fock program for atoms and diatomic molecules is presented. This is an updated and extended version of the program published in this journal in 1996. It can be used to obtain reference, Hartree-Fock limit values of total energies and multipole moments for a wide range of diatomic molecules and their ions in order to calibrate existing and develop new basis sets, calculate (hyper)polarizabilities (αzz, βzzz, γzzzz, Az,zz, Bzz,zz) of atoms, homonuclear and heteronuclear diatomic molecules and their ions via the finite field method, perform DFT-type calculations using LDA or B88 exchange functionals and LYP or VWN correlations ones or the self-consistent multiplicative constant method, perform one-particle calculations with (smooth) Coulomb and Krammers-Henneberger potentials and take account of finite nucleus models. The program is easy to install and compile (tarball+configure+make) and can be used to perform calculations within double- or quadruple-precision arithmetic. Catalogue identifier: ADEB_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADEB_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 2 No. of lines in distributed program, including test data, etc.: 171196 No. of bytes in distributed program, including test data, etc.: 9481802 Distribution format: tar.gz Programming language: Fortran 77, C. Computer: any 32- or 64-bit platform. Operating system: Unix/Linux. RAM: Case dependent, from few MB to many GB Classification: 16.1. Catalogue identifier of previous version: ADEB_v1_0 Journal reference of previous version: Comput. Phys. Comm. 98(1996)346 Does the new version supersede the previous version?: Yes Nature of problem: The program finds virtually exact solutions of the Hartree-Fock and density functional theory type equations for atoms, diatomic molecules and their ions

  20. The time-dependent Hartree-Fock equations with Coulomb two-body interaction

    International Nuclear Information System (INIS)

    Chadam, J.M.; Glassey, R.T.

    1975-06-01

    The existence and uniqueness of global solutions to the Cauchy problem is proved in the space of ''smooth'' density matrices for the time-dependent Hartree-Fock equations describing the motion of finite Fermi systems interacting via a Coulomb two-body potential [fr

  1. Ground state hydrogen conformations and vibrational analysis of 1,2-dihdroxyanthraquinone (alizarin) molecule by AB initio Hartree-Fock and density functional theory calculations

    International Nuclear Information System (INIS)

    Delta, E.; Ucun, F.; Saglam, A.

    2010-01-01

    The ground state hydrogen conformations of 1,2-dihydroxyanthraquinone (alizarin) molecule have been investigated using ab initio Hartree-Fock (HF) and density functional theory (B3LYP) methods with 6-31G(d,p) basis set. The calculations indicate that the compound in the ground state exist with the doubly bonded O atom linked intra molecularly by the two hydrogen bonds. The vibrational analyses of the ground state conformation of the compound were also made and its optimized geometry parameters were given.

  2. Dirac-Hartree-Fock studies of X-ray transitions in meitnerium

    International Nuclear Information System (INIS)

    Thierfelder, C.; Schwerdtfeger, P.; Hessberger, F.P.; Hofmann, S.

    2008-01-01

    The K -shell and L -shell ionizations potentials for 268 109 Mt were calculated at the Dirac-Hartree-Fock level taking into account quantum electrodynamic and finite nuclear-size effects. The K α1 transition energies for different ionization states are accurately predicted and compared with recent experiments in the α -decay of 272 111 Rg. (orig.)

  3. Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.

    Science.gov (United States)

    Khoromskaia, Venera; Khoromskij, Boris N

    2015-12-21

    We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, first appeared as an accurate tensor calculus for the 3D Hartree potential using 1D complexity operations, and have evolved to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in O(n log n) complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D n × n × n Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D "density fitting" scheme, which yield an almost irreducible number of product basis functions involved in the 3D convolution integrals, depending on a threshold ε > 0. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excitation energies, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is towards the tensor-based Hartree-Fock numerical scheme for finite lattices, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a L × L × L lattice manifests the linear in L computational work, O(L), instead of the usual O(L(3) log L) scaling by the Ewald-type approaches.

  4. Axially deformed solution of the Skyrme-Hartree-Fock-Bogoliubov equations using the transformed harmonic oscillator basis (II) HFBTHO v2.00d: A new version of the program

    Science.gov (United States)

    Stoitsov, M. V.; Schunck, N.; Kortelainen, M.; Michel, N.; Nam, H.; Olsen, E.; Sarich, J.; Wild, S.

    2013-06-01

    We describe the new version 2.00d of the code HFBTHO that solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogoliubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the modified Broyden method for non-linear problems, (ii) optional breaking of reflection symmetry, (iii) calculation of axial multipole moments, (iv) finite temperature formalism for the HFB method, (v) linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations, (vi) blocking of quasi-particles in the Equal Filling Approximation (EFA), (vii) framework for generalized energy density with arbitrary density-dependences, and (viii) shared memory parallelism via OpenMP pragmas. Program summaryProgram title: HFBTHO v2.00d Catalog identifier: ADUI_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUI_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 3 No. of lines in distributed program, including test data, etc.: 167228 No. of bytes in distributed program, including test data, etc.: 2672156 Distribution format: tar.gz Programming language: FORTRAN-95. Computer: Intel Pentium-III, Intel Xeon, AMD-Athlon, AMD-Opteron, Cray XT5, Cray XE6. Operating system: UNIX, LINUX, WindowsXP. RAM: 200 Mwords Word size: 8 bits Classification: 17.22. Does the new version supercede the previous version?: Yes Catalog identifier of previous version: ADUI_v1_0 Journal reference of previous version: Comput. Phys. Comm. 167 (2005) 43 Nature of problem: The solution of self-consistent mean-field equations for weakly-bound paired nuclei requires a correct description of the asymptotic properties of nuclear quasi-particle wave functions. In the present implementation, this is achieved by using the single-particle wave functions

  5. Comparison of model Hartree-Fock type calculation schemes involving various non-degenerate and quasi-degenerate intrinsic Hamiltonians

    International Nuclear Information System (INIS)

    Amusa, A.

    1983-03-01

    Different Hamiltonians and their corresponding rotationally degenerate intrinsic counterparts are employed in the study of 18 O nucleus under the normal Hartree-Fock, as well as under six other Hartree-Fock type variational calculation schemes. The results are compared and then assessed in the light of their closeness or otherwise to the full 1s-0d basis shell model calculations for this nucleus. The use of these schemes for other shells is also considered. (author)

  6. Exponential convergence and acceleration of Hartree-Fock calculations

    International Nuclear Information System (INIS)

    Bonaccorso, A.; Di Toro, M.; Lomnitz-Adler, J.

    1979-01-01

    It is shown that one can expect an exponential behaviour for the convergence of the Hartree-Fock solution during the HF iteration procedure. This property is used to extrapolate some collective degrees of freedom, in this case the shape, in order to speed up the self-consistent calculation. For axially deformed nuclei the method is applied to the quadrupole moment which corresponds to a simple scaling transformation on the single particle wave functions. Results are shown for the deformed nuclei 20 Ne and 28 Si with a Skyrme interaction. (Auth.)

  7. The spectrum of 12C in a multi-configuration Hartree-Fock Basis

    International Nuclear Information System (INIS)

    Amos, K.; Morrison, I.; Smith, R.; Schmid, K.W.

    1981-01-01

    The energy level spectrum of 12 C is calculated in a truncated but large shell model space of projected one particle-one hole Hartree Fock determinants using a realistic G-matrix. Predictions of electromagnetic decays and electron scattering form factors are compared with experimental values

  8. Relativistic description of nuclear systems in the Hartree-Fock approximation

    International Nuclear Information System (INIS)

    Bouyssy, A.; Mathiot, J.F.; Nguyen Van Giai; Marcos, S.

    1986-03-01

    The structure of infinite nuclear matter and finite nuclei is studied in the framework of the relativistic Hartree-Fock approximation. A particular attention is paid to the contribution of isovector mesons. (π,p). A satisfactory description of binding energies and densities can be obtained for light as well as heavy nuclei. The spin-orbit splittings are well reproduced. Connections with non-relativistic formulations are also discussed

  9. Restricted Hartree Fock using complex-valued orbitals: A long-known but neglected tool in electronic structure theory

    Energy Technology Data Exchange (ETDEWEB)

    Small, David W.; Sundstrom, Eric J.; Head-Gordon, Martin [Department of Chemistry, University of California, Berkeley, California 94720, USA and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)

    2015-01-14

    Restricted Hartree Fock using complex-valued orbitals (cRHF) is studied. We introduce an orbital pairing theorem, with which we obtain a concise connection between cRHF and real-valued RHF, and use it to uncover the close relationship between cRHF, unrestricted Hartree Fock, and generalized valence bond perfect pairing. This enables an intuition for cRHF, contrasting with the generally unintuitive nature of complex orbitals. We also describe an efficient computer implementation of cRHF and its corresponding stability analysis. By applying cRHF to the Be + H{sub 2} insertion reaction, a Woodward-Hoffmann violating reaction, and a symmetry-driven conical intersection, we demonstrate in genuine molecular systems that cRHF is capable of removing certain potential energy surface singularities that plague real-valued RHF and related methods. This complements earlier work that showed this capability in a model system. We also describe how cRHF is the preferred RHF method for certain radicaloid systems like singlet oxygen and antiaromatic molecules. For singlet O{sub 2}, we show that standard methods fail even at the equilibrium geometry. An implication of this work is that, regardless of their individual efficacies, cRHF solutions to the HF equations are fairly commonplace.

  10. Electronic correlation without double counting via a combination of spin projected Hartree-Fock and density functional theories

    Energy Technology Data Exchange (ETDEWEB)

    Garza, Alejandro J.; Jiménez-Hoyos, Carlos A. [Department of Chemistry, Rice University, Houston, Texas 77251-1892 (United States); Scuseria, Gustavo E. [Department of Chemistry and Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892, USA and Chemistry Department, Faculty of Science, King Abdulaziz University, Jeddah 21589 (Saudi Arabia)

    2014-06-28

    Several schemes to avoid the double counting of correlations in methods that merge multireference wavefunctions with density functional theory (DFT) are studied and here adapted to a combination of spin-projected Hartree-Fock (SUHF) and DFT. The advantages and limitations of the new method, denoted SUHF+f{sub c}DFT, are explored through calculations on benchmark sets in which the accounting of correlations is challenging for pure SUHF or DFT. It is shown that SUHF+f{sub c}DFT can greatly improve the description of certain molecular properties (e.g., singlet-triplet energy gaps) which are not improved by simple addition of DFT dynamical correlation to SUHF. However, SUHF+f{sub c}DFT is also shown to have difficulties dissociating certain types of bonds and describing highly charged ions with static correlation. Possible improvements to the current SUHF+f{sub c}DFT scheme are discussed in light of these results.

  11. A Hartree-Fock program for atomic structure calculations

    International Nuclear Information System (INIS)

    Mitroy, J.

    1999-01-01

    The Hartree-Fock equations for a general open shell atom are described. The matrix equations that result when the single particle orbitals are written in terms of a linear combination of analytic basis functions are derived. Attention is paid to the complexities that occur when open shells are present. The specifics of a working FORTRAN program which is available for public use are described. The program has the flexibility to handle either Slater-type orbitals or Gaussian-type orbitals. It can be obtained over the internet at http://lacebark.ntu.edu.au/j_mitroy/research/atomic.htm Copyright (1999) CSIRO Australia

  12. Method of renormalization potential for one model of Hartree-Fock-Slater type

    CERN Document Server

    Zasorin, Y V

    2002-01-01

    A new method of the potential renormalization for the quasiclassical model of the Hartree-Fock-Slater real potential is proposed. The method makes it possible to easily construct the wave functions and contrary to the majority od similar methods it does not require the knowledge of the real-type potential

  13. Self-consistent field description of high spin states in rare earth nuclei. [Hartree-Fock-Bogolyubov Theory

    Energy Technology Data Exchange (ETDEWEB)

    Goodman, A L [Carnegie-Mellon Univ., Pittsburgh, Pa. (USA)

    1976-07-12

    The Hartree-Fock-Bogolyubov cranking equations are solved for /sup 168/ /sup 170/Yb and /sup 174/Hf. Deformation and pairing properties are both obtained with a G-matrix derived from the Reid soft-core potential. The high spin anomalies are attributed to the disappearance of the neutron pair gap in /sup 168/Yb, the realignment of an isub(13/2) neutron pair in /sup 170/Yb, and a combination of these two mechanisms in /sup 174/Hf. Two bands intersecting at high spin are found for /sup 174/Hf.

  14. Relativity and pseudopotentials in the Hartree-Fock-Slater method

    International Nuclear Information System (INIS)

    Snijders, J.G.

    1979-01-01

    The methodological problems involved in electronic structure determinations of compounds containing heavy elements by the Hartree-Fock-Slater scheme are investigated. It is shown that the effect of the inner electrons can be simulated by a so called pseudopotential, so that only the valence electrons have to be treated explicitly which constitutes a considerable reduction of computation time. It is further shown that a pseudopotential calculation is able to achieve an accuracy that is comparable to the results of a calculation including the core. (Auth.)

  15. A Hartree-Fock-Slater-Boltzmann-Saha method for detailed atomic structure and equation of state of plasmas

    International Nuclear Information System (INIS)

    Jiang Minhao; Meng Xujun

    2005-01-01

    The effect of the free electron background in plasmas is introduced in Hartree-Fock-Slater self-consistent field atomic model to correct the single electron energies for each electron configuration, and to provide accurate atomic data for Boltzmann-Saha equation. In the iteration process chemical potential is adjusted to change the free electron background to satisfy simultaneously the conservation of the free electrons in Saha equation as well as in Hartree-Fock-Slater self-consistent field atomic model. As examples the equations of state of the carbon and aluminum plasmas are calculated to show the applicability of this method. (authors)

  16. Decomposition of the configuration-interaction coefficients in the multiconfiguration time-dependent Hartree-Fock method

    Energy Technology Data Exchange (ETDEWEB)

    Lötstedt, Erik, E-mail: lotstedt@chem.s.u-tokyo.ac.jp; Kato, Tsuyoshi; Yamanouchi, Kaoru [Department of Chemistry, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan)

    2016-04-21

    An approximate implementation of the multiconfiguration time-dependent Hartree-Fock method is proposed, in which the matrix of configuration-interaction coefficients is decomposed into a product of matrices of smaller dimension. The applicability of this method in which all the configurations are kept in the expansion of the wave function, while the configuration-interaction coefficients are approximately calculated, is discussed by showing the results on three model systems: a one-dimensional model of a beryllium atom, a one-dimensional model of a carbon atom, and a one-dimensional model of a chain of four hydrogen atoms. The time-dependent electronic dynamics induced by a few-cycle, long-wavelength laser pulse is found to be well described at a lower computational cost compared to the standard multiconfiguration time-dependent Hartree-Fock treatment. Drawbacks of the method are also discussed.

  17. Molecular Structure And Vibrational Frequencies of Tetrafluoro isophthalonitrile By Hartree-Fock And Density Functional Theory Calculations

    International Nuclear Information System (INIS)

    Ayikoglu, A.

    2008-01-01

    The molecular structure, vibrational frequencies and corresponding vibrational assignments of tetrafluoro isophthalonitrile (TFPN) in the ground state have been calculated using the Hartree-Fock (HF) and density functional methods (B3LYP) with 6-311++G (d, p) basis set. The calculations were utilized in the CS symmetry of TFPN. The obtained vibrational frequencies and optimized geometric parameters (bond lengths and bond angles) were seen to be in good agreement with the experimental data. The comparison of the observed and calculated results showed that the B3LYP method is superior to the HF method for both the vibrational frequencies and geometric parameters

  18. The role of the form factor and short-range correlation in the relativistic Hartree-Fock model for nuclear matter

    Science.gov (United States)

    Hu, J.; Toki, H.; Wen, W.; Shen, H.

    2010-03-01

    The role of the form factor and short-range correlation in nuclear matter is studied within the relativistic Hartree-Fock approximation. We take, first, the mean-field approximation for meson fields and obtain the fluctuation terms of mesons to be used for the Fock energies. We introduce form factors in the meson-nucleon coupling vertices to take into account the finite-size effect of the nucleon. We use further the unitary correlation operator method for the treatment of the short-range correlation. The form factors of the size ( Λ ˜ 1.0 -2.0GeV) of the nucleon-nucleon interaction cut down largely the contribution of the ρ -meson in the Fock term. The short-range correlation effect is not large but has a significant effect on the pion and ρ -meson energies in the relativistic Hartree-Fock approximation for nuclear matter.

  19. Toroidal Superheavy Nuclei in Skyrme-Hartree-Fock Approach

    International Nuclear Information System (INIS)

    Staszczak, A.; Wong, Cheuk-Yin

    2009-01-01

    Within the self-consistent constraint Skyrme-Hartree-Fock+BCS model (SHF+BCS), we found equilibrium toroidal nuclear density distributions in the region of superheavy elements. For nuclei with a sufficient oblate deformation (Q 20 < -200 b), it becomes energetically favorable to change the genus of nuclear surface from 0 to 1, i.e., to switch the shape from a biconcave disc to a torus. The energy of the toroidal (genus=1) SHF+BCS solution relative to the compact (genus=0) ground state energy is strongly dependent both on the atomic number Z and the mass number A. We discuss the region of Z and A where the toroidal SHF+BCS total energy begins to be a global minimum

  20. Conformational and vibrational analysis of 5-hydroxy 2-nitrobenzaldehyde by AB initio hartree-fock, density functional theory calculations

    International Nuclear Information System (INIS)

    Cinakli, S.; Sert, Y.; Boeyuekata, M.; Ucun, F.

    2010-01-01

    The vibrational spectra of benzaldehyde and its derivatives have been studied earlier. The substitution of a functional group changes the spectra markedly. Recent spectroscopic studies of the benzaldehyde and their derivatives have been motivated because the vibrational spectra are very useful for understanding of specific biological process and in the analysis of relatively complex systems. The optimized molecular structure, vibrational frequencies and corresponding vibrational assignments, the total energy calculations, relative energies, the mean vibrational deviations of the two planar O-cis and O-trans roomers of 5-Hydroxy 2-nitrobenzaldehydes have been calculated using ab initio Hartree Fock (HF) and Density Functional Theory (B3LYP) with 6-311++G(d,p) basis set. All computations have been performed on personal computer using the Gaussian 03 program package. The calculations were adapted to Cs symmetries of all the molecules. The O-trans rotomers with lower energy of all the molecules have been found as preferential rotomers in the ground state.

  1. The role of the form factor and short-range correlation in the relativistic Hartree-Fock model for nuclear matter

    International Nuclear Information System (INIS)

    Hu, J.; Toki, H.; Wen, W.; Shen, H.

    2010-01-01

    The role of the form factor and short-range correlation in nuclear matter is studied within the relativistic Hartree-Fock approximation. We take, first, the mean-field approximation for meson fields and obtain the fluctuation terms of mesons to be used for the Fock energies. We introduce form factors in the meson-nucleon coupling vertices to take into account the finite-size effect of the nucleon. We use further the unitary correlation operator method for the treatment of the short-range correlation. The form factors of the size (Λ∝1.0 -2.0 GeV) of the nucleon-nucleon interaction cut down largely the contribution of the ρ-meson in the Fock term. The short-range correlation effect is not large but has a significant effect on the pion and ρ-meson energies in the relativistic Hartree-Fock approximation for nuclear matter. (orig.)

  2. Orbital and total atomic momentum expectation values with Roothaan-Hartree-Fock wave functions

    International Nuclear Information System (INIS)

    De La Vega, J.M.G.; Miguel, B.

    1993-01-01

    Orbital and total momentum expectation values are computed using the Roothaan-Hartree-Fock wave functions of Clementi and Roetti. These values are calculated analytically and may be used to study the quality of basis sets. Tabulations for ground and excited states of atoms from Z = 2 to Z = 54 are presented. 23 refs., 1 tab

  3. Odd-even mass differences from self-consistent mean field theory

    International Nuclear Information System (INIS)

    Bertsch, G. F.; Bertulani, C. A.; Nazarewicz, W.; Schunck, N.; Stoitsov, M. V.

    2009-01-01

    We survey odd-even nuclear binding energy staggering using density functional theory with several treatments of the pairing interaction including the BCS, Hartree-Fock-Bogoliubov, and the Hartree-Fock-Bogoliubov with the Lipkin-Nogami approximation. We calculate the second difference of binding energies and compare the results with 443 measured neutron energy differences in isotope chains and 418 measured proton energy differences in isotone chains. The particle-hole part of the energy functional is taken as the SLy4 Skyrme parametrization, and the pairing part of the functional is based on a contact interaction with possible density dependence. An important feature of the data, reproduced by the theory, is the sharp gap quenching at magic numbers. With the strength of the interaction as a free parameter, the theory can reproduce the data to an rms accuracy of about 0.25 MeV. This is slightly better than a single-parameter phenomenological description but slightly poorer than the usual two-parameter phenomenological form c/A α . The following conclusions can be made about the performance of common parametrization of the pairing interaction: (i) there is a weak preference for a surface-peaked neutron-neutron pairing, which might be attributable to many-body effects, (ii) a larger strength is required in the proton pairing channel than in the neutron pairing channel, and (iii) pairing strengths adjusted to the well-known spherical isotope chains are too weak to give a good overall fit to the mass differences

  4. A simple and efficient dispersion correction to the Hartree-Fock theory (2): Incorporation of a geometrical correction for the basis set superposition error.

    Science.gov (United States)

    Yoshida, Tatsusada; Hayashi, Takahisa; Mashima, Akira; Chuman, Hiroshi

    2015-10-01

    One of the most challenging problems in computer-aided drug discovery is the accurate prediction of the binding energy between a ligand and a protein. For accurate estimation of net binding energy ΔEbind in the framework of the Hartree-Fock (HF) theory, it is necessary to estimate two additional energy terms; the dispersion interaction energy (Edisp) and the basis set superposition error (BSSE). We previously reported a simple and efficient dispersion correction, Edisp, to the Hartree-Fock theory (HF-Dtq). In the present study, an approximation procedure for estimating BSSE proposed by Kruse and Grimme, a geometrical counterpoise correction (gCP), was incorporated into HF-Dtq (HF-Dtq-gCP). The relative weights of the Edisp (Dtq) and BSSE (gCP) terms were determined to reproduce ΔEbind calculated with CCSD(T)/CBS or /aug-cc-pVTZ (HF-Dtq-gCP (scaled)). The performance of HF-Dtq-gCP (scaled) was compared with that of B3LYP-D3(BJ)-bCP (dispersion corrected B3LYP with the Boys and Bernadi counterpoise correction (bCP)), by taking ΔEbind (CCSD(T)-bCP) of small non-covalent complexes as 'a golden standard'. As a critical test, HF-Dtq-gCP (scaled)/6-31G(d) and B3LYP-D3(BJ)-bCP/6-31G(d) were applied to the complex model for HIV-1 protease and its potent inhibitor, KNI-10033. The present results demonstrate that HF-Dtq-gCP (scaled) is a useful and powerful remedy for accurately and promptly predicting ΔEbind between a ligand and a protein, albeit it is a simple correction procedure. Copyright © 2015 Elsevier Ltd. All rights reserved.

  5. Hartree-Fock calculation of nuclear binding energy of sodium isotopes

    International Nuclear Information System (INIS)

    Campi, X.; Flocard, H.

    1975-01-01

    Mass spectrometer measurements of the neutron rich sodium isotopes show a sudden increase at 31 Na in the values of the two neutron separation energies. The spherical shell model naturally predicts a sudden decrease at 32 Na after the N=20 shell closure. It is proposed that the explanation for this disagreement lies in the fact that sodium isotopes in this mass region are strongly deformed due to the filling of negative parity orbitals from the 1f(7/2) shell. Hartree-Fock calculations are presented in support of this conjecture [fr

  6. Influence of the Dirac-Hartree-Fock starting potential on the parity-nonconserving electric-dipole-transition amplitudes in cesium and thallium

    Science.gov (United States)

    Perger, W. F.; Das, B. P.

    1987-01-01

    The parity-nonconserving electric-dipole-transition amplitudes for the 6s1/2-7s1/2 transition in cesium and the 6p1/2-7p1/2 transition in thallium have been calculated by the Dirac-Hartree-Fock method. The effects of using different Dirac-Hartree-Fock atomic core potentials are examined and the transition amplitudes for both the length and velocity gauges are given. It is found that the parity-nonconserving transition amplitudes exhibit a greater dependence on the starting potential for thallium than for cesium.

  7. Obtaining Hartree-Fock and density functional theory doubly excited states with Car-Parrinello density matrix search

    Science.gov (United States)

    Liang, Wenkel; Isborn, Christine M.; Li, Xiaosong

    2009-11-01

    The calculation of doubly excited states is one of the major problems plaguing the modern day excited state workhorse methodology of linear response time dependent Hartree-Fock (TDHF) and density function theory (TDDFT). We have previously shown that the use of a resonantly tuned field within real-time TDHF and TDDFT is able to simultaneously excite both the α and β electrons to achieve the two-electron excited states of minimal basis H2 and HeH+ [C. M. Isborn and X. Li, J. Chem. Phys. 129, 204107 (2008)]. We now extend this method to many electron systems with the use of our Car-Parrinello density matrix search (CP-DMS) with a first-principles fictitious mass method for wave function optimization [X. Li, C. L. Moss, W. Liang, and Y. Feng, J. Chem. Phys. 130, 234115 (2009)]. Real-time TDHF/TDDFT is used during the application of the laser field perturbation, driving the electron density toward the doubly excited state. The CP-DMS method then converges the density to the nearest stationary state. We present these stationary state doubly excited state energies and properties at the HF and DFT levels for H2, HeH+, lithium hydride, ethylene, and butadiene.

  8. Treatment of the intrinsic Hamiltonian in particle-number nonconserving theories

    International Nuclear Information System (INIS)

    Hergert, H.; Roth, R.

    2009-01-01

    We discuss the implications of using an intrinsic Hamiltonian in theories without particle-number conservation, e.g., the Hartree-Fock-Bogoliubov approximation, where the Hamiltonian's particle-number dependence leads to discrepancies if one naively replaces the particle-number operator by its expectation value. We develop a systematic expansion that fixes this problem and leads to an a posteriori justification of the widely-used one- plus two-body form of the intrinsic kinetic energy in nuclear self-consistent field methods. The expansion's convergence properties as well as its practical applications are discussed for several sample nuclei.

  9. Classic Multi-Configuration-Dirac-Fock and Hartree-Fock-Relativistic methods integrated into a program package for the RAL-IBM mainframe with automatic comparative output

    International Nuclear Information System (INIS)

    Cowan, R.D.; Grant, I.P.; Fawcett, B.C.; Rose, S.J.

    1985-11-01

    A Multi-Configuration-Dirac-Fock (MCDF) computer program is adapted to interface with the Hartree-Fock-Relativistic (HFR) program for the RAL IBM mainframe computer. The two codes are integrated into a package which includes the Zeeman Laboratory Slater parameter optimisation routines as well as new RAL routines to further process the HFR and MCDF output. A description of the adaptions to MCDF and new output extensions is included in this report, and details are given regarding HFR FORTRAN subroutines, and lists of Job Control Language (JCL) files for the complete package. (author)

  10. Hartree-Fock energies of the doubly excited states of the boron isoelectronic sequence

    International Nuclear Information System (INIS)

    El-Sherbini, T.M.; Mansour, H.M.; Farrag, A.A.; Rahman, A.A.

    1985-08-01

    Hartree-Fock energies of the 1s 2 2s 2p ns( 4 P), 1s 2 2s 2p np ( 4 P, 4 D) and 1s 2 2s 2p nd ( 4 P, 4 D); n=3-6 states in the boron isoelectronic sequence are reported. The results show a fairly good agreement with the experimental data of Bromander for O IV. (author)

  11. Approximate energy correction for particle number summetry breaking in constrained Hartree-Fock plus BCS calculations

    International Nuclear Information System (INIS)

    Redon, N.; Meyer, J.; Meyer, M.

    1989-01-01

    An approximate restoration of the particle number symmetry, a la Lipkin-Nogami, is numerically investigated in the context of Constrained Hartree-Fock plus BCS calculations. Its effect is assessed in a variety of physical situations like potential energy landscapes in transitional nuclei, shape isomerism at low spin and fission barriers of actinide nuclei

  12. Positron and electron energy bands in several ionic crystals using restricted Hartree-Fock method

    Science.gov (United States)

    Kunz, A. B.; Waber, J. T.

    1981-08-01

    Using a restricted Hartree-Fock formalism and suitably localized and symmetrized wave functions, both the positron and electron energy bands were calculated for NaF, MgO and NiO. The lowest positron state at Γ 1 lies above the vacuum level and negative work functions are predicted. Positron annihilation rates were calculated and found to be in good agreement with measured lifetimes.

  13. Spin Hartree-Fock approach to studying quantum Heisenberg antiferromagnets in low dimensions

    Science.gov (United States)

    Werth, A.; Kopietz, P.; Tsyplyatyev, O.

    2018-05-01

    We construct a new mean-field theory for a quantum (spin-1/2) Heisenberg antiferromagnet in one (1D) and two (2D) dimensions using a Hartree-Fock decoupling of the four-point correlation functions. We show that the solution to the self-consistency equations based on two-point correlation functions does not produce any unphysical finite-temperature phase transition, in accord with the Mermin-Wagner theorem, unlike the common approach based on the mean-field equation for the order parameter. The next-neighbor spin-spin correlation functions, calculated within this approach, reproduce closely the strong renormalization by quantum fluctuations obtained via a Bethe ansatz in 1D and a small renormalization of the classical antiferromagnetic state in 2D. The heat capacity approximates with reasonable accuracy the full Bethe ansatz result at all temperatures in 1D. In 2D, we obtain a reduction of the peak height in the heat capacity at a finite temperature that is accessible by high-order 1 /T expansions.

  14. Application of the resonating Hartree-Fock random phase approximation to the Lipkin model

    International Nuclear Information System (INIS)

    Nishiyama, S.; Ishida, K.; Ido, M.

    1996-01-01

    We have applied the resonating Hartree-Fock (Res-HF) approximation to the exactly solvable Lipkin model by utilizing a newly developed orbital-optimization algorithm. The Res-HF wave function was superposed by two Slater determinants (S-dets) which give two corresponding local energy minima of monopole ''deformations''. The self-consistent Res-HF calculation gives an excellent ground-state correlation energy. There exist excitations due to small vibrational fluctuations of the orbitals and mixing coefficients around their stationary values. They are described by a new approximation called the resonating Hartree-Fock random phase approximation (Res-HF RPA). Matrices of the second-order variation of the Res-HF energy have the same structures as those of the Res-HF RPA's matrices. The quadratic steepest descent of the Res-HF energy in the orbital optimization is considered to include certainly both effects of RPA-type fluctuations up to higher orders and their mode-mode couplings. It is a very important and interesting task to apply the Res-HF RPA to the Lipkin model with the use of the stationary values and to prove the above argument. It turns out that the Res-HF RPA works far better than the usual HF RPA and the renormalized one. We also show some important features of the Res-HF RPA. (orig.)

  15. A correction for the Hartree-Fock density of states for jellium without screening

    International Nuclear Information System (INIS)

    Blair, Alexander I.; Kroukis, Aristeidis; Gidopoulos, Nikitas I.

    2015-01-01

    We revisit the Hartree-Fock (HF) calculation for the uniform electron gas, or jellium model, whose predictions—divergent derivative of the energy dispersion relation and vanishing density of states (DOS) at the Fermi level—are in qualitative disagreement with experimental evidence for simple metals. Currently, this qualitative failure is attributed to the lack of screening in the HF equations. Employing Slater’s hyper-Hartree-Fock (HHF) equations, derived variationally, to study the ground state and the excited states of jellium, we find that the divergent derivative of the energy dispersion relation and the zero in the DOS are still present, but shifted from the Fermi wavevector and energy of jellium to the boundary between the set of variationally optimised and unoptimised HHF orbitals. The location of this boundary is not fixed, but it can be chosen to lie at arbitrarily high values of wavevector and energy, well clear from the Fermi level of jellium. We conclude that, rather than the lack of screening in the HF equations, the well-known qualitative failure of the ground-state HF approximation is an artifact of its nonlocal exchange operator. Other similar artifacts of the HF nonlocal exchange operator, not associated with the lack of electronic correlation, are known in the literature

  16. Application of an effective gauge-invariant model to nuclear matter in the relativistic Hartree-Fock approximation

    Energy Technology Data Exchange (ETDEWEB)

    Bernardos, P. [Universidad de Cantabria, Departamento de Matematica Aplicada y Ciencias de la Computacion, 39005, Santander (Spain); Fomenko, V.N. [St Petersburg University for Railway Engineering, Department of Mathematics, 190031, St Petersburg (Russian Federation); Marcos, S.; Niembro, R. [Universidad de Cantabria, Departamento de Fisica Moderna, 39005, Santander (Spain); Lopez-Quelle, M. [Universidad de Cantabria, Departamento de Fisica Aplicada, 39005, Santander (Spain); Savushkin, L.N. [St Petersburg University for Telecommunications, Department of Physics, 191186, St Petersburg (Russian Federation)

    2001-02-01

    An effective nuclear model describing {omega}-, {rho}- and axial-mesons as gauge fields is applied to nuclear matter in the relativistic Hartree-Fock approximation. The isoscalar two-pion exchange is simulated by a scalar field s similar to that used in the conventional relativistic mean-field approach. Two more scalar fields are essential ingredients of the present treatment: the {sigma}-field, the chiral partner of the pion, and the {sigma}-field, the Higgs field for the {omega}-meson. Two versions of the model are used depending on whether the {sigma}-field is considered as a dynamical variable or 'frozen', by taking its mass as infinite. The model contains four free parameters in the first case and three in the second one which are fitted to the nuclear matter saturation conditions. The nucleon and meson effective masses, compressibility modulus and symmetry energy are calculated. The results prove the reliability of the Dirac-Hartree-Fock approach within the linear realization of the chiral symmetry. (author)

  17. Equilibration in the time-dependent Hartree-Fock approach probed with the Wigner distribution function

    International Nuclear Information System (INIS)

    Loebl, N.; Maruhn, J. A.; Reinhard, P.-G.

    2011-01-01

    By calculating the Wigner distribution function in the reaction plane, we are able to probe the phase-space behavior in the time-dependent Hartree-Fock scheme during a heavy-ion collision in a consistent framework. Various expectation values of operators are calculated by evaluating the corresponding integrals over the Wigner function. In this approach, it is straightforward to define and analyze quantities even locally. We compare the Wigner distribution function with the smoothed Husimi distribution function. Different reaction scenarios are presented by analyzing central and noncentral 16 O + 16 O and 96 Zr + 132 Sn collisions. Although we observe strong dissipation in the time evolution of global observables, there is no evidence for complete equilibration in the local analysis of the Wigner function. Because the initial phase-space volumes of the fragments barely merge and mean values of the observables are conserved in fusion reactions over thousands of fm/c, we conclude that the time-dependent Hartree-Fock method provides a good description of the early stage of a heavy-ion collision but does not provide a mechanism to change the phase-space structure in a dramatic way necessary to obtain complete equilibration.

  18. Molecular structures and vibrational frequencies of xanthine and its methyl derivatives (caffeine and theobromine) by ab initio Hartree-Fock and density functional theory calculations

    Science.gov (United States)

    Ucun, Fatih; Sağlam, Adnan; Güçlü, Vesile

    2007-06-01

    The molecular structures, vibrational frequencies and corresponding vibrational assignments of xanthine and its methyl derivatives (caffeine and theobromine) have been calculated using ab initio Hartree-Fock (HF) and density functional theory (B3LYP) methods with 6-31G(d, p) basis set level. The calculations were utilized to the CS symmetries of the molecules. The obtained vibrational frequencies and optimised geometric parameters (bond lengths and bond angles) were seen to be well agreement with the experimental data. The used scale factors which have been obtained the ratio of the frequency values of the strongest peaks in the calculated and experimental spectra seem to cause the gained vibrations well corresponding to the experimental ones. Theoretical infrared intensities and Raman activities are also reported.

  19. Coupled Hartree-Fock calculation of {sup 13} C shielding tensors in acetylene clusters

    Energy Technology Data Exchange (ETDEWEB)

    Craw, John Simon; Nascimento, Marco Antonio Chaer [Universidade Federal, Rio de Janeiro, RJ (Brazil). Inst. de Quimica

    1992-12-31

    The coupled Hartree Fock method has been used to calculate ab-initio carbon magnetic shielding tensors for small clusters of acetylene molecules. The chemical shift increases from the monomer to the dimer and trimer. This is mainly due increased diamagnetism, which is imperfectly cancelled by increased paramagnetism due to loss of axial symmetry. Anisotropic effects are shown to be small in both the dimer the and trimer. (author) 21 refs., 2 tabs.

  20. Correlation corrections to the Hartree-Fock perturbation theory of atomic and molecular properties. Dipole polarizabilities of He, Be and Ne

    International Nuclear Information System (INIS)

    Sadlej, A.J.

    1980-01-01

    The problem of the most efficient perturbation calculation of the correlation contributions to atomic and molecular properties is discussed. The method which is based on the coupled Hartree-Fock (CHF) perturbation theory appears to be the most promising one. The CHF-based perturbation theory of correlation effects is applied to the calculation of the second-order correlation contributions to the electric dipole polarizabilities of He, Be and Ne. The numerical approach employed in this paper consists in computing first the electric-field-dependent SCF functions. Then, the field dependent second-order correlation energy is calculated. The electric dipole polarizabilities, accurate through the second-order in correlation, are obtained via the numerical differentiation of the field-dependent energies with respect to the external electric field strength. In order to avoid the use of very large basis sets the so-called electric-field-variant (EFV) orbitals are employed in the present study. The CHF results obtained in this paper are of the same accuracy as the best literature data. In addition of the second-order correlation correction the final values of the electric dipole polarizability differ from the accurate or experimental results by less than a few per cent. (author)

  1. Large scale nuclear structure studies

    International Nuclear Information System (INIS)

    Faessler, A.

    1985-01-01

    Results of large scale nuclear structure studies are reported. The starting point is the Hartree-Fock-Bogoliubov solution with angular momentum and proton and neutron number projection after variation. This model for number and spin projected two-quasiparticle excitations with realistic forces yields in sd-shell nuclei similar good results as the 'exact' shell-model calculations. Here the authors present results for a pf-shell nucleus 46 Ti and results for the A=130 mass region where they studied 58 different nuclei with the same single-particle energies and the same effective force derived from a meson exchange potential. They carried out a Hartree-Fock-Bogoliubov variation after mean field projection in realistic model spaces. In this way, they determine for each yrast state the optimal mean Hartree-Fock-Bogoliubov field. They apply this method to 130 Ce and 128 Ba using the same effective nucleon-nucleon interaction. (Auth.)

  2. Charge- and parity-projected Hartree-Fock method for the strong tensor correlation and its application to the alpha particle

    International Nuclear Information System (INIS)

    Sugimoto, Satoru; Ikeda, Kiyomi; Toki, Hiroshi

    2004-01-01

    We propose a new mean-field-type framework which can treat the strong correlation induced by the tensor force. To treat the tensor correlation we break the charge and parity symmetries of a single-particle state and restore these symmetries of the total system by the projection method. We perform the charge and parity projections before variation and obtain a Hartree-Fock-like equation, which is solved self-consistently. We apply the Hartree-Fock-like equation to the alpha particle and find that by breaking the parity and charge symmetries, the correlation induced by the tensor force is obtained in the projected mean-field framework. We emphasize that the projection before the variation is important to pick up the tensor correlation in the present framework

  3. Dispersion corrected hartree-fock and density functional theory for organic crystal structure prediction.

    Science.gov (United States)

    Brandenburg, Jan Gerit; Grimme, Stefan

    2014-01-01

    We present and evaluate dispersion corrected Hartree-Fock (HF) and Density Functional Theory (DFT) based quantum chemical methods for organic crystal structure prediction. The necessity of correcting for missing long-range electron correlation, also known as van der Waals (vdW) interaction, is pointed out and some methodological issues such as inclusion of three-body dispersion terms are discussed. One of the most efficient and widely used methods is the semi-classical dispersion correction D3. Its applicability for the calculation of sublimation energies is investigated for the benchmark set X23 consisting of 23 small organic crystals. For PBE-D3 the mean absolute deviation (MAD) is below the estimated experimental uncertainty of 1.3 kcal/mol. For two larger π-systems, the equilibrium crystal geometry is investigated and very good agreement with experimental data is found. Since these calculations are carried out with huge plane-wave basis sets they are rather time consuming and routinely applicable only to systems with less than about 200 atoms in the unit cell. Aiming at crystal structure prediction, which involves screening of many structures, a pre-sorting with faster methods is mandatory. Small, atom-centered basis sets can speed up the computation significantly but they suffer greatly from basis set errors. We present the recently developed geometrical counterpoise correction gCP. It is a fast semi-empirical method which corrects for most of the inter- and intramolecular basis set superposition error. For HF calculations with nearly minimal basis sets, we additionally correct for short-range basis incompleteness. We combine all three terms in the HF-3c denoted scheme which performs very well for the X23 sublimation energies with an MAD of only 1.5 kcal/mol, which is close to the huge basis set DFT-D3 result.

  4. Ground-state properties of axially deformed Sr isotopes in Skyrme-Hartree-Fock-Bogolyubov method

    International Nuclear Information System (INIS)

    Yilmaz, A.H.; Bayram, T.; Demirci, M.; Engin, B.; Bayram, T.

    2010-01-01

    Binding energies, the mean-square nuclear radii, neutron radii, quadrupole moments and deformation parameters to axially deformed Strontium isotopes were evaluated using Hartree-Fock-Bogolyubov method. Shape coexistence was also discussed. The results were compared with experimental data and some estimates obtained within some nuclear models. The calculations were performed for SIy4 set of Skyrme forces and for wide range of the neutron numbers of Sr isotopes

  5. Hartree-Fock limit values of multipole moments, polarizabilities, and hyperpolarizabilities for atoms and diatomic molecules

    Science.gov (United States)

    Kobus, Jacek

    2015-02-01

    Recently it has been demonstrated that the finite difference Hartree-Fock method can be used to deliver highly accurate values of electric multipole moments together with polarizabilities αz z,Az ,z z , and hyperpolarizabilities βz z z, γz z z,Bz z ,z z , for the ground states of various atomic and diatomic systems. Since these results can be regarded as de facto Hartree-Fock limit values their quality is of the utmost importance. This paper reexamines the use of the finite field method to calculate these electric properties, discusses its accuracy, and presents an updated list of the properties for the following atoms and diatomic molecules: H-, He, Li, Li+,Li2 +,Li-,Be2 + , Be, B+,C2 + , Ne, Mg2 +, Mg, Al+,Si2 + , Ar, K+,Ca2 +,Rb+,Sr2 +,Zr4 +,He2 , Be2,N2,F2,O2 , HeNe, LiH2 +, LiCl, LiBr, BH, CO, FH, NaCl, and KF. The potential energy curves and the dependence of the electric properties on the internuclear distance is also studied for He2,LiH+,Be2 , and HeNe systems.

  6. Molecular Structure And Vibrational Frequencies of 2,3,4 Nitro anilines By Hartree-Fock And Density Functional Theory Calculations

    International Nuclear Information System (INIS)

    Sert, Y.

    2008-01-01

    The optimised molecular structure, vibrational frequencies and corresponding vibrational assignments of 2-, 3- and 4- nitro anilines have been calculated using the Hartree-Fock (HF) and density functional methods (B3LYP) with 6-311++G (d, p) basis set. The calculations were adapted to the C S symmetries of all the molecules. The calculated vibrational frequencies and geometric parameters (bond lengths and bond angles) were seen to be in good agreement with the experimental data. The comparison of the experimental and theoretical results showed that the HF method is superior to the B3LYP method for both the vibrational frequencies and geometric parameters

  7. Time-dependent Hartree--Fock method: description of heavy-ion collisions and allowance for correlations

    International Nuclear Information System (INIS)

    Maedler, P.

    1984-01-01

    The review describes the application of the time-dependent Hartree--Fock method to the description of heavy-ion interactions at energies of order 10 MeV/nucleon. The fundamentals of the method are presented and qualitative properties of its results are discussed. Realistic calculations of fusion reactions, deep inelastic collisions, and particle emission are presented and compared with the corresponding experimental data. Various approaches that generalize the method by taking into account correlations are considered

  8. Density-dependent Hartree-Fock response functions in quasi-elastic electron scattering on 12C and related sum rules

    International Nuclear Information System (INIS)

    Kohno, M.

    1983-01-01

    We report fully consistent calculations of the longitudinal and transverse response functions of the inclusive quasi-elastic electron scattering on 12 C in the Hartree-Fock approximation. The distorted wave for the outgoing nucleon is constructed from the same non-local Hartree-Fock field as in the ground-state description. Thus the orthogonality and Pauli principle requirements are naturally satisfied. The theoretical prediction, based on the standard density-dependent effective interaction (GO force), shows a good correspondence to the experimental data. Since the calculated response functions automatically satisfy the relevant sum rule, this work illuminates the well-known puzzle concerning the longitudinal part, which remains to be solved. We study the energy-weighted sum rules and discuss effects beyond the mean-field approximation. Meson-exchange-current contributions to the transverse response function are also estimated and found to be small due to cancellations among them. (orig.)

  9. Self-consistent Hartree-Fock RPA calculations in 208Pb

    Science.gov (United States)

    Taqi, Ali H.; Ali, Mohammed S.

    2018-01-01

    The nuclear structure of 208Pb is studied in the framework of the self-consistent random phase approximation (SCRPA). The Hartree-Fock mean field and single particle states are used to implement a completely SCRPA with Skyrme-type interactions. The Hamiltonian is diagonalised within a model space using five Skyrme parameter sets, namely LNS, SkI3, SkO, SkP and SLy4. In view of the huge number of the existing Skyrme-force parameterizations, the question remains which of them provide the best description of data. The approach attempts to accurately describe the structure of the spherical even-even nucleus 208Pb. To illustrate our approach, we compared the binding energy, charge density distribution, excitation energy levels scheme with the available experimental data. Moreover, we calculated isoscalar and isovector monopole, dipole, and quadrupole transition densities and strength functions.

  10. Comparison of the surface friction model with the time-dependent Hartree-Fock method

    International Nuclear Information System (INIS)

    Froebrich, P.

    1984-01-01

    A comparison is made between the classical phenomenological surface friction model and a time-dependent Hartree-Fock study by Dhar for the system 208 Pb+ 74 Ge at E/sub lab/(Pb) = 1600 MeV. The general trends for energy loss, mean values for charge and mass, interaction times and energy-angle correlations turn out to be fairly similar in both methods. However, contrary to Dhar, the events close to capture are interpreted as normal deep-inelastic, i.e., not as fast fission processes

  11. Physically asymptotic Hartree-Fock stationary-phase approximant to the many-body S-matrix

    International Nuclear Information System (INIS)

    Griffin, J.J.; Dworzecka, M.

    1982-01-01

    The Asymptotic Hartree-Fock Approximant replaces the physically non-asymptotic (and dynamically nontrivial) external translation of the FISP result with the asymptotic and dynamically trivial translational evolution of Dirac-TDHF by adding an explicit restriction upon the acceptable channel states. It is therefore preferable under the principle of commensurability, which judges the expected output of physical descriptions in terms of the physical assumptions they incorporate. Further insight into the relationship between the TDSHF and FISP methods will reward careful comparison of the respective expressions, in specific cases

  12. A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. I. General formalism and application to open-shell states.

    Science.gov (United States)

    Miranda, R P; Fisher, A J; Stella, L; Horsfield, A P

    2011-06-28

    The solution of the time-dependent Schrödinger equation for systems of interacting electrons is generally a prohibitive task, for which approximate methods are necessary. Popular approaches, such as the time-dependent Hartree-Fock (TDHF) approximation and time-dependent density functional theory (TDDFT), are essentially single-configurational schemes. TDHF is by construction incapable of fully accounting for the excited character of the electronic states involved in many physical processes of interest; TDDFT, although exact in principle, is limited by the currently available exchange-correlation functionals. On the other hand, multiconfigurational methods, such as the multiconfigurational time-dependent Hartree-Fock (MCTDHF) approach, provide an accurate description of the excited states and can be systematically improved. However, the computational cost becomes prohibitive as the number of degrees of freedom increases, and thus, at present, the MCTDHF method is only practical for few-electron systems. In this work, we propose an alternative approach which effectively establishes a compromise between efficiency and accuracy, by retaining the smallest possible number of configurations that catches the essential features of the electronic wavefunction. Based on a time-dependent variational principle, we derive the MCTDHF working equation for a multiconfigurational expansion with fixed coefficients and specialise to the case of general open-shell states, which are relevant for many physical processes of interest.

  13. Assessing the role of Hartree-Fock exchange, correlation energy and long range corrections in evaluating ionization potential, and electron affinity in density functional theory.

    Science.gov (United States)

    Vikramaditya, Talapunur; Lin, Shiang-Tai

    2017-06-05

    Accurate determination of ionization potentials (IPs), electron affinities (EAs), fundamental gaps (FGs), and HOMO, LUMO energy levels of organic molecules play an important role in modeling and predicting the efficiencies of organic photovoltaics, OLEDs etc. In this work, we investigate the effects of Hartree Fock (HF) Exchange, correlation energy, and long range corrections in predicting IP and EA in Hybrid Functionals. We observe increase in percentage of HF exchange results in increase of IPs and decrease in EAs. Contrary to the general expectations inclusion of both HF exchange and correlation energy (from the second order perturbation theory MP2) leads to poor prediction. Range separated Hybrid Functionals are found to be more reliable among various DFT Functionals investigated. DFT Functionals predict accurate IPs whereas post HF methods predict accurate EAs. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

  14. Hartree-Fock+BCS approach to unstable nuclei with the Skyrme force

    International Nuclear Information System (INIS)

    Tajima, Naoki

    2001-01-01

    We reanalyze the results of our extensive Hartree-Fock+BCS calculation from new points of view paying attention to the properties of unstable nuclei. The calculation has been done with the Skyrme SIII force for the ground and shape isomeric states of 1029 even-even nuclei ranging 2≤Z≤114. We also discuss the advantages of the employed three-dimensional Cartesian-mesh representation, especially on its remarkably high precision with apparently coarse meshes when applied to atomic nuclei. In Appendices we give the coefficients of finite-point numerical differentiation and integration formulae suitable for Cartesian mesh representation and elucidate the features of each formula and the differences from a method based on the Fourier transformation. (author)

  15. Long-range corrected density functional theory with accelerated Hartree-Fock exchange integration using a two-Gaussian operator [LC-ωPBE(2Gau)].

    Science.gov (United States)

    Song, Jong-Won; Hirao, Kimihiko

    2015-10-14

    Since the advent of hybrid functional in 1993, it has become a main quantum chemical tool for the calculation of energies and properties of molecular systems. Following the introduction of long-range corrected hybrid scheme for density functional theory a decade later, the applicability of the hybrid functional has been further amplified due to the resulting increased performance on orbital energy, excitation energy, non-linear optical property, barrier height, and so on. Nevertheless, the high cost associated with the evaluation of Hartree-Fock (HF) exchange integrals remains a bottleneck for the broader and more active applications of hybrid functionals to large molecular and periodic systems. Here, we propose a very simple yet efficient method for the computation of long-range corrected hybrid scheme. It uses a modified two-Gaussian attenuating operator instead of the error function for the long-range HF exchange integral. As a result, the two-Gaussian HF operator, which mimics the shape of the error function operator, reduces computational time dramatically (e.g., about 14 times acceleration in C diamond calculation using periodic boundary condition) and enables lower scaling with system size, while maintaining the improved features of the long-range corrected density functional theory.

  16. The semi-classical limit of the time dependent Hartree-Fock equation. II. The Wick symbol of the solution

    OpenAIRE

    Amour, Laurent; Khodja, Mohamed; Nourrigat, Jean

    2011-01-01

    We study the Wick symbol of a solution of the time dependent Hartree Fock equation, under weaker hypotheses than those needed for the Weyl symbol in the first paper with thesame title. With similar, we prove some kind of Ehrenfest theorem for observables that are not pseudo-differential operators.

  17. On particle emission in the time-dependent Hartree-Fock approximation

    International Nuclear Information System (INIS)

    Maedler, P.

    1984-01-01

    Investigations of fast particle emission in the time-dependent Hartree-Fock mean-field approximation (TDHF) have been performed for one-dimensional slab collisions. For a fixed target mass number and incident velocity the total yields of PEP exhibit pronounced srtructures as a function of the pro ectile mass number, which strongly correcate with the binding energy of the last nucleon in the projectnle. This is in explicit disagreement with experiment. The conclusion has been drawn that the Fermi-jet mechanism cannot be responsible for most of the fast particles observed in experiment, even if quantum diffraction is taken into account (as in TDHF). After PEP emission large amplitude density oscillations, which are the only possible modes in the slab geometry, are found to be damped by further particle emission

  18. Systematic study of even-even nuclei with Hartree-Fock+BCS method using Skyrme SIII force

    Energy Technology Data Exchange (ETDEWEB)

    Tajima, Naoki; Takahara, Satoshi; Onishi, Naoki [Tokyo Univ. (Japan). Coll. of Arts and Sciences

    1997-03-01

    We have applied the Hartree-Fock+BCS method with Skyrme SIII force formulated in a three-dimensional Cartesian-mesh representation to even-even nuclei with 2 {<=} Z {<=} 114. We discuss the results concerning the atomic masses, the quadrupole (m=0, 2) and hexadecapole (m=0, 2, 4) deformations, the skin thicknesses, and the halo radii. We also discuss the energy difference between oblate and prolate solutions and the shape difference between protons and neutrons. (author)

  19. Ab initio Hartree-Fock study on surface desorption process in tritium release

    International Nuclear Information System (INIS)

    Taniguchi, M.; Tanaka, S.

    1998-01-01

    Dissociative adsorption of hydrogen on Li 2 O (110) surface has been investigated with ab initio Hartree-Fock quantum chemical calculation technique. Heat of adsorption and surface potential energy for H 2 dissociative adsorption were evaluated by calculating the total energy of the system. The calculated results on adsorption heat indicated that H 2 adsorption is endothermic. However, when an oxygen vacancy exists adjacent to the adsorption site, the heat of adsorption became less endothermic and the activation energy required to dissociate the H-H bonding was smaller than that for the terrace site. This is considered to be caused by the excess charge localized near the defect. (orig.)

  20. Possibility of ΛΛ pairing and its dependence on background density in a relativistic Hartree-Bogoliubov model

    International Nuclear Information System (INIS)

    Tanigawa, Tomonori; Matsuzaki, Masayuki; Chiba, Satoshi

    2003-01-01

    We calculate a ΛΛ pairing gap in binary mixed matter of nucleons and Λ hyperons within the relativistic Hartree-Bogoliubov model. Λ hyperons to be paired up are immersed in background nucleons in a normal state. The gap is calculated with a one-boson-exchange interaction obtained from a relativistic Lagrangian. It is found that at background density ρ N =2.5ρ 0 the ΛΛ pairing gap is very small, and that a denser background makes it rapidly suppressed. This result suggests a mechanism, specific to mixed matter dealt with relativistic models, of its dependence on the nucleon density. An effect of weaker ΛΛ attraction on the gap is also examined in connection with the revised information of the ΛΛ interaction

  1. Exploration of (super-)heavy elements using the Skyrme-Hartree-Fock model

    International Nuclear Information System (INIS)

    Erler, Jochen

    2011-01-01

    Motivated by the steadily increasing number of known nuclei and nuclear properties, theories of nuclear structure are presently a field of intense research. This work concentrates on the self-consistent description of nuclei in terms of the Skyrme-Hartree-Fock (SHF) approach. The extrapolation of nuclear shell structure to the region of super-heavy elements (SHE) using the SHF model, the dependence on different parameterization and the influence of collective correlation will be studied. The general scope of this work are large scale calculation for a global survey of properties of SHE like binding energies, separation energies and decay characteristics and lifetimes. These calculations were done in a collaboration with the theory group of the GSI in Darmstadt and have the aim to develop a database of lifetimes and reaction rates for α, β-decay and spontaneous fission in a very wide range with proton numbers 86 ≤ Z ≤ 120 and neutron numbers up to N ∼ 260 relevant for the astrophysical r-process. The results of this study for example predictions of a possible islands of very stable nuclei and information of favored decay mode for each nuclei are also applicable in the recent experimental synthesis of exotic SHE. For these calculation a framework to calculate β-decay half-lives within the SHF model has been developed and the existing axial SHF code has been extended to compute β-transition matrix elements and so to provide an estimation of half-lives. (orig.)

  2. Exploration of (super-)heavy elements using the Skyrme-Hartree-Fock model

    Energy Technology Data Exchange (ETDEWEB)

    Erler, Jochen

    2011-01-31

    Motivated by the steadily increasing number of known nuclei and nuclear properties, theories of nuclear structure are presently a field of intense research. This work concentrates on the self-consistent description of nuclei in terms of the Skyrme-Hartree-Fock (SHF) approach. The extrapolation of nuclear shell structure to the region of super-heavy elements (SHE) using the SHF model, the dependence on different parameterization and the influence of collective correlation will be studied. The general scope of this work are large scale calculation for a global survey of properties of SHE like binding energies, separation energies and decay characteristics and lifetimes. These calculations were done in a collaboration with the theory group of the GSI in Darmstadt and have the aim to develop a database of lifetimes and reaction rates for {alpha}, {beta}-decay and spontaneous fission in a very wide range with proton numbers 86 {<=} Z {<=} 120 and neutron numbers up to N {approx} 260 relevant for the astrophysical r-process. The results of this study for example predictions of a possible islands of very stable nuclei and information of favored decay mode for each nuclei are also applicable in the recent experimental synthesis of exotic SHE. For these calculation a framework to calculate {beta}-decay half-lives within the SHF model has been developed and the existing axial SHF code has been extended to compute {beta}-transition matrix elements and so to provide an estimation of half-lives. (orig.)

  3. Time-Dependent Hartree-Fock Approach to Nuclear Pasta at Finite Temperature

    International Nuclear Information System (INIS)

    Schuetrumpf, B; Maruhn, J A; Klatt, M A; Mecke, K; Reinhard, P-G; Iida, K

    2013-01-01

    We present simulations of neutron-rich matter at subnuclear densities, like supernova matter, with the time-dependent Hartree-Fock approximation at temperatures of several MeV. The initial state consists of α particles randomly distributed in space that have a Maxwell-Boltzmann distribution in momentum space. Adding a neutron background initialized with Fermi distributed plane waves the calculations reflect a reasonable approximation of astrophysical matter. This matter evolves into spherical, rod-like, and slab-like shapes and mixtures thereof. The simulations employ a full Skyrme interaction in a periodic three-dimensional grid. By an improved morphological analysis based on Minkowski functionals, all eight pasta shapes can be uniquely identified by the sign of only two valuations, namely the Euler characteristic and the integral mean curvature.

  4. Time-Dependent Hartree-Fock Approach to Nuclear Pasta at Finite Temperature

    Science.gov (United States)

    Schuetrumpf, B.; Klatt, M. A.; Iida, K.; Maruhn, J. A.; Mecke, K.; Reinhard, P.-G.

    2013-03-01

    We present simulations of neutron-rich matter at subnuclear densities, like supernova matter, with the time-dependent Hartree-Fock approximation at temperatures of several MeV. The initial state consists of α particles randomly distributed in space that have a Maxwell-Boltzmann distribution in momentum space. Adding a neutron background initialized with Fermi distributed plane waves the calculations reflect a reasonable approximation of astrophysical matter. This matter evolves into spherical, rod-like, and slab-like shapes and mixtures thereof. The simulations employ a full Skyrme interaction in a periodic three-dimensional grid. By an improved morphological analysis based on Minkowski functionals, all eight pasta shapes can be uniquely identified by the sign of only two valuations, namely the Euler characteristic and the integral mean curvature.

  5. Skyrme-Hartree-Fock in the realm of nuclear mean field models

    International Nuclear Information System (INIS)

    Reinhard, P.G.; Reiss, C.; Maruhn, J.; Bender, M.; Buervenich, T.; Greiner, W.

    2000-01-01

    We discuss and compare two brands of nuclear mean field models, the Skyrme-Hartree-Fock scheme (SHF) and the relativistic mean field model (RMF). Similarities and differences are worked out on a formal basis and with respect to the models performance in describing nuclear data. The bulk observables of stable nuclei are all described very well. Differences come up when extrapolating to exotic nuclei. The typically larger asymmetry energy in RMF leads to a larger neutron skin. Superheavy nuclei are found to be very sensitive on the single particle levels particularly on the spin orbit splitting. Ground state correlations from collective surface vibrations can have a significant effect on difference observables, as two-nucleon separation energy and two-nucleon shell gap. (author)

  6. Time-dependent Hartree-Fock calculation of the escape width of the giant monopole resonance in 16O

    International Nuclear Information System (INIS)

    Pacheco, J.M.; Maglione, E.; Broglia, R.A.

    1988-01-01

    The damping of the giant monopole resonance in 16 O is calculated within the framework of the time-dependent Hartree-Fock approximation. The strength function contains two peaks, centered at around 25 and 33 MeV, with escape widths of ∼11 and ∼2 MeV, associated with the 1p(0p) -1 and 1s(0s) -1 configurations, respectively

  7. Efficient exact-exchange time-dependent density-functional theory methods and their relation to time-dependent Hartree-Fock.

    Science.gov (United States)

    Hesselmann, Andreas; Görling, Andreas

    2011-01-21

    A recently introduced time-dependent exact-exchange (TDEXX) method, i.e., a response method based on time-dependent density-functional theory that treats the frequency-dependent exchange kernel exactly, is reformulated. In the reformulated version of the TDEXX method electronic excitation energies can be calculated by solving a linear generalized eigenvalue problem while in the original version of the TDEXX method a laborious frequency iteration is required in the calculation of each excitation energy. The lowest eigenvalues of the new TDEXX eigenvalue equation corresponding to the lowest excitation energies can be efficiently obtained by, e.g., a version of the Davidson algorithm appropriate for generalized eigenvalue problems. Alternatively, with the help of a series expansion of the new TDEXX eigenvalue equation, standard eigensolvers for large regular eigenvalue problems, e.g., the standard Davidson algorithm, can be used to efficiently calculate the lowest excitation energies. With the help of the series expansion as well, the relation between the TDEXX method and time-dependent Hartree-Fock is analyzed. Several ways to take into account correlation in addition to the exact treatment of exchange in the TDEXX method are discussed, e.g., a scaling of the Kohn-Sham eigenvalues, the inclusion of (semi)local approximate correlation potentials, or hybrids of the exact-exchange kernel with kernels within the adiabatic local density approximation. The lowest lying excitations of the molecules ethylene, acetaldehyde, and pyridine are considered as examples.

  8. The Hartree-Fock approximation for s-d shell even-even nuclei with N different of Z

    International Nuclear Information System (INIS)

    Oliveira, P.C. de.

    1981-02-01

    Using the Hartree-Fock approximation method for 22 Ne, 26 Mg and 30 Si nuclei with different kinds of two-body interactions, the electric quadrupole moments and projected energy levels, of angular momentum J=0,2,4,6..., are determined. The Peierls-Yoccoz projection m ethod is used to determine the wave function with well-defined angular momentum. A comparison is made, with the experimental results and the ones obtained by other authors. (Author) [pt

  9. The positronium and the dipositronium in a Hartree-Fock approximation of quantum electrodynamics

    Science.gov (United States)

    Sok, Jérémy

    2016-02-01

    The Bogoliubov-Dirac-Fock (BDF) model is a no-photon approximation of quantum electrodynamics. It allows to study relativistic electrons in interaction with the Dirac sea. A state is fully characterized by its one-body density matrix, an infinite rank non-negative projector. We prove the existence of the para-positronium, the bound state of an electron and a positron with antiparallel spins, in the BDF model represented by a critical point of the energy functional in the absence of an external field. We also prove the existence of the dipositronium, a molecule made of two electrons and two positrons that also appears as a critical point. More generally, for any half integer j ∈ 1/2 + Z + , we prove the existence of a critical point of the energy functional made of 2j + 1 electrons and 2j + 1 positrons.

  10. Ab-initio Hartree-Fock study of tritium desorption from Li{sub 2}O

    Energy Technology Data Exchange (ETDEWEB)

    Taniguchi, Masaki; Tanaka, Satoru [Tokyo Univ. (Japan). Faculty of Engineering

    1998-03-01

    Dissociative adsorption of hydrogen on Li{sub 2}O (110) surface has been investigated with ab-initio Hartree-Fock quantum chemical calculation technique. Heat of adsorption and potential energy surface for H{sub 2} dissociative adsorption was evaluated by calculating the total energy of the system. Calculation results on adsorption heat indicated that H{sub 2} adsorption is endothermic. However, when oxygen vacancy exists adjacent to the adsorption sites, heat of adsorption energy became less endothermic and the activation energy required to dissociate the H-H bonding was smaller than that for the terrace site. This is considered to be caused by the excess charge localized near the defect. (author)

  11. Genealogical electronic coupling procedure incorporating the Hartree--Fock interacting space and suitable for degenerate point groups. Application to excited states of BH3

    International Nuclear Information System (INIS)

    Swope, W.C.; Schaefer, H.F. III; Yarkony, D.R.

    1980-01-01

    The use of Clebsch--Gordan-type coupling coefficients for finite point groups is applied to the problem of constructing symmetrized N-electron wave functions (configurations) for use by the Hartree--Fock SCF and CI methods of determining electronic wave functions for molecular systems. The configurations are eigenfunctions of electronic spin operators, and transform according to a particular irreducible representation of the relevant group of spatial operations which leave the Born--Oppenheimer Hamiltonian invariant. The method proposed for constructing the configurations involves a genealogical coupling procedure. It is particularly useful for studies of molecules which belong to a group which has multiply degenerate irreducible representations. The advantage of the method is that it results in configurations which are real linear combinations of determinants of real symmetry orbitals. This procedure for constructing configurations also allows for the identification of configurations which have no matrix element of the Hamiltonian with a reference configuration. It is therefore possible to construct a Hartree--Fock interacting space of configurations which can speed the convergence of a CI wave function. The coupling method is applied to a study of the ground and two excited electronic states of BH 3 in its D/sub 3h/ geometry. The theoretical approach involved Hartree--Fock SCF calculations followed by single and double substitution CI calculations, both of which employed double-zeta plus polarization quality basis sets

  12. Fractional quantum Hall effect: Construction of the Hartree-Fock state by using translational covariance

    International Nuclear Information System (INIS)

    Ferrari, R.; I.N.F.N., Trento

    1994-01-01

    The formalism introduced in a previous paper is used for discussing the Coulomb interaction of many electrons moving in two space-dimensions in the presence of a strong magnetic field. The matrix element of the coulomb interaction is evaluated in the new basis, whose states are invariant under discrete translations. This paper is devoted to the case of low filling factor, thus the authors limit themselves to the lowest Landau level and to spins all oriented along the magnetic field. For the case of filling factor ν f = 1/u they give an Ansatz on the state of many electrons which provides a good approximated solution of the Hartree-Fock equation. For general filling factor ν f = u'/u a trial state is given which converges very rapidly to a solution of the self-consistent equation. They generalize the Hartree-Fock equation by considering some correlation: all quantum states are allowed for the u' electrons with the same translation quantum numbers. Numerical results are given for the mean energy and the energy bands, for some values of the filling factor (ν f = 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5, 4/5). The results agree numerically with the Charge Density Wave approach. The boundary conditions are shown to be very important: only large systems (degeneracy of Landau level over 200) are not affected by the boundaries. Therefore results obtained on small scale systems are somewhat unreliable. The relevance of the results for the Fractional Quantum Hall Effect is briefly discussed

  13. Symplectic manifolds, coadjoint orbits, and Mean Field Theory

    International Nuclear Information System (INIS)

    Rosensteel, G.

    1986-01-01

    Mean field theory is given a geometrical interpretation as a Hamiltonian dynamical system. The Hartree-Fock phase space is the Grassmann manifold, a symplectic submanifold of the projective space of the full many-fermion Hilbert space. The integral curves of the Hartree-Fock vector field are the time-dependent Hartree-Fock solutions, while the critical points of the energy function are the time-independent states. The mean field theory is generalized beyond determinants to coadjoint orbit spaces of the unitary group; the Grassmann variety is the minimal coadjoint orbit

  14. Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations

    DEFF Research Database (Denmark)

    Nam, Phan Thanh; Napiorkowski, Marcin; Solovej, Jan Philip

    2016-01-01

    We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our...

  15. Projected quasiparticle theory for molecular electronic structure

    Science.gov (United States)

    Scuseria, Gustavo E.; Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.; Samanta, Kousik; Ellis, Jason K.

    2011-09-01

    We derive and implement symmetry-projected Hartree-Fock-Bogoliubov (HFB) equations and apply them to the molecular electronic structure problem. All symmetries (particle number, spin, spatial, and complex conjugation) are deliberately broken and restored in a self-consistent variation-after-projection approach. We show that the resulting method yields a comprehensive black-box treatment of static correlations with effective one-electron (mean-field) computational cost. The ensuing wave function is of multireference character and permeates the entire Hilbert space of the problem. The energy expression is different from regular HFB theory but remains a functional of an independent quasiparticle density matrix. All reduced density matrices are expressible as an integration of transition density matrices over a gauge grid. We present several proof-of-principle examples demonstrating the compelling power of projected quasiparticle theory for quantum chemistry.

  16. Analytic formulae for the Hartree-Fock order parameter at arbitrary p/q filling factors for the 2DEG in a magnetic field

    International Nuclear Information System (INIS)

    Cabo Monte Oca, A. de.

    1994-07-01

    Analytic expressions for order parameters are given for the previously introduced general class of Hartree Fock states at arbitrary filling factors ν=p/q for odd q values. The order parameters are expressed as sums of magnetic translations eigenvalues over the filled single electron states. Simple summation formulae for the band spectra in terms of the same eigenvalues are also presented. The energy per particle at ν=1/3 is calculated for various states differing in the way of filling of the 1/3 of the orbitals. The calculated energies are not competing with the usual CDW results. However the high degree of electron overlapping allows for the next corrections to modify this situation. The discussion suggests these Hartree-Fock Slater determinants as interesting alternatives for the Tao-Thouless parent states which may correct their anomalous symmetry and correlation functions properties. (author). 28 refs

  17. Time dependent density matrix theory and effective interaction

    Energy Technology Data Exchange (ETDEWEB)

    Tohyama, Mitsuru [Kyorin Univ., Mitaka, Tokyo (Japan). School of Medicine

    1998-07-01

    A correlated ground state of {sup 16}O and an E2 giant resonance built on it are calculated using an extended version of the time-dependent Hartree-Fock theory called the time-dependent density-matrix theory (TDDM). The Skyrme force is used in the calculation of both a mean field and two-body correlations. It is found that TDDM gives reasonable ground-state correlations and a large spreading width of the E2 giant resonance when single-particle states in the continuum are treated appropriately. (author)

  18. Angular momentum projection on a mesh of cranked Hartree-Fock wave functions

    International Nuclear Information System (INIS)

    Baye, D.; Heenen, P.

    1984-01-01

    A method for projecting on angular momentum wave functions discretized on a three-dimensional Cartesian mesh is presented. The method is based on a matrix representation of the rotation operator. It is applied to cranked Hartree-Fock wave functions calculated for 24 Mg with a simple interaction. In this case, the accuracy of the projected matrix elements is estimated to be of the order of 0.1%. An extensive comparison of the projected and cranking energies is made. The validity of the cranking method as an approximation to a variation-after-projection calculation seems to be wider than usually expected. The study of the fission barrier of 24 Mg for the channel 4 He- 16 O- 4 He shows that the cranking predictions for these very deformed states are quite reliable

  19. Multiconfiguration Dirac-Hartree-Fock calculations of energy levels and radiative rates of Fe VII

    Science.gov (United States)

    Li, Yang; Xu, Xiaokai; Li, Bowen; Jönsson, Per; Chen, Ximeng

    2018-06-01

    Detailed calculations are performed for 134 fine-structure levels of the 3p63d2, 3p63d4s, 3p53d3 and 3p63d4p configurations in Fe VII using the multiconfiguration Dirac-Hartree-Fock (MCDHF) and relativistic configuration interaction (RCI) methods. Important electron correlation effects are systematically accounted for through active space (AS) expansions. Our results compare well with experimental measurements, emphasizing the importance of a careful treatment of electron correlation, and provide some missing data in the NIST atomic database. The data obtained are expected to be useful in astrophysical applications, particularly for the research of the solar coronal plasma.

  20. Time-dependent Hartree-Fock approach to nuclear ``pasta'' at finite temperature

    Science.gov (United States)

    Schuetrumpf, B.; Klatt, M. A.; Iida, K.; Maruhn, J. A.; Mecke, K.; Reinhard, P.-G.

    2013-05-01

    We present simulations of neutron-rich matter at subnuclear densities, like supernova matter, with the time-dependent Hartree-Fock approximation at temperatures of several MeV. The initial state consists of α particles randomly distributed in space that have a Maxwell-Boltzmann distribution in momentum space. Adding a neutron background initialized with Fermi distributed plane waves the calculations reflect a reasonable approximation of astrophysical matter. This matter evolves into spherical, rod-like, and slab-like shapes and mixtures thereof. The simulations employ a full Skyrme interaction in a periodic three-dimensional grid. By an improved morphological analysis based on Minkowski functionals, all eight pasta shapes can be uniquely identified by the sign of only two valuations, namely the Euler characteristic and the integral mean curvature. In addition, we propose the variance in the cell density distribution as a measure to distinguish pasta matter from uniform matter.

  1. Description of plasmon-like band in silver clusters: the importance of the long-range Hartree-Fock exchange in time-dependent density-functional theory simulations.

    Science.gov (United States)

    Rabilloud, Franck

    2014-10-14

    Absorption spectra of Ag20 and Ag55(q) (q = +1, -3) nanoclusters are investigated in the framework of the time-dependent density functional theory in order to analyse the role of the d electrons in plasmon-like band of silver clusters. The description of the plasmon-like band from calculations using density functionals containing an amount of Hartree-Fock exchange at long range, namely, hybrid and range-separated hybrid (RSH) density functionals, is in good agreement with the classical interpretation of the plasmon-like structure as a collective excitation of valence s-electrons. In contrast, using local or semi-local exchange functionals (generalized gradient approximations (GGAs) or meta-GGAs) leads to a strong overestimation of the role of d electrons in the plasmon-like band. The semi-local asymptotically corrected model potentials also describe the plasmon as mainly associated to d electrons, though calculated spectra are in fairly good agreement with those calculated using the RSH scheme. Our analysis shows that a portion of non-local exchange modifies the description of the plasmon-like band.

  2. Ab Initio periodic Hartree-Fock study of group IA cations in ANA-type zeolites

    International Nuclear Information System (INIS)

    Anchell, J.L.; White, J.C.; Thompson, M.R.; Hess, A.C.

    1994-01-01

    This study investigates the electronic structure of Group IA cations intercalated into zeolites with the analcime (ANA) framework using ab initio periodic Hartree-Fock theory. The purpose of the study is to gain a better understanding of the role played by electron-donating species in zeolites in general, with specific applications to materials that have been suggested as storage matrices for radioactive materials. The effect of the intercalated species (Na, K, Rb, and Cs) on the electronic structure of the zeolite is presented on the basis of an analysis of the total and projected density of states, Mulliken charges, and charge density differences. The results of those analyses indicate that, relative to a charge neutral atomic state, the Group IA species donate an electron to the zeolite lattice and interact most strongly with the s and p atomic states of oxygen as the species are moved through the lattice. In addition, estimates of the self-diffusion constants of Na, K, Rb, and Cs based upon a one-dimensional diffusion model parameterized from the ab initio total energy data will be presented. 24 refs., 8 figs., 4 tabs

  3. Koopmans' theorem in the Hartree-Fock method. General formulation

    Science.gov (United States)

    Plakhutin, Boris N.

    2018-03-01

    This work presents a general formulation of Koopmans' theorem (KT) in the Hartree-Fock (HF) method which is applicable to molecular and atomic systems with arbitrary orbital occupancies and total electronic spin including orbitally degenerate (OD) systems. The new formulation is based on the full set of variational conditions imposed upon the HF orbitals by the variational principle for the total energy and the conditions imposed by KT on the orbitals of an ionized electronic shell [B. N. Plakhutin and E. R. Davidson, J. Chem. Phys. 140, 014102 (2014)]. Based on these conditions, a general form of the restricted open-shell HF method is developed, whose eigenvalues (orbital energies) obey KT for the whole energy spectrum. Particular attention is paid to the treatment of OD systems, for which the new method gives a number of unexpected results. For example, the present method gives four different orbital energies for the triply degenerate atomic level 2p in the second row atoms B to F. Based on both KT conditions and a parallel treatment of atoms B to F within a limited configuration interaction approach, we prove that these four orbital energies, each of which is triply degenerate, are related via KT to the energies of different spin-dependent ionization and electron attachment processes (2p)N → (2p ) N ±1. A discussion is also presented of specific limitations of the validity of KT in the HF method which arise in OD systems. The practical applicability of the theory is verified by comparing KT estimates of the ionization potentials I2s and I2p for the second row open-shell atoms Li to F with the relevant experimental data.

  4. Energy Levels and B(E2) transition rates in the Hartree-Fock approximation with the Skyrme force

    International Nuclear Information System (INIS)

    Oliveira, D.R. de; Mizrahi, S.S.

    1976-11-01

    The Hartree-Fock approximation with the Skyrme force is applied to the A = 4n type of nuclei in the s-d shell. Energy levels and electric quadrupole transition probabilities within the ground states band are calculated from the projected states of good angular momentum. Strong approximations are made but the results concerning the spectra are better than those obtained with more sophisticated density independent two-body interactions. The transition rates are less sensitive to the interaction, as previously verified

  5. Finite-temperature coupled-cluster, many-body perturbation, and restricted and unrestricted Hartree-Fock study on one-dimensional solids: Luttinger liquids, Peierls transitions, and spin- and charge-density waves.

    Science.gov (United States)

    Hermes, Matthew R; Hirata, So

    2015-09-14

    One-dimensional (1D) solids exhibit a number of striking electronic structures including charge-density wave (CDW) and spin-density wave (SDW). Also, the Peierls theorem states that at zero temperature, a 1D system predicted by simple band theory to be a metal will spontaneously dimerize and open a finite fundamental bandgap, while at higher temperatures, it will assume the equidistant geometry with zero bandgap (a Peierls transition). We computationally study these unique electronic structures and transition in polyyne and all-trans polyacetylene using finite-temperature generalizations of ab initio spin-unrestricted Hartree-Fock (UHF) and spin-restricted coupled-cluster doubles (CCD) theories, extending upon previous work [He et al., J. Chem. Phys. 140, 024702 (2014)] that is based on spin-restricted Hartree-Fock (RHF) and second-order many-body perturbation (MP2) theories. Unlike RHF, UHF can predict SDW as well as CDW and metallic states, and unlike MP2, CCD does not diverge even if the underlying RHF reference wave function is metallic. UHF predicts a gapped SDW state with no dimerization at low temperatures, which gradually becomes metallic as the temperature is raised. CCD, meanwhile, confirms that electron correlation lowers the Peierls transition temperature. Furthermore, we show that the results from all theories for both polymers are subject to a unified interpretation in terms of the UHF solutions to the Hubbard-Peierls model using different values of the electron-electron interaction strength, U/t, in its Hamiltonian. The CCD wave function is shown to encompass the form of the exact solution of the Tomonaga-Luttinger model and is thus expected to describe accurately the electronic structure of Luttinger liquids.

  6. Derivation of an adiabatic time-dependent Hartree-Fock formalism from a variational principle

    International Nuclear Information System (INIS)

    Brink, D.M.; Giannoni, M.J.; Veneroni, M.

    1975-10-01

    A derivation of the adiabatic time-dependent Hartree-Fock formalism is given, which is based on a variational principle analogous to Hamilton's principle in classical mechanics. The method leads to a Hamiltonian for collective motion which separates into a potential and a kinetic energy and gives mass and potential parameters in terms of the nucleon-nucleon interaction. The adiabatic approximation assumes slow motion but not small amplitudes and can therefore describe anharmonic effects. The RPA is a limiting case where both amplitudes and velocities are small. The variational approach provides a consistent way of extracting coordinated and momenta from the density matrix and of obtaining equations of motion when particular trial forms for this density matrix are chosen. One such choice leads to Thouless-Valatin formula. An other choice leads to irrotational hydrodynamics [fr

  7. Limits of Nuclear Stability

    CERN Document Server

    Nerlo-Pomorska, B; Kleban, M

    2003-01-01

    The modern version of the liquid-drop model (LSD) is compared with the macroscopic part of the binding energy evaluated within the Hartree-Fock- Bogoliubov procedure with the Gogny force and the relativistic mean field theory. The parameters of a liquid-drop like mass formula which approximate on the average the self-consistent results are compared with other models. The limits of nuclear stability predicted by these models are discussed.

  8. Spin polarization, orbital occupation and band gap opening in vanadium dioxide: The effect of screened Hartree-Fock exchange

    KAUST Repository

    Wang, Hao

    2014-07-01

    The metal-insulator transition of VO2 so far has evaded an accurate description by density functional theory. The screened hybrid functional of Heyd, Scuseria and Ernzerhof leads to reasonable solutions for both the low-temperature monoclinic and high-temperature rutile phases only if spin polarization is excluded from the calculations. We explore whether a satisfactory agreement with experiment can be achieved by tuning the fraction of Hartree Fock exchange (α) in the density functional. It is found that two branches of locally stable solutions exist for the rutile phase for 12.5%≤α≤20%. One is metallic and has the correct stability as compared to the monoclinic phase, the other is insulating with lower energy than the metallic branch. We discuss these observations based on the V 3d orbital occupations and conclude that α=10% is the best possible choice for spin-polarized VO2 calculations. © 2014 Elsevier B.V. All rights reserved.

  9. Quasiparticle method in relativistic mean-field theories of nuclear structure

    International Nuclear Information System (INIS)

    Ai, H.

    1988-01-01

    In recent years, in order to understand the success of Dirac phenomenology, relativistic Brueckner-Hartree-Fock (RBHF) theory has been developed. This theory is a relativistic many-body theory of nuclear structure. Based upon the RBHF theory, which is characterized as having no free parameters other than those introduced in fitting free-space nucleon-nucleon scattering data, we construct an effective interaction. This interaction, when treated in a relativistic Hartree-Fock approximation, reproduces, rather accurately, the nucleon self-energy in nuclear matter, Migdal parameters obtained via relativistic Brueckner-Hartree-Fock calculations, and the saturation curves calculated with the full relativistic Brueckner-Hartree-Fock theory. This effective interaction is constructed by adding a number of pseudoparticles to the mesons used to construct one-boson-exchange (OBE) models of the nuclear force. The pseudoparticles have relatively large masses and either real or imaginary coupling constants. (For example, exchange of a pseudo-sigma with an imaginary coupling constant has the effect of reducing the scalar attraction arising from sigma exchange, while exchange of a pseudo-omega with an imaginary coupling constant has the effect of reducing the repulsion arising from omega exchange. The terms beyond the Born term in the case of pion exchange are well simulated by pseudo-sigma exchange with a real coupling constant.) The effective interaction constructed here may be used for calculations of the properties of finite nuclei in a relativistic Hartree-Fock approximation

  10. Effect of Hartree-Fock exact exchange on intramolecular magnetic coupling constants of organic diradicals

    Science.gov (United States)

    Cho, Daeheum; Ko, Kyoung Chul; Ikabata, Yasuhiro; Wakayama, Kazufumi; Yoshikawa, Takeshi; Nakai, Hiromi; Lee, Jin Yong

    2015-01-01

    The intramolecular magnetic coupling constant (J) of diradical systems linked with five- or six-membered aromatic rings was calculated to obtain the scaling factor (experimental J/calculated J ratio) for various density functional theory (DFT) functionals. Scaling factors of group A (PBE, TPSSh, B3LYP, B97-1, X3LYP, PBE0, and BH&HLYP) and B (M06-L, M06, M06-2X, and M06-HF) were shown to decrease as the amount of Hartree-Fock exact exchange (HFx) increases, in other words, overestimation of calculated J becomes more severe as the HFx increases. We further investigated the effect of HFx fraction of DFT functional on J value, spin contamination, and spin density distributions by comparing the B3LYP analogues containing different amount of HFx. It was revealed that spin contamination and spin densities at each atom increases as the HFx increases. Above all, newly developed BLYP-5 functional, which has 5% of HFx, was found to have the scaling factor of 1.029, indicating that calculated J values are very close to that of experimental values without scaling. BLYP-5 has potential to be utilized for accurate evaluation of intramolecular magnetic coupling constant (J) of diradicals linked by five- or six-membered aromatic ring couplers.

  11. Effect of Hartree-Fock exact exchange on intramolecular magnetic coupling constants of organic diradicals

    Energy Technology Data Exchange (ETDEWEB)

    Cho, Daeheum; Ko, Kyoung Chul; Lee, Jin Yong, E-mail: jinylee@skku.edu [Department of Chemistry, Sungkyunkwan University, Suwon 440-746 (Korea, Republic of); Ikabata, Yasuhiro; Wakayama, Kazufumi; Yoshikawa, Takeshi [Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555 (Japan); Nakai, Hiromi, E-mail: nakai@waseda.jp [Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555 (Japan); Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555 (Japan); CREST, Japan Science and Technology Agency, Tokyo 102-0075 (Japan); Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Katsura, Kyoto 615-8520 (Japan)

    2015-01-14

    The intramolecular magnetic coupling constant (J) of diradical systems linked with five- or six-membered aromatic rings was calculated to obtain the scaling factor (experimental J/calculated J ratio) for various density functional theory (DFT) functionals. Scaling factors of group A (PBE, TPSSh, B3LYP, B97-1, X3LYP, PBE0, and BH and HLYP) and B (M06-L, M06, M06-2X, and M06-HF) were shown to decrease as the amount of Hartree-Fock exact exchange (HFx) increases, in other words, overestimation of calculated J becomes more severe as the HFx increases. We further investigated the effect of HFx fraction of DFT functional on J value, spin contamination, and spin density distributions by comparing the B3LYP analogues containing different amount of HFx. It was revealed that spin contamination and spin densities at each atom increases as the HFx increases. Above all, newly developed BLYP-5 functional, which has 5% of HFx, was found to have the scaling factor of 1.029, indicating that calculated J values are very close to that of experimental values without scaling. BLYP-5 has potential to be utilized for accurate evaluation of intramolecular magnetic coupling constant (J) of diradicals linked by five- or six-membered aromatic ring couplers.

  12. Pairing in exotic neutron-rich nuclei near the drip line and in the crust of neutron stars

    Science.gov (United States)

    Pastore, A.; Margueron, J.; Schuck, P.; Viñas, X.

    2013-09-01

    Exotic and drip-line nuclei as well as nuclei immersed in a low-density gas of neutrons in the inner crust of neutron stars are systematically investigated with respect to their neutron pairing properties. This is done using Skyrme density-functional and different pairing forces such as a density-dependent contact interaction and a separable form of a finite-range Gogny interaction. Hartree-Fock-Bogoliubov (HFB) and Bardeen-Cooper-Schrieffer (BCS) theories are compared. It is found that neutron pairing is reduced towards the drip line while overcast by strong shell effects. Furthermore, resonances in the continuum can have an important effect counterbalancing the tendency of reduction and leading to a persistence of pairing at the drip line. It is also shown that in these systems the difference between HFB and BCS approaches can be quantitatively large.

  13. Automatic Differentiation in Quantum Chemistry with Applications to Fully Variational Hartree-Fock.

    Science.gov (United States)

    Tamayo-Mendoza, Teresa; Kreisbeck, Christoph; Lindh, Roland; Aspuru-Guzik, Alán

    2018-05-23

    Automatic differentiation (AD) is a powerful tool that allows calculating derivatives of implemented algorithms with respect to all of their parameters up to machine precision, without the need to explicitly add any additional functions. Thus, AD has great potential in quantum chemistry, where gradients are omnipresent but also difficult to obtain, and researchers typically spend a considerable amount of time finding suitable analytical forms when implementing derivatives. Here, we demonstrate that AD can be used to compute gradients with respect to any parameter throughout a complete quantum chemistry method. We present DiffiQult , a Hartree-Fock implementation, entirely differentiated with the use of AD tools. DiffiQult is a software package written in plain Python with minimal deviation from standard code which illustrates the capability of AD to save human effort and time in implementations of exact gradients in quantum chemistry. We leverage the obtained gradients to optimize the parameters of one-particle basis sets in the context of the floating Gaussian framework.

  14. Similarity transformed equation of motion coupled-cluster theory based on an unrestricted Hartree-Fock reference for applications to high-spin open-shell systems.

    Science.gov (United States)

    Huntington, Lee M J; Krupička, Martin; Neese, Frank; Izsák, Róbert

    2017-11-07

    The similarity transformed equation of motion coupled-cluster approach is extended for applications to high-spin open-shell systems, within the unrestricted Hartree-Fock (UHF) formalism. An automatic active space selection scheme has also been implemented such that calculations can be performed in a black-box fashion. It is observed that both the canonical and automatic active space selecting similarity transformed equation of motion (STEOM) approaches perform about as well as the more expensive equation of motion coupled-cluster singles doubles (EOM-CCSD) method for the calculation of the excitation energies of doublet radicals. The automatic active space selecting UHF STEOM approach can therefore be employed as a viable, lower scaling alternative to UHF EOM-CCSD for the calculation of excited states in high-spin open-shell systems.

  15. Similarity transformed equation of motion coupled-cluster theory based on an unrestricted Hartree-Fock reference for applications to high-spin open-shell systems

    Science.gov (United States)

    Huntington, Lee M. J.; Krupička, Martin; Neese, Frank; Izsák, Róbert

    2017-11-01

    The similarity transformed equation of motion coupled-cluster approach is extended for applications to high-spin open-shell systems, within the unrestricted Hartree-Fock (UHF) formalism. An automatic active space selection scheme has also been implemented such that calculations can be performed in a black-box fashion. It is observed that both the canonical and automatic active space selecting similarity transformed equation of motion (STEOM) approaches perform about as well as the more expensive equation of motion coupled-cluster singles doubles (EOM-CCSD) method for the calculation of the excitation energies of doublet radicals. The automatic active space selecting UHF STEOM approach can therefore be employed as a viable, lower scaling alternative to UHF EOM-CCSD for the calculation of excited states in high-spin open-shell systems.

  16. Multi-configuration Dirac-Hartree-Fock (MCDHF) calculations for Ni XXV

    Science.gov (United States)

    Singh, Narendra; Aggarwal, Sunny

    2018-03-01

    We present accurate 165 fine-structure energy levels related to the configurations 1s22s2, 1s22p2, 1s2nƖn‧l‧ (n = 2, n‧ = 2, 3, 4, 5, Ɩ = s,p Ɩ‧ = s, p, d, f, g) of Ni XXV which may be useful ion for astrophysical and fusion plasma. For the calculations of energy levels and radiative rates, we have used the multiconfiguration Dirac-Hartree-Fock (MCDHF) method employed in GRASP2K code. The calculations are carried out in the active space approximation with the inclusion of the Breit interaction, the finite nuclear size effect, and quantum electrodynamic corrections. The transition wavelengths, transition probabilities, line strengths, and absorption oscillator strengths are reported for electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), magnetic quadrupole (M2) transitions from the ground state. We have compared our calculated results with available theoretical and experimental data and good agreement is achieved. We predict new energy levels, oscillator strengths, line strengths and transition probabilities, where no other experimental or theoretical results are available. The present complete set of results should be of great help in line identification and the interpretation of spectra, as well as in the modelling and diagnostics of astrophysical and fusion plasmas.

  17. Microscopic descriptions of the superdeformed bands in the region A 190: Bohr and Routhian Hamiltonians in the Hartree-Fock-Bogolyubov approximation

    International Nuclear Information System (INIS)

    Libert, J.; Girod, M.; Delaroche, J-P.; Berger, J-F.; Romain, P.; Peru, S.

    1997-01-01

    The superdeformed bands of the nuclei in the region A = 190 were described by two microscopic approaches using Gogny D1 finite range interaction. The first one consists in building a Bohr Hamiltonian in the framework of Gauss overlap approximation (GOA) of the generator-coordinate method, starting from Hartree-Fock-Bogolyubov solutions under quadrupole constraints. This collective Hamiltonian microscopically determined for five quadrupolar variables is then diagonalized by a projection method on a collective based adapted to the large variety of the deformations to be considered. A special attention was given to the precise definition of the under-barrier collective wavefunctions (for which an original method of solving the collective Schroedinger equation was developed) in order to described correctly the lifetime of the shape isomeric states. The other approach, that of Routhian is based also on the Hartree-Fock-Bogolyubov approximation. The calculations are carried out with and without restoring the broken symmetry associated to the particle numbers (as given by Lipkin-Nogami). The results (excitation energies, moments of inertia, etc...) of the two calculation methods are compared with most recent experimental data. The existence of the superdeformed bands corresponding to vibrational excitations similar to those appearing in β and γ bands is proposed

  18. Analysis of the half-projected Hartree--Fock function: density matrix, natural orbitals, and configuration interaction equivalence

    International Nuclear Information System (INIS)

    Smeyers, Y.G.; Delgado-Barrio, G.

    1976-01-01

    The half-projected Hartree--Fock function for singlet states (HPHF) is analyzed in terms of natural electronic configurations. For this purpose the HPHF spinless density matrix and its natural orbitals are first deduced. It is found that the HPHF function does not contain any contribution from odd-times excited configurations. It is seen in addition, in the case of the singlet ground states, this function is approximately equivalent to two closed-shell configurations, although the nature of the excited one depends on the nuclear geometry. An example is given in the case of the LiH ground state. Finally, the application of this model for studying systems of more than two atoms is criticized

  19. Oscillator strength of partially ionized high-Z atom on Hartree-Fock Slater model

    International Nuclear Information System (INIS)

    Nakamura, S.; Nishikawa, T.; Takabe, H.; Mima, K.

    1991-01-01

    The Hartree-Fock Slater (HFS) model has been solved for the partially ionized gold ions generated when an intense laser light is irradiated on a gold foil target. The resultant energy levels are compared with those obtained by a simple screened hydrogenic model with l-splitting effect (SHML). It is shown that the energy levels are poorly model by SHML as the ionization level becomes higher. The resultant wave functions are used to evaluate oscillator strength of important line radiations and compared with those obtained by a simple model using hydrogenic wave functions. Its demonstrated that oscillator strength of the 4p-4d and 4d-4f lines are well modeled by the simple method, while the 4-5 transitions such as 4f-5g, 4d-5f, 4p-5d, and 4f-5p forming the so-called N-band emission are poorly modeled and HFS results less strong line emissions. (author)

  20. Sixty years of broken symmetries in quantum physics (from the Bogoliubov theory of superfluidity to the Standard Model)

    International Nuclear Information System (INIS)

    Shirkov, Dmitrii V

    2009-01-01

    This is a retrospective historical review of the ideas that led to the concept of the spontaneous symmetry breaking (SSB), the issue that has been implemented in quantum field theory in the form of the Higgs mechanism. The key stages covered include: the Bogoliubov microscopic theory of superfluidity (1946); the Bardeen-Cooper-Schrieffer-Bogoliubov microscopic theory of superconductivity (1957); superconductivity as superfluidity of Cooper pairs (Bogoliubov, 1958); the extension of the SSB concept to simple quantum field models (early 1960s); triumph of the Higgs model in electroweak theory (early 1980s). The role and status of the Higgs mechanism in the current Standard Model are discussed. (oral issue of the journal 'uspekhi fizicheskikh nauk')

  1. Structure factors for tunneling ionization rates of molecules: General Hartree-Fock-based integral representation

    Science.gov (United States)

    Madsen, Lars Bojer; Jensen, Frank; Dnestryan, Andrey I.; Tolstikhin, Oleg I.

    2017-07-01

    In the leading-order approximation of the weak-field asymptotic theory (WFAT), the dependence of the tunneling ionization rate of a molecule in an electric field on its orientation with respect to the field is determined by the structure factor of the ionizing molecular orbital. The WFAT yields an expression for the structure factor in terms of a local property of the orbital in the asymptotic region. However, in general quantum chemistry approaches molecular orbitals are expanded in a Gaussian basis which does not reproduce their asymptotic behavior correctly. This hinders the application of the WFAT to polyatomic molecules, which are attracting increasing interest in strong-field physics. Recently, an integral-equation approach to the WFAT for tunneling ionization of one electron from an arbitrary potential has been developed. The structure factor is expressed in an integral form as a matrix element involving the ionizing orbital. The integral is not sensitive to the asymptotic behavior of the orbital, which resolves the difficulty mentioned above. Here, we extend the integral representation for the structure factor to many-electron systems treated within the Hartree-Fock method and show how it can be implemented on the basis of standard quantum chemistry software packages. We validate the methodology by considering noble-gas atoms and the CO molecule, for which accurate structure factors exist in the literature. We also present benchmark results for CO2 and for NH3 in the pyramidal and planar geometries.

  2. An HFB scheme in natural orbitals

    International Nuclear Information System (INIS)

    Reinhard, P.G.; Rutz, K.; Maruhn, J.A.

    1997-01-01

    We present a formulation of the Hartree-Fock-Bogoliubov (HFB) equations which solves the problem directly in the basis of natural orbitals. This provides a very efficient scheme which is particularly suited for large scale calculations on coordinate-space grids. (orig.)

  3. Linear response calculation using the canonical-basis TDHFB with a schematic pairing functional

    International Nuclear Information System (INIS)

    Ebata, Shuichiro; Nakatsukasa, Takashi; Yabana, Kazuhiro

    2011-01-01

    A canonical-basis formulation of the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory is obtained with an approximation that the pair potential is assumed to be diagonal in the time-dependent canonical basis. The canonical-basis formulation significantly reduces the computational cost. We apply the method to linear-response calculations for even-even nuclei. E1 strength distributions for proton-rich Mg isotopes are systematically calculated. The calculation suggests strong Landau damping of giant dipole resonance for drip-line nuclei.

  4. Influence of quadrupole pairing on backbending

    International Nuclear Information System (INIS)

    Faessler, A.; Wakai, M.

    1978-01-01

    The backbending phenomenon is attributed to the Coriolis antipairing and the rotational alignment effects. We can consider both effects simultaneously by applying the cranked Hartree-Fock-Bogoliubov theory to the description of the rotational motion of nuclei. In usual treatments of the backbending, however, only the monopole pairing force is considered and pairing forces of other types are neglected. This may be the main reason for starting of the backbending at too small total angular momentum in theoretical results. (orig.) [de

  5. Nuclear Pasta at Finite Temperature with the Time-Dependent Hartree-Fock Approach

    Science.gov (United States)

    Schuetrumpf, B.; Klatt, M. A.; Iida, K.; Maruhn, J. A.; Mecke, K.; Reinhard, P.-G.

    2016-01-01

    We present simulations of neutron-rich matter at sub-nuclear densities, like supernova matter. With the time-dependent Hartree-Fock approximation we can study the evolution of the system at temperatures of several MeV employing a full Skyrme interaction in a periodic three-dimensional grid [1]. The initial state consists of α particles randomly distributed in space that have a Maxwell-Boltzmann distribution in momentum space. Adding a neutron background initialized with Fermi distributed plane waves the calculations reflect a reasonable approximation of astrophysical matter. The matter evolves into spherical, rod-like, connected rod-like and slab-like shapes. Further we observe gyroid-like structures, discussed e.g. in [2], which are formed spontaneously choosing a certain value of the simulation box length. The ρ-T-map of pasta shapes is basically consistent with the phase diagrams obtained from QMD calculations [3]. By an improved topological analysis based on Minkowski functionals [4], all observed pasta shapes can be uniquely identified by only two valuations, namely the Euler characteristic and the integral mean curvature. In addition we propose the variance in the cell-density distribution as a measure to distinguish pasta matter from uniform matter.

  6. Nuclear Pasta at Finite Temperature with the Time-Dependent Hartree-Fock Approach

    International Nuclear Information System (INIS)

    Schuetrumpf, B; Maruhn, J A; Klatt, M A; Mecke, K; Reinhard, P-G; Iida, K

    2016-01-01

    We present simulations of neutron-rich matter at sub-nuclear densities, like supernova matter. With the time-dependent Hartree-Fock approximation we can study the evolution of the system at temperatures of several MeV employing a full Skyrme interaction in a periodic three-dimensional grid [1].The initial state consists of α particles randomly distributed in space that have a Maxwell-Boltzmann distribution in momentum space. Adding a neutron background initialized with Fermi distributed plane waves the calculations reflect a reasonable approximation of astrophysical matter.The matter evolves into spherical, rod-like, connected rod-like and slab-like shapes. Further we observe gyroid-like structures, discussed e.g. in [2], which are formed spontaneously choosing a certain value of the simulation box length. The ρ-T-map of pasta shapes is basically consistent with the phase diagrams obtained from QMD calculations [3]. By an improved topological analysis based on Minkowski functionals [4], all observed pasta shapes can be uniquely identified by only two valuations, namely the Euler characteristic and the integral mean curvature.In addition we propose the variance in the cell-density distribution as a measure to distinguish pasta matter from uniform matter. (paper)

  7. The contribution of Skyrme Hartree-Fock calculations to the understanding of the shell model

    International Nuclear Information System (INIS)

    Zamick, L.

    1984-01-01

    The authors present a detailed comparison of Skyrme Hartree-Fock and the shell model. The H-F calculations are sensitive to the parameters that are chosen. The H-F results justify the use of effective charges in restricted model space calculations by showing that the core contribution can be large. Further, the H-F results roughly justify the use of a constant E2 effective charge, but seem to yield nucleus dependent E4 effective charges. The H-F can yield results for E6 and higher multipoles, which would be zero in s-d model space calculations. On the other side of the coin in H-F the authors can easily consider only the lowest rotational band, whereas in the shell model one can calculate the energies and properties of many more states. In the comparison some apparent problems remain, in particular E4 transitions in the upper half of the s-d shell

  8. On minimal energy Hartree-Fock states for the 2DEG at fractional fillings

    International Nuclear Information System (INIS)

    Cabo Montes Oca, A. de.

    1995-08-01

    Approximate minimal energy solutions of the previously discussed general class of Hartree-Fock (HF) states of the 2DEG at 1/3 and 2/3 filling factors are determined. Their selfenergy spectrum is evaluated. Wannier states associated to the filled Bloch states are introduced in a lattice having three flux quanta per cell. They allow to rewrite approximately the ν = 1/3 HF Hamiltonian as sum of three independent tight-binding model Hamiltonians, one describing the dynamics in the band of occupied states and the other ones in the tow bands of excited states. The magnitude of the hopping integral indicates the enhanced role which should have the correlation energy in the present situation with respect to the case of the Yoshioka and Lee second order energy calculation for the lowest energy HF state. Finally, the discussion also suggests the Wannier function, which spreads an electron into a three quanta area, as a physical model for the composite fermion mean field one particle state. (author). 11 refs, 5 figs

  9. Pairing correlations. I. Description of odd nuclei in mean-field theories

    International Nuclear Information System (INIS)

    Duguet, T.; Bonche, P.; Heenen, P.-H.; Meyer, J.

    2002-01-01

    In order to extract informations on pairing correlations in nuclei from experimental masses, the different contributions to odd-even mass differences are investigated within the Skyrme Hartree-Fock-Bogoliubov (HFB) method. In this part of the paper, the description of odd nuclei within HFB is discussed since it is the key point for the understanding of the above mentioned contributions. To go from an even nucleus to an odd one, the advantage of a two steps process is demonstrated and its physical content is discussed. New results concerning time-reversal symmetry breaking in odd nuclei are also reported

  10. Dynamic and static correlation functions in the inhomogeneous Hartree-Fock-state approach with random-phase-approximation fluctuations

    International Nuclear Information System (INIS)

    Lorenzana, J.; Grynberg, M.D.; Yu, L.; Yonemitsu, K.; Bishop, A.R.

    1992-11-01

    The ground state energy, and static and dynamic correlation functions are investigated in the inhomogeneous Hartree-Fock (HF) plus random phase approximation (RPA) approach applied to a one-dimensional spinless fermion model showing self-trapped doping states at the mean field level. Results are compared with homogeneous HF and exact diagonalization. RPA fluctuations added to the generally inhomogeneous HF ground state allows the computation of dynamical correlation functions that compare well with exact diagonalization results. The RPA correction to the ground state energy agrees well with the exact results at strong and weak coupling limits. We also compare it with a related quasi-boson approach. The instability towards self-trapped behaviour is signaled by a RPA mode with frequency approaching zero. (author). 21 refs, 10 figs

  11. Investigation of the hyperfine properties of deoxy hemoglobin based on its electronic structure obtained by Hartree-Fock-Roothan procedure

    Energy Technology Data Exchange (ETDEWEB)

    Lata, K. Ramani [State University of New York at Albany, Department of Physics (United States); Sahoo, N. [University of Texas M.D. Anderson Cancer Center, Department of Radiation Physics (United States); Dubey, Archana [University of Central Florida, Department of Physics (United States); Scheicher, R. H. [Uppsala University, Condensed Matter Theory Group, Department of Physics and Materials Science (Sweden); Badu, S. R.; Pink, R. H.; Mahato, Dip N. [State University of New York at Albany, Department of Physics (United States); Schulte, A. F.; Saha, H. P. [University of Central Florida, Department of Physics (United States); Maharjan, N. B. [State University of New York at Albany, Department of Physics (United States); Chow, Lee [University of Central Florida, Department of Physics (United States); Das, T. P., E-mail: tpd56@albany.edu [State University of New York at Albany, Department of Physics (United States)

    2008-01-15

    The electronic structure of the heme unit of deoxyhemoglobin including the proximal imidazole has been studied using the first-principles Hartree-Fock procedure. Our results for the {sup 57m}Fe isomer shift and asymmetry parameter are in very good agreement with the values obtained from Moessbauer spectroscopy measurements. The {sup 57m}Fe nuclear quadrupole coupling constant is smaller than the experimental result and possible ways to improve the agreement in the future are discussed. Improved analysis of the Moessbauer data, removing some approximations made for deriving the magnetic hyperfine tensor for the {sup 57m}Fe nucleus, is suggested to allow quantitative comparison with our results in the future.

  12. Bogoliubov transformations and fermion condensates in lattice field theories

    International Nuclear Information System (INIS)

    Caracciolo, Sergio; Palumbo, Fabrizio; Viola, Giovanni

    2009-01-01

    We apply generalized Bogoliubov transformations to the transfer matrix of relativistic field theories regularized on a lattice. We derive the conditions these transformations must satisfy to factorize the transfer matrix into two terms which propagate fermions and antifermions separately, and we solve the relative equations under some conditions. We relate these equations to the saddle point approximation of a recent bosonization method and to the Foldy-Wouthuysen transformations which separate positive from negative energy states in the Dirac Hamiltonian

  13. Single determinantal reaction theory as a Schroedinger analog: the time-dependent S-matrix Hartree-Fock method

    International Nuclear Information System (INIS)

    Griffin, J.J.; Lichtner, P.C.; Dworzecka, M.; Kan, K.K.

    1979-01-01

    It is suggested that the TDHF method be viewed, not as an approximation to but as a model of the exact Schroedinger system; that is, as a gedanken many-body experiment whose analysis with digital computers provides data worthy in itself of theoretical study. From such a viewpoint attention is focused on the structural analogies of the TDHF system with the exact theory rather than upon its quantitative equivalence, and the TDHF many-body system is studied as a challenge of its own which, although much simpler than the realistic problem, may still offer complexity enough to educate theorists in the present state of knowledge. In this spirit, the TDHF description of continuum reactions can be restructured from an initial-value problem into a form analogous to the S-matrix version of the Schroedinger theory. The resulting TD-S-HF theory involves only self-consistent single determinantal solutions of the TDHF equations and invokes time averaging to obtain a consistent interpretation of the TDHF analogs of quantities which are constant in the exact theory, such as the S-matrix and the asymptotic reaction channel characteristics. Periodic solutions then play the role of stationary eigenstates in the construction of suitable asymptotic reaction channels. If these periodic channel states occur only at discrete energies, then the resulting channels are mutually orthogonal (on the time average) and the theory exhibits a structure fully analogous to the exact theory. In certain special cases where the periodic solutions are known to occur as an energy continuum, the requirement that the periodicity of the channel solutions be gauge invariant provides a natural requantization condition which (suggestively) turns out to be identical with the Bohr-Sommerfeld quantization rule. 11 references

  14. Spiral magnetism in the single-band Hubbard model: the Hartree-Fock and slave-boson approaches.

    Science.gov (United States)

    Igoshev, P A; Timirgazin, M A; Gilmutdinov, V F; Arzhnikov, A K; Irkhin, V Yu

    2015-11-11

    The ground-state magnetic phase diagram is investigated within the single-band Hubbard model for square and different cubic lattices. The results of employing the generalized non-correlated mean-field (Hartree-Fock) approximation and generalized slave-boson approach by Kotliar and Ruckenstein with correlation effects included are compared. We take into account commensurate ferromagnetic, antiferromagnetic, and incommensurate (spiral) magnetic phases, as well as phase separation into magnetic phases of different types, which was often lacking in previous investigations. It is found that the spiral states and especially ferromagnetism are generally strongly suppressed up to non-realistically large Hubbard U by the correlation effects if nesting is absent and van Hove singularities are well away from the paramagnetic phase Fermi level. The magnetic phase separation plays an important role in the formation of magnetic states, the corresponding phase regions being especially wide in the vicinity of half-filling. The details of non-collinear and collinear magnetic ordering for different cubic lattices are discussed.

  15. Microscopic theory of light exotic nuclei. Shell Models Embedded in the Continuum

    International Nuclear Information System (INIS)

    Bennaceur, K.

    1999-01-01

    The recent advances in experimental nuclear physics make it possible to study nuclear systems far from the beta stability line. The discovery of new phenomena, like halos or neutron skins, requires the development of new theoretical models which enable to study these systems. The first part of this work is devoted to the development and the applications of the Shell Model Embedded in the Continuum (SMEC). This new formalism allows to take into account the correlations between the bound and scattering states of loosely bound nuclei. SMEC is applied here to the study of the spectroscopy of the Mirror nuclei 8 B- 8 Li and 17 F- 17 O. It can also be used to calculate the cross sections of the elastic scattering, the Coulomb breakup processes and the radiative n,p capture processes. The results concerning the reactions of astrophysical interest: 18 O(p, γ) 17 F and 7 Be(p, γ) 8 B, are discussed in details. This last reaction is very important because the disintegration of 8 B is the main source of High energy neutrinos in the sun. The second part of this work is related to the analysis of pairing interaction for weakly bound nuclei. We have developed a new approach, based on the Hartree-Fock-Bogolyubov (HFB) theory, that allows to study the pairing correlations between bound and scattering states, both resonant and not resonant ones. The 'particle-hole' potential is replaced by a model potential for which the solutions are analytically known. This method allows to analyse the effect of pairing on bound and resonant states, independently of their energy position. We have clearly demonstrated that the non-resonant continuum plays a crucial role in the loosely bound nuclei and that solving the HFB equations in the coordinate space is the only method that permits to treat this problem correctly. (author)

  16. Bose-Einstein condensates in atomic gases: simple theoretical results

    International Nuclear Information System (INIS)

    Castin, Y.

    2001-01-01

    The author presents the theory of the Bose-Einstein condensation along with a discussion of experimental tests. The author deals successively with the following topics: - the ideal Bose gas in a trap (first in a harmonic trap and then in a more general trap), - a model for the atomic interaction, - interacting Bose gas in the Hartree-Fock approximation, - properties of the condensate wavefunction, - the Gross-Pitaevskii equation, - Bogoliubov approach and thermodynamical stability, - phase coherence properties at the Bose-Einstein condensate, and - symmetry-breaking description of condensates. (A.C.)

  17. Application of the RPA method based on the cranked Hartree-Fock-Bogolyubov model in 168Er and 158Dy

    International Nuclear Information System (INIS)

    Kvasil, J.; Khariev, M.M.; Cwiok, S.; Mikhajlov, I.N.; Khoriev, B.

    1984-01-01

    The Random Phase Approximation (RPA) based on the Cranked Hartree-Fock-Bogolyubov (CHFB) model is used for the study of low-lying nuclear states near the yrast line in 158 Dy and 168 Er. The relation of the spurious unphysical states connected with the nucleus centre of mass rotational motion to the solutions of RPA equations of motion is cleared up. The calculated level energies and reduced probabilities B(E2) are compared with experimental ones. The dependence of the residual interaction strength constants and the nucleus moment of inertia on the angular momentum is discussed. The experimental characteristics of low-lying states up to approx. 2 MeV are reproduced by the CHFB+RPA model. (author)

  18. Relation between generalized Bogoliubov and Bogoliubov-de Gennes approaches including Nambu-Goldstone mode

    International Nuclear Information System (INIS)

    Mine, M.; Okumura, M.; Yamanaka, Y.

    2005-01-01

    The two approaches of consistent quantum field theory for systems of the trapped Bose-Einstein condensates are known, one is the Bogoliubov-de Gennes approach and the other is the generalized Bogoliubov approach. In this paper, we investigate the relation between the two approaches and show that they are formally equivalent to each other. To do this one must carefully treat the Nambu-Goldstone mode which plays a crucial role in the condensation. It is emphasized that the choice of vacuum is physically relevant

  19. Combining density functional and incremental post-Hartree-Fock approaches for van der Waals dominated adsorbate-surface interactions: Ag2/graphene

    International Nuclear Information System (INIS)

    Lara-Castells, María Pilar de; Mitrushchenkov, Alexander O.; Stoll, Hermann

    2015-01-01

    A combined density functional (DFT) and incremental post-Hartree-Fock (post-HF) approach, proven earlier to calculate He-surface potential energy surfaces [de Lara-Castells et al., J. Chem. Phys. 141, 151102 (2014)], is applied to describe the van der Waals dominated Ag 2 /graphene interaction. It extends the dispersionless density functional theory developed by Pernal et al. [Phys. Rev. Lett. 103, 263201 (2009)] by including periodic boundary conditions while the dispersion is parametrized via the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)]. Starting with the elementary cluster unit of the target surface (benzene), continuing through the realistic cluster model (coronene), and ending with the periodic model of the extended system, modern ab initio methodologies for intermolecular interactions as well as state-of-the-art van der Waals-corrected density functional-based approaches are put together both to assess the accuracy of the composite scheme and to better characterize the Ag 2 /graphene interaction. The present work illustrates how the combination of DFT and post-HF perspectives may be efficient to design simple and reliable ab initio-based schemes in extended systems for surface science applications

  20. Microscopic theories for collective motions of large amplitude

    International Nuclear Information System (INIS)

    Souza Cruz, F.F. de.

    1986-01-01

    The many proposals of ''Collective Paths'' that have appeared in literature, were derived through a local analysis of the Time Dependent Hartree Fock dynamics. Those proposals were compared and validity conditions obtained for Semiclassical Hamiltonians which have only quadratic terms in momenta. A careful analysis of the parametrization of Slater Determinants allowed us to exploit the geometrical features of the Time Dependent Hartree Fock Theory and construct the Paths in a covariant way. The analysis was applied to a three level model (Su(3)). (author) [pt

  1. Nucleon and isobar properties in a relativistic Hartree-Fock calculation with vector Richardson potential and various radial forms for scalar mass terms

    International Nuclear Information System (INIS)

    Dey, J.; Dey, M.; Mukhopadhyay, G.; Samanta, B.C.

    1989-01-01

    Mean field models of the nucleon and the delta are established with the two-quark vector Richardson potential along with various prescriptions for a running quark mass. This is taken to be a one-particle operator in the Dirac-Hartree Fock formalism. An effective density dependent one body potential U(ρ) for quarks at a given density ρ inside the nucleon is derived. It shows an interesting structure. Asymptotic freedom and confinement properties are built-in at high and low densities in U (ρ) and the model dependence is restricted to the intermediate desnsities. (author) [pt

  2. Hartree-Fock study of the Anderson metal-insulator transition in the presence of Coulomb interaction: Two types of mobility edges and their multifractal scaling exponents

    Science.gov (United States)

    Lee, Hyun-Jung; Kim, Ki-Seok

    2018-04-01

    We investigate the role of Coulomb interaction in the multifractality of Anderson metal-insulator transition, where the Coulomb interaction is treated within the Hartree-Fock approximation, but disorder effects are taken into account exactly. An innovative technical aspect in our simulation is to utilize the Ewald-sum technique, which allows us to introduce the long-range nature of the Coulomb interaction into Hartree-Fock self-consistent equations of order parameters more accurately. This numerical simulation reproduces the Altshuler-Aronov correction in a metallic state and the Efros-Shklovskii pseudogap in an insulating phase, where the density of states ρ (ω ) is evaluated in three dimensions. Approaching the quantum critical point of a metal-insulator transition from either the metallic or insulting phase, we find that the density of states is given by ρ (ω ) ˜|ω| 1 /2 , which determines one critical exponent of the McMillan-Shklovskii scaling theory. Our main result is to evaluate the eigenfunction multifractal scaling exponent αq, given by the Legendre transformation of the fractal dimension τq, which characterizes the scaling behavior of the inverse participation ratio with respect to the system size L . Our multifractal analysis leads us to identify two kinds of mobility edges, one of which occurs near the Fermi energy and the other of which appears at a high energy, where the density of states at the Fermi energy shows the Coulomb-gap feature. We observe that the multifractal exponent at the high-energy mobility edge remains to be almost identical to that of the Anderson localization transition in the absence of Coulomb interactions. On the other hand, we find that the multifractal exponent near the Fermi energy is more enhanced than that at the high-energy mobility edge, suspected to result from interaction effects. However, both the multifractal exponents do not change even if the strength of the Coulomb interaction varies. We also show that the

  3. A comprehensive analysis of molecule-intrinsic quasi-atomic, bonding, and correlating orbitals. I. Hartree-Fock wave functions

    International Nuclear Information System (INIS)

    West, Aaron C.; Schmidt, Michael W.; Gordon, Mark S.; Ruedenberg, Klaus

    2013-01-01

    Through a basis-set-independent web of localizing orbital-transformations, the electronic wave function of a molecule is expressed in terms of a set of orbitals that reveal the atomic structure and the bonding pattern of a molecule. The analysis is based on resolving the valence orbital space in terms of an internal space, which has minimal basis set dimensions, and an external space. In the internal space, oriented quasi-atomic orbitals and split-localized molecular orbitals are determined by new, fast localization methods. The density matrix between the oriented quasi-atomic orbitals as well as the locations of the split-localized orbitals exhibit atomic populations and inter-atomic bonding patterns. A correlation-adapted quasi-atomic basis is determined in the external orbital space. The general formulations are specified in detail for Hartree-Fock wave functions. Applications to specific molecules exemplify the general scheme

  4. Combining density functional and incremental post-Hartree-Fock approaches for van der Waals dominated adsorbate-surface interactions: Ag{sub 2}/graphene

    Energy Technology Data Exchange (ETDEWEB)

    Lara-Castells, María Pilar de, E-mail: Pilar.deLara.Castells@csic.es [Instituto de Física Fundamental (C.S.I.C.), Serrano 123, E-28006 Madrid (Spain); Mitrushchenkov, Alexander O. [Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallée (France); Stoll, Hermann [Institut für Theoretische Chemie, Universität Stuttgart, D-70550 Stuttgart (Germany)

    2015-09-14

    A combined density functional (DFT) and incremental post-Hartree-Fock (post-HF) approach, proven earlier to calculate He-surface potential energy surfaces [de Lara-Castells et al., J. Chem. Phys. 141, 151102 (2014)], is applied to describe the van der Waals dominated Ag{sub 2}/graphene interaction. It extends the dispersionless density functional theory developed by Pernal et al. [Phys. Rev. Lett. 103, 263201 (2009)] by including periodic boundary conditions while the dispersion is parametrized via the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)]. Starting with the elementary cluster unit of the target surface (benzene), continuing through the realistic cluster model (coronene), and ending with the periodic model of the extended system, modern ab initio methodologies for intermolecular interactions as well as state-of-the-art van der Waals-corrected density functional-based approaches are put together both to assess the accuracy of the composite scheme and to better characterize the Ag{sub 2}/graphene interaction. The present work illustrates how the combination of DFT and post-HF perspectives may be efficient to design simple and reliable ab initio-based schemes in extended systems for surface science applications.

  5. A constrained approximation for nuclear barrier penetration and fission

    International Nuclear Information System (INIS)

    Tang, H.H.K.; Negele, J.W.; Massachusetts Inst. of Tech., Cambridge; Massachusetts Inst. of Tech., Cambridge

    1983-01-01

    An approximation to the time-dependent mean-field theory for barrier penetration by a nucleus is obtained in terms of constrained Hartree-Fock wave functions and a coherent velocity field. A discrete approximation to the continuum theory suitable for practical numerical calculations is presented and applied to three illustrative models. Potential application of the theory to the study of nuclear fission is discussed. (orig.)

  6. Nonlinear many-body reaction theories from nuclear mean field approximations

    International Nuclear Information System (INIS)

    Griffin, J.J.

    1983-01-01

    Several methods of utilizing nonlinear mean field propagation in time to describe nuclear reaction have been studied. The property of physical asymptoticity is analyzed in this paper, which guarantees that the prediction by a reaction theory for the physical measurement of internal fragment properties shall not depend upon the precise location of the measuring apparatus. The physical asymptoticity is guaranteed in the Schroedinger collision theory of a scuttering system with translationally invariant interaction by the constancy of the S-matrix elements and by the translational invariance of the internal motion for well-separated fragments. Both conditions are necessary for the physical asymptoticity. The channel asymptotic single-determinantal propagation can be described by the Dirac-TDHF (time dependent Hartree-Fock) time evolution. A new asymptotic Hartree-Fock stationary phase (AHFSP) description together with the S-matrix time-dependent Hartree-Fock (TD-S-HF) theory constitute the second example of a physically asymptotic nonlinear many-body reaction theory. A review of nonlinear mean field many-body reaction theories shows that initial value TDHF is non-asymptotic. The TD-S-HF theory is asymptotic by the construction. The gauge invariant periodic quantized solution of the exact Schroedinger problem has been considered to test whether it includes all of the exact eigenfunctions as it ought to. It did, but included as well an infinity of all spurions solutions. (Kato, T.)

  7. Gogny interactions with tensor terms

    Energy Technology Data Exchange (ETDEWEB)

    Anguiano, M.; Lallena, A.M.; Bernard, R.N. [Universidad de Granada, Departamento de Fisica Atomica, Molecular y Nuclear, Granada (Spain); Co' , G. [INFN, Lecce (Italy); De Donno, V. [Universita del Salento, Dipartimento di Matematica e Fisica ' ' E. De Giorgi' ' , Lecce (Italy); Grasso, M. [Universite Paris-Sud, Institut de Physique Nucleaire, IN2P3-CNRS, Orsay (France)

    2016-07-15

    We present a perturbative approach to include tensor terms in the Gogny interaction. We do not change the values of the usual parameterisations, with the only exception of the spin-orbit term, and we add tensor terms whose only free parameters are the strengths of the interactions. We identify observables sensitive to the presence of the tensor force in Hartree-Fock, Hartree-Fock-Bogoliubov and random phase approximation calculations. We show the need of including two tensor contributions, at least: a pure tensor term and a tensor-isospin term. We show results relevant for the inclusion of the tensor term for single-particle energies, charge-conserving magnetic excitations and Gamow-Teller excitations. (orig.)

  8. Transferability and accuracy by combining dispersionless density functional and incremental post-Hartree-Fock theories: Noble gases adsorption on coronene/graphene/graphite surfaces

    Energy Technology Data Exchange (ETDEWEB)

    Lara-Castells, María Pilar de, E-mail: Pilar.deLara.Castells@csic.es; Bartolomei, Massimiliano [Instituto de Física Fundamental (C.S.I.C.), Serrano 123, E-28006 Madrid (Spain); Mitrushchenkov, Alexander O. [Laboratoire Modélisation et Simulation Multi Echelle, Université Paris-Est, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallée (France); Stoll, Hermann [Institut für Theoretische Chemie, Universität Stuttgart, D-70550 Stuttgart (Germany)

    2015-11-21

    The accuracy and transferability of the electronic structure approach combining dispersionless density functional theory (DFT) [K. Pernal et al., Phys. Rev. Lett. 103, 263201 (2009)] with the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)], are validated for the interaction between the noble-gas Ne, Ar, Kr, and Xe atoms and coronene/graphene/graphite surfaces. This approach uses the method of increments for surface cluster models to extract intermonomer dispersion-like (2- and 3-body) correlation terms at coupled cluster singles and doubles and perturbative triples level, while periodic dispersionless density functionals calculations are performed to estimate the sum of Hartree-Fock and intramonomer correlation contributions. Dispersion energy contributions are also obtained using DFT-based symmetry-adapted perturbation theory [SAPT(DFT)]. An analysis of the structure of the X/surface (X = Ne, Ar, Kr, and Xe) interaction energies shows the excellent transferability properties of the leading intermonomer correlation contributions across the sequence of noble-gas atoms, which are also discussed using the Drude oscillator model. We further compare these results with van der Waals-(vdW)-corrected DFT-based approaches. As a test of accuracy, the energies of the low-lying nuclear bound states supported by the laterally averaged X/graphite potentials (X = {sup 3}He, {sup 4}He, Ne, Ar, Kr, and Xe) are calculated and compared with the best estimations from experimental measurements and an atom-bond potential model using the ab initio-assisted fine-tuning of semiempirical parameters. The bound-state energies determined differ by less than 6–7 meV (6%) from the atom-bond potential model. The crucial importance of including incremental 3-body dispersion-type terms is clearly demonstrated, showing that the SAPT(DFT) approach effectively account for these terms. With the deviations from the best experimental-based estimations smaller than 2.3 meV (1.9%), the

  9. 2nd derivatives of the electronic energy in density functional theory

    Energy Technology Data Exchange (ETDEWEB)

    Dam, H. van

    2001-08-01

    This document details the equations needed to implement the calculation of vibrational frequencies within the density functional formalism of electronic structure theory. This functionality has been incorporated into the CCP1 DFT module and the required changes to the application programmers interface are outlined. Throughout it is assumed that an implementation of Hartree-Fock vibrational frequencies is available that can be modified to incorporate the density functional formalism. Employing GAMESS-UK as an example the required changes to the Hartree-Fock code are outlined. (author)

  10. Microscopic descriptions of the superdeformed bands in the region A 190: Bohr and Routhian Hamiltonians in the Hartree-Fock-Bogolyubov approximation; Descriptions microscopiques des bandes superdeformees dans la region A 190: Hamiltonien de Bohr et Routhian a l`approximation de Hartee-Fock-Bogolyubov

    Energy Technology Data Exchange (ETDEWEB)

    Libert, J. [Centre d`Etudes Nucleaires, Bordeaux-1 Univ., 33 Gradignan (France); Girod, M.; Delaroche, J-P.; Berger, J-F.; Romain, P.; Peru, S. [CEA Centre d`Etudes de Bruyeres-le-Chatel, 91 (France)

    1997-06-01

    The superdeformed bands of the nuclei in the region A = 190 were described by two microscopic approaches using Gogny D1 finite range interaction. The first one consists in building a Bohr Hamiltonian in the framework of Gauss overlap approximation (GOA) of the generator-coordinate method, starting from Hartree-Fock-Bogolyubov solutions under quadrupole constraints. This collective Hamiltonian microscopically determined for five quadrupolar variables is then diagonalized by a projection method on a collective based adapted to the large variety of the deformations to be considered. A special attention was given to the precise definition of the under-barrier collective wavefunctions (for which an original method of solving the collective Schroedinger equation was developed) in order to described correctly the lifetime of the shape isomeric states. The other approach, that of Routhian is based also on the Hartree-Fock-Bogolyubov approximation. The calculations are carried out with and without restoring the broken symmetry associated to the particle numbers (as given by Lipkin-Nogami). The results (excitation energies, moments of inertia, etc...) of the two calculation methods are compared with most recent experimental data. The existence of the superdeformed bands corresponding to vibrational excitations similar to those appearing in {beta} and {gamma} bands is proposed

  11. Quantum treatment of protons with the reduced explicitly correlated Hartree-Fock approach

    Energy Technology Data Exchange (ETDEWEB)

    Sirjoosingh, Andrew; Pak, Michael V.; Brorsen, Kurt R.; Hammes-Schiffer, Sharon, E-mail: shs3@illinois.edu [Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Ave., Urbana, Illinois 61801 (United States)

    2015-06-07

    The nuclear-electronic orbital (NEO) approach treats select nuclei quantum mechanically on the same level as the electrons and includes nonadiabatic effects between the electrons and the quantum nuclei. The practical implementation of this approach is challenging due to the significance of electron-nucleus dynamical correlation. Herein, we present a general extension of the previously developed reduced NEO explicitly correlated Hartree-Fock (RXCHF) approach, in which only select electronic orbitals are explicitly correlated to each quantum nuclear orbital via Gaussian-type geminal functions. Approximations of the electronic exchange between the geminal-coupled electronic orbitals and the other electronic orbitals are also explored. This general approach enables computationally tractable yet accurate calculations on molecular systems with quantum protons. The RXCHF method is applied to the hydrogen cyanide (HCN) and FHF{sup −} systems, where the proton and all electrons are treated quantum mechanically. For the HCN system, only the two electronic orbitals associated with the CH covalent bond are geminal-coupled to the proton orbital. For the FHF{sup −} system, only the four electronic orbitals associated with the two FH covalent bonds are geminal-coupled to the proton orbital. For both systems, the RXCHF method produces qualitatively accurate nuclear densities, in contrast to mean field-based NEO approaches. The development and implementation of the RXCHF method provide the framework to perform calculations on systems such as proton-coupled electron transfer reactions, where electron-proton nonadiabatic effects are important.

  12. The relation between the Gross-Pitaevskii and Bogoliubov descriptions of a dilute Bose gas

    International Nuclear Information System (INIS)

    Leggett, A J

    2003-01-01

    I formulate a 'pseudo-paradox' in the theory of a dilute Bose gas with repulsive interactions: the standard expression for the ground state energy within the Gross-Pitaevskii (GP) approximation is lower than that in the Bogoliubov approximation, and hence, by the standard variational argument, the former should prima facie be a better approximation than the latter to the true ground state - a conclusion which is of course opposite to the established wisdom concerning this problem. It is shown that the pseudo-paradox is (unsurprisingly) resolved by a correct transcription of the two-body scattering theory to the many-body case; however, contrary to what appears to be a widespread belief, the resolution has nothing to do with any spurious ultraviolet divergences which result from the replacement of the true interatomic potential by a delta-function pseudopotential. Rather, it relates to an infrared divergence which has the consequence that (a) the most obvious form of the GP 'approximation' actually does not correspond to any well-defined ansatz for the many-body wavefunction, and (b) that the 'best shot' at such a wavefunction always produces an energy which exceeds, or at best equals, that calculated in the Bogoliubov approximation. In fact, the necessity of the latter may be seen as a consequence of the need to reduce the Fock term in the energy, which is absent in the two-particle problem but dominant in the many-body case; it does this by increasing the density correlations, at distances less than or approximately equal to the correlation length ξ, above the value extrapolated from the two-body case. As a by-product I devise an alternative formulation of the Bogoliubov approximation which does not require the explicit replacement of the true interatomic potential by a delta-function pseudopotential

  13. The relation between the Gross-Pitaevskii and Bogoliubov descriptions of a dilute Bose gas

    Energy Technology Data Exchange (ETDEWEB)

    Leggett, A J [Department of Physics, University of Illinois at Urbana-Champaign, IL 61801-3080 (United States)

    2003-07-01

    I formulate a 'pseudo-paradox' in the theory of a dilute Bose gas with repulsive interactions: the standard expression for the ground state energy within the Gross-Pitaevskii (GP) approximation is lower than that in the Bogoliubov approximation, and hence, by the standard variational argument, the former should prima facie be a better approximation than the latter to the true ground state - a conclusion which is of course opposite to the established wisdom concerning this problem. It is shown that the pseudo-paradox is (unsurprisingly) resolved by a correct transcription of the two-body scattering theory to the many-body case; however, contrary to what appears to be a widespread belief, the resolution has nothing to do with any spurious ultraviolet divergences which result from the replacement of the true interatomic potential by a delta-function pseudopotential. Rather, it relates to an infrared divergence which has the consequence that (a) the most obvious form of the GP 'approximation' actually does not correspond to any well-defined ansatz for the many-body wavefunction, and (b) that the 'best shot' at such a wavefunction always produces an energy which exceeds, or at best equals, that calculated in the Bogoliubov approximation. In fact, the necessity of the latter may be seen as a consequence of the need to reduce the Fock term in the energy, which is absent in the two-particle problem but dominant in the many-body case; it does this by increasing the density correlations, at distances less than or approximately equal to the correlation length {xi}, above the value extrapolated from the two-body case. As a by-product I devise an alternative formulation of the Bogoliubov approximation which does not require the explicit replacement of the true interatomic potential by a delta-function pseudopotential.

  14. Ground state phase diagram of extended attractive Hubbard model

    International Nuclear Information System (INIS)

    Robaszkiewicz, S.; Chao, K.A.; Micnas, R.

    1980-08-01

    The ground state phase diagram of the extended Hubbard model with intraatomic attraction has been derived in the Hartree-Fock approximation formulated in terms of the Bogoliubov variational approach. For a given value of electron density, the nature of the ordered ground state depends essentially on the sign and the strength of the nearest neighbor coupling. (author)

  15. The emission of heavy clusters described in the mean-field HFB theory: the case of 242Cm

    International Nuclear Information System (INIS)

    Robledo, L.M.; Warda, M.

    2008-01-01

    The emission of a nucleus of 34 Si by the parent 96 242 Cm is a process in the diffuse borderline between cluster emission and standard mass asymmetric fission. In this paper we analyze in a microscopic framework such process using the standard mean field techniques used to describe cluster emission. They include Hartree-Fock-Bogoliubov constrained calculations with the Gogny D1S interaction and the octupole moment operator as the collective coordinate to describe the process. Collective masses and all kind of zero point energy corrections are considered which allows for a parameter free estimation of the process' half-life. The agreement with experiment is quite satisfactory. (author)

  16. Charge transfer excitations from excited state Hartree-Fock subsequent minimization scheme

    International Nuclear Information System (INIS)

    Theophilou, Iris; Tassi, M.; Thanos, S.

    2014-01-01

    Photoinduced charge-transfer processes play a key role for novel photovoltaic phenomena and devices. Thus, the development of ab initio methods that allow for an accurate and computationally inexpensive treatment of charge-transfer excitations is a topic that nowadays attracts a lot of scientific attention. In this paper we extend an approach recently introduced for the description of single and double excitations [M. Tassi, I. Theophilou, and S. Thanos, Int. J. Quantum Chem. 113, 690 (2013); M. Tassi, I. Theophilou, and S. Thanos, J. Chem. Phys. 138, 124107 (2013)] to allow for the description of intermolecular charge-transfer excitations. We describe an excitation where an electron is transferred from a donor system to an acceptor one, keeping the excited state orthogonal to the ground state and avoiding variational collapse. These conditions are achieved by decomposing the space spanned by the Hartree-Fock (HF) ground state orbitals into four subspaces: The subspace spanned by the occupied orbitals that are localized in the region of the donor molecule, the corresponding for the acceptor ones and two more subspaces containing the virtual orbitals that are localized in the neighborhood of the donor and the acceptor, respectively. Next, we create a Slater determinant with a hole in the subspace of occupied orbitals of the donor and a particle in the virtual subspace of the acceptor. Subsequently we optimize both the hole and the particle by minimizing the HF energy functional in the corresponding subspaces. Finally, we test our approach by calculating the lowest charge-transfer excitation energies for a set of tetracyanoethylene-hydrocarbon complexes that have been used earlier as a test set for such kind of excitations

  17. Quantum scattering theory of a single-photon Fock state in three-dimensional spaces.

    Science.gov (United States)

    Liu, Jingfeng; Zhou, Ming; Yu, Zongfu

    2016-09-15

    A quantum scattering theory is developed for Fock states scattered by two-level systems in three-dimensional free space. It is built upon the one-dimensional scattering theory developed in waveguide quantum electrodynamics. The theory fully quantizes the incident light as Fock states and uses a non-perturbative method to calculate the scattering matrix.

  18. Projected coupled cluster theory.

    Science.gov (United States)

    Qiu, Yiheng; Henderson, Thomas M; Zhao, Jinmo; Scuseria, Gustavo E

    2017-08-14

    Coupled cluster theory is the method of choice for weakly correlated systems. But in the strongly correlated regime, it faces a symmetry dilemma, where it either completely fails to describe the system or has to artificially break certain symmetries. On the other hand, projected Hartree-Fock theory captures the essential physics of many kinds of strong correlations via symmetry breaking and restoration. In this work, we combine and try to retain the merits of these two methods by applying symmetry projection to broken symmetry coupled cluster wave functions. The non-orthogonal nature of states resulting from the application of symmetry projection operators furnishes particle-hole excitations to all orders, thus creating an obstacle for the exact evaluation of overlaps. Here we provide a solution via a disentanglement framework theory that can be approximated rigorously and systematically. Results of projected coupled cluster theory are presented for molecules and the Hubbard model, showing that spin projection significantly improves unrestricted coupled cluster theory while restoring good quantum numbers. The energy of projected coupled cluster theory reduces to the unprojected one in the thermodynamic limit, albeit at a much slower rate than projected Hartree-Fock.

  19. Instability of the cranked Hartree-Fock-Bogoliubov field in backbending region

    International Nuclear Information System (INIS)

    Horibata, Takatoshi; Onishi, Naoki.

    1981-07-01

    The stability condition of the cranked HFB field is examined explicitly by solving the eigen value equation for the second order variation of the energy, which is reduced to an algebraic equation through a coupled dispersion formula. We confirm that the HFB field is unstable in the backbending region of irregular rotational band, even though the frequency of the softest RPA mode stays in positive value. We investigate properties of the softest mode in detail. (author)

  20. Study of superdeformation at zero spin with Skyrme-Hartree-Fock method

    Energy Technology Data Exchange (ETDEWEB)

    Takahara, S; Tajima, N; Onishi, N [Tokyo Univ. (Japan)

    1998-03-01

    Superdeformed (SD) bands have been studied extensively both experimentally and theoretically in the last decade. Since the first observation in {sup 152}Dy in 1986, SD bands have been found in four mass regions, i.e., A {approx} 80, 130, 150 and 190. While these SD bands have been observed only at high spins so far, they may also be present at zero spin like fission isomers in actinide nuclei: The familiar generic argument on the strong shell effect at axis ratio 2:1 does not assume rotations. If non-fissile SD isomers exist at zero spin, they may be utilized to develop new experimental methods to study exotic states, in a similar manner as short-lived high-spin isomers are planned to be utilized as projectiles of fusion reactions in order to populate very high-spin near-yrast states. They will also be useful to test theoretical models whether the models can describe correctly the large deformations of rare-earth nuclei without further complications due to rotations. In this report, we employ the Skyrme-Hartree-Fock method to study the SD states at zero spin. First, we compare various Skyrme force parameter sets to test whether they can reproduce the extrapolated excitation energy of the SD band head of {sup 194}Hg. Second, we systematically search large-deformation solutions with the SkM{sup *} force. The feature of our calculations is that the single-particle wavefunctions are expressed in a three-dimensional-Cartesian-mesh representation. This representation enables one to obtain solutions of various shapes (including SD) without preparing a basis specific to each shape. Solving the mean-field equations in this representation requires, however, a large amount of computation which can be accomplished only with present supercomputers. (author)

  1. Semiclassical approximations in a mean-field theory with collision terms

    International Nuclear Information System (INIS)

    Galetti, D.

    1986-01-01

    Semiclassical approximations in a mean-field theory with collision terms are discussed taking the time dependent Hartree-Fock method as framework in the obtainment of the relevant parameters.(L.C.) [pt

  2. The soliton solution of the PHI24 field theory in the Hartree approximation

    International Nuclear Information System (INIS)

    Altenbokum, M.

    1984-01-01

    In this thesis in a simple model which possesses at the classical level a soliton solution a quantum-mechanical soliton sector shall be constructed in a Hartree-Fock approximation without application of semiclassical procedures. To this belongs beside the determination of the excitation spectrum of the applied Hamiltonian the knowledge of the corresponding infinitely-much eigenfunctions. The existing translational invariance of a classical soliton solution which implies the existence of a degenerated ground state by presence of a massless excitation is removed by quantum fluctuations. By removing of this degeneration conventional approximation procedures for this sector of the Hilbert space become for the first time immediately possible. (HSI) [de

  3. Transition mechanism of nuclear phase

    International Nuclear Information System (INIS)

    Kubo, T.; Sakata, F.; Marumori, T.; Iwasawa, K.; Hashimoto, Y.

    1993-01-01

    A general theory capable of exploring the microscopic structure of the time-dependent Hartree-Fock (TDHF) manifold is summarized. It is discussed that each stable fixed point in the TDHF-manifold represents a dynamical stable mean-field which is not reached by means of the conventional static Hartree-Fock (HF) or constrained Hartree-Fock (CHF) theories. A feasibility of the theory is shown by applying it to a simple model Hamiltonian. (orig.)

  4. Spin Density Distribution in Open-Shell Transition Metal Systems: A Comparative Post-Hartree-Fock, Density Functional Theory, and Quantum Monte Carlo Study of the CuCl2 Molecule.

    Science.gov (United States)

    Caffarel, Michel; Giner, Emmanuel; Scemama, Anthony; Ramírez-Solís, Alejandro

    2014-12-09

    We present a comparative study of the spatial distribution of the spin density of the ground state of CuCl2 using Density Functional Theory (DFT), quantum Monte Carlo (QMC), and post-Hartree-Fock wave function theory (WFT). A number of studies have shown that an accurate description of the electronic structure of the lowest-lying states of this molecule is particularly challenging due to the interplay between the strong dynamical correlation effects in the 3d shell and the delocalization of the 3d hole over the chlorine atoms. More generally, this problem is representative of the difficulties encountered when studying open-shell metal-containing molecular systems. Here, it is shown that qualitatively different results for the spin density distribution are obtained from the various quantum-mechanical approaches. At the DFT level, the spin density distribution is found to be very dependent on the functional employed. At the QMC level, Fixed-Node Diffusion Monte Carlo (FN-DMC) results are strongly dependent on the nodal structure of the trial wave function. Regarding wave function methods, most approaches not including a very high amount of dynamic correlation effects lead to a much too high localization of the spin density on the copper atom, in sharp contrast with DFT. To shed some light on these conflicting results Full CI-type (FCI) calculations using the 6-31G basis set and based on a selection process of the most important determinants, the so-called CIPSI approach (Configuration Interaction with Perturbative Selection done Iteratively) are performed. Quite remarkably, it is found that for this 63-electron molecule and a full CI space including about 10(18) determinants, the FCI limit can almost be reached. Putting all results together, a natural and coherent picture for the spin distribution is proposed.

  5. Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (VII) HFODD (v2.49t): A new version of the program

    International Nuclear Information System (INIS)

    Schunck, Nicolas F.; McDonnell, J.; Sheikh, J.A.; Staszczak, A.; Stoitsov, Mario; Dobaczewski, J.; Toivanen, P.

    2012-01-01

    We describe the new version (v2.49t) of the code HFODD which solves the nuclear Skyrme Hartree-Fock (HF) or Skyrme Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite temperature formalism for the HFB and HF+BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected.

  6. Large quantum systems: a mathematical and numerical perspective; Systemes quantiques a grand nombre de particules: une perspective mathematique et numerique

    Energy Technology Data Exchange (ETDEWEB)

    Lewin, M.

    2009-06-15

    This thesis is devoted to the mathematical study of variational models for large quantum systems. The mathematical methods are that of nonlinear analysis, calculus of variations, partial differential equations, spectral theory, and numerical analysis. The first part contains some results on finite systems. We study several approximations of the N-body Schroedinger equation for electrons in an atom or a molecule, and then the so-called Hartree-Fock- Bogoliubov model for a system of fermions interacting via the gravitational force. In a second part, we propose a new method allowing to prove the existence of the thermodynamic limit of Coulomb quantum systems. Then, we construct two Hartree-Fock-type models for infinite systems. The first is a relativistic theory deduced from Quantum Electrodynamics, allowing to describe the behavior of electrons, coupled to that of Dirac's vacuum which can become polarized. The second model describes a nonrelativistic quantum crystal in the presence of a charged defect. A new numerical method is also proposed. The last part of the thesis is devoted to spectral pollution, a phenomenon which is observed when trying to approximate eigenvalues in a gap of the essential spectrum of a self-adjoint operator, for instance for periodic Schroedinger operators or Dirac operators. (author)

  7. Large quantum systems: a mathematical and numerical perspective

    International Nuclear Information System (INIS)

    Lewin, M.

    2009-06-01

    This thesis is devoted to the mathematical study of variational models for large quantum systems. The mathematical methods are that of nonlinear analysis, calculus of variations, partial differential equations, spectral theory, and numerical analysis. The first part contains some results on finite systems. We study several approximations of the N-body Schroedinger equation for electrons in an atom or a molecule, and then the so-called Hartree-Fock- Bogoliubov model for a system of fermions interacting via the gravitational force. In a second part, we propose a new method allowing to prove the existence of the thermodynamic limit of Coulomb quantum systems. Then, we construct two Hartree-Fock-type models for infinite systems. The first is a relativistic theory deduced from Quantum Electrodynamics, allowing to describe the behavior of electrons, coupled to that of Dirac's vacuum which can become polarized. The second model describes a nonrelativistic quantum crystal in the presence of a charged defect. A new numerical method is also proposed. The last part of the thesis is devoted to spectral pollution, a phenomenon which is observed when trying to approximate eigenvalues in a gap of the essential spectrum of a self-adjoint operator, for instance for periodic Schroedinger operators or Dirac operators. (author)

  8. Ab initio Hartree-Fock and density functional theory investigations on the conformational stability, molecular structure and vibrational spectra of 5-chloro-3-(2-(4-methylpiperazin-1-yl)-2-oxoethyl)benzo[d]thiazol-2(3H)-one drug molecule.

    Science.gov (United States)

    Taşal, Erol; Kumalar, Mustafa

    2012-09-01

    In this work, the experimental and theoretical spectra of 5-chloro-3-(2-(4-methylpiperazin-1-yl)-2-oxoethyl)benzo[d]thiazol-2(3H)-one molecule (abbreviated as 5CMOT) are studied. The molecular geometry and vibrational frequencies are calculated in the ground state of molecule using ab initio Hartree-Fock (HF) and Density Function Theory (DFT) methods with 6-311++G(d,p), 6-31G++(d,p), 6-31G(d,p), 6-31G(d) and 6-31G basis sets. Three staggered stable conformers were observed on the torsional potential energy surfaces. The complete assignments were performed on the basis of the total energy distribution (TED) of the vibrational modes calculated. The comparison of the theoretical and experimental geometries of the title compound indicated that the X-ray parameters fairly well agree with the theoretically obtained values for the most stable conformer. The theoretical results showed an excellent agreement with the experimental values. The calculated HOMO and LUMO energies show that the charge transfer occurs within the molecule. Copyright © 2012 Elsevier B.V. All rights reserved.

  9. Studies of the electron density in the highest occupied molecular orbitals of PH 3, PF 3 and P(CH 3) 3 by electron momentum spectroscopy and Hartree-Fock, MRSD-CI and DFT calculations

    Science.gov (United States)

    Rolke, J.; Brion, C. E.

    1996-06-01

    The spherically averaged momentum profiles for the highest occupied molecular orbitals of PF 3 and P(CH 3) 3 have been obtained by electron momentum spectroscopy. The measurements provide a stringent test of basis set effects and the quality of ab-initio methods in the description of these larger molecular systems. As in previous work on the methyl-substituted amines, intuitive arguments fail to predict the correct amount of s- and p-type contributions to the momentum profile while delocalized molecular orbital concepts provide a more adequate description of the HOMOs. The experimental momentum profiles have been compared with theoretical momentum profiles calculated at the level of the target Hartree-Fock approximation with a range of basis sets. New Hartree-Fock calculations are also presented for the HOMO of PH 3 and compared to previously published experimental and theoretical momentum profiles. The experimental momentum profiles have further been compared to calculations at the level of the target Kohn-Sham approximation using density functional theory with the local density approximation and also with gradient corrected (non-local) exchange correlation potentials. In addition, total energies and dipole moments have been calculated for all three molecules by the various theoretical methods and compared to experimental values. Calculated 'density difference maps' show the regions where the HOMO momentum and position electron densities of PF 3 and P(CH 3) 3 change relative to the corresponding HOMO density of PH 3. The results suggest that methyl groups have an electron-attracting effect (relative to H) on the HOMO charge density in trimethyl phosphines. These conclusions are supported by a consideration of dipole moments and the 31P NMR chemical shifts for PH 3, PF 3 and P(CH 3) 3.

  10. Time-dependent non-equilibrium dielectric response in QM/continuum approaches

    Energy Technology Data Exchange (ETDEWEB)

    Ding, Feizhi; Lingerfelt, David B.; Li, Xiaosong, E-mail: benedetta.mennucci@unipi.it, E-mail: li@chem.washington.edu [Department of Chemistry, University of Washington, Seattle, Washington 98195 (United States); Mennucci, Benedetta, E-mail: benedetta.mennucci@unipi.it, E-mail: li@chem.washington.edu [Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via Risorgimento 35, 56126 Pisa (Italy)

    2015-01-21

    The Polarizable Continuum Models (PCMs) are some of the most inexpensive yet successful methods for including the effects of solvation in quantum-mechanical calculations of molecular systems. However, when applied to the electronic excitation process, these methods are restricted to dichotomously assuming either that the solvent has completely equilibrated with the excited solute charge density (infinite-time limit), or that it retains the configuration that was in equilibrium with the solute prior to excitation (zero-time limit). This renders the traditional PCMs inappropriate for resolving time-dependent solvent effects on non-equilibrium solute electron dynamics like those implicated in the instants following photoexcitation of a solvated molecular species. To extend the existing methods to this non-equilibrium regime, we herein derive and apply a new formalism for a general time-dependent continuum embedding method designed to be propagated alongside the solute’s electronic degrees of freedom in the time domain. Given the frequency-dependent dielectric constant of the solvent, an equation of motion for the dielectric polarization is derived within the PCM framework and numerically integrated simultaneously with the time-dependent Hartree fock/density functional theory equations. Results for small molecular systems show the anticipated dipole quenching and electronic state dephasing/relaxation resulting from out-of-phase charge fluctuations in the dielectric and embedded quantum system.

  11. Time-dependent restricted-active-space self-consistent eld theory: Formulation and application to laser-driven many-electron dynamics

    DEFF Research Database (Denmark)

    Miyagi, Haruhide; Madsen, Lars Bojer

    We have developed a new theoretical framework for time-dependent many-electron problems named time-dependent restricted-active-space self-consistent field (TD-RASSCF) theory. The theory generalizes the multicongurational time-dependent Hartree-Fock (MCTDHF) theory by truncating the expansion...

  12. A microscopic theory of the nuclear collective motion

    International Nuclear Information System (INIS)

    Baranger, M.

    1975-01-01

    A microscopic theory of the nuclear collective model is reviewed, discussions being concentrated, mainly, on the shape motion. An adiabatic time dependent Hartree-Fock method is used. Kinetic energy using the cranking model is obtained. The generator coordinate method is discussed [pt

  13. Molecular wave function and effective adiabatic potentials calculated by extended multi-configuration time-dependent Hartree-Fock method

    Energy Technology Data Exchange (ETDEWEB)

    Kato, Tsuyoshi; Ide, Yoshihiro; Yamanouchi, Kaoru [Department of Chemistry, School of Science, The University of Tokyo, 7-3-1, Hongo Bunkyo-ku, Tokyo, 113-0033 (Japan)

    2015-12-31

    We first calculate the ground-state molecular wave function of 1D model H{sub 2} molecule by solving the coupled equations of motion formulated in the extended multi-configuration time-dependent Hartree-Fock (MCTDHF) method by the imaginary time propagation. From the comparisons with the results obtained by the Born-Huang (BH) expansion method as well as with the exact wave function, we observe that the memory size required in the extended MCTDHF method is about two orders of magnitude smaller than in the BH expansion method to achieve the same accuracy for the total energy. Second, in order to provide a theoretical means to understand dynamical behavior of the wave function, we propose to define effective adiabatic potential functions and compare them with the conventional adiabatic electronic potentials, although the notion of the adiabatic potentials is not used in the extended MCTDHF approach. From the comparison, we conclude that by calculating the effective potentials we may be able to predict the energy differences among electronic states even for a time-dependent system, e.g., time-dependent excitation energies, which would be difficult to be estimated within the BH expansion approach.

  14. Images of a Bose-Einstein condensates: diagonal dynamical Bogoliubov vacuum

    International Nuclear Information System (INIS)

    Dziarmaga, J.; Sacha, K.; Karkuszewski, Z.

    2005-01-01

    Evolution of a Bose-Einstein condensate subject to a time-dependent external perturbation can be described by a time-dependent Bogoliubov theory: a condensate initially in its ground state evolves into a time-dependent excited state which can be formally written as a time-dependent Bogoliubov vacuum annihilated by time-dependent quasiparticle annihilation operators. We prove that any Bogoliubov vacuum can be brought to a diagonal form in a time-dependent orthonormal basis. This diagonal form is taylored for simulations of quantum measurements on excited condensates. As an example we work out a model of atomic interferometer where a trap potential is split in two parts by a potential barrier, and then atoms are released by opening the double-well trap potential. In the Gross-Pitaevskii approximation the released atoms give a high contrast interference pattern with repeatable position of interference fringes. In the two-mode tight-binding approximation the effect of phase diffusion makes the position of fringes fluctuate from experiment to experiment but every single realisation of experiment gives a high quality interference pattern. The time-dependent Bogoliubov theory is a more realistic description of the experiment which goes beyond both approximations. Using the diagonal time-dependent Bogoliubov vacuum we show that in addition to position fluctuations the interference pattern is also loosing its high quality contrast. (author)

  15. Hartree-Fock implementation using a Laguerre-based wave function for the ground state and correlation energies of two-electron atoms.

    Science.gov (United States)

    King, Andrew W; Baskerville, Adam L; Cox, Hazel

    2018-03-13

    An implementation of the Hartree-Fock (HF) method using a Laguerre-based wave function is described and used to accurately study the ground state of two-electron atoms in the fixed nucleus approximation, and by comparison with fully correlated (FC) energies, used to determine accurate electron correlation energies. A variational parameter A is included in the wave function and is shown to rapidly increase the convergence of the energy. The one-electron integrals are solved by series solution and an analytical form is found for the two-electron integrals. This methodology is used to produce accurate wave functions, energies and expectation values for the helium isoelectronic sequence, including at low nuclear charge just prior to electron detachment. Additionally, the critical nuclear charge for binding two electrons within the HF approach is calculated and determined to be Z HF C =1.031 177 528.This article is part of the theme issue 'Modern theoretical chemistry'. © 2018 The Author(s).

  16. A few methods for the theory of collective motions and collisions

    International Nuclear Information System (INIS)

    Giraud, B.G.

    1984-01-01

    In this series of lectures the time-dependent Hartree-Fock theory of nuclear motions and collisions are treated for collective motion only. For the theory of collisions a representation, the boosted shell model, is proposed in which matrix elements of the T-matrix are easier to evaluate via a variational principle

  17. RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅱ)-MICROMORPHIC CONTINUUM THEORY AND COUPLE STRESS THEORY

    Institute of Scientific and Technical Information of China (English)

    戴天民

    2003-01-01

    The purpose is to reestablish the balance laws of momentum, angular momentumand energy and to derive the corresponding local and nonlocal balance equations formicromorphic continuum mechanics and couple stress theory. The desired results formicromorphic continuum mechanics and couple stress theory are naturally obtained via directtransitions and reductions from the coupled conservation law of energy for micropolarcontinuum theory, respectively. The basic balance laws and equation s for micromorphiccontinuum mechanics and couple stress theory are constituted by combining these resultsderived here and the traditional conservation laws and equations of mass and microinertiaand the entropy inequality. The incomplete degrees of the former related continuum theoriesare clarified. Finally, some special cases are conveniently derived.

  18. Translationally invariant self-consistent field theories

    International Nuclear Information System (INIS)

    Shakin, C.M.; Weiss, M.S.

    1977-01-01

    We present a self-consistent field theory which is translationally invariant. The equations obtained go over to the usual Hartree-Fock equations in the limit of large particle number. In addition to deriving the dynamic equations for the self-consistent amplitudes we discuss the calculation of form factors and various other observables

  19. Axially deformed solution of the Skyrme-Hartree-Fock-Bogolyubov equations using the transformed harmonic oscillator basis (III) HFBTHO (v3.00): A new version of the program

    Science.gov (United States)

    Perez, R. Navarro; Schunck, N.; Lasseri, R.-D.; Zhang, C.; Sarich, J.

    2017-11-01

    We describe the new version 3.00 of the code HFBTHO that solves the nuclear Hartree-Fock (HF) or Hartree-Fock-Bogolyubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the full Gogny force in both particle-hole and particle-particle channels, (ii) the calculation of the nuclear collective inertia at the perturbative cranking approximation, (iii) the calculation of fission fragment charge, mass and deformations based on the determination of the neck, (iv) the regularization of zero-range pairing forces, (v) the calculation of localization functions, (vi) a MPI interface for large-scale mass table calculations. Program Files doi:http://dx.doi.org/10.17632/c5g2f92by3.1 Licensing provisions: GPL v3 Programming language: FORTRAN-95 Journal reference of previous version: M.V. Stoitsov, N. Schunck, M. Kortelainen, N. Michel, H. Nam, E. Olsen, J. Sarich, and S. Wild, Comput. Phys. Commun. 184 (2013). Does the new version supersede the previous one: Yes Summary of revisions: 1. the Gogny force in both particle-hole and particle-particle channels was implemented; 2. the nuclear collective inertia at the perturbative cranking approximation was implemented; 3. fission fragment charge, mass and deformations were implemented based on the determination of the position of the neck between nascent fragments; 4. the regularization method of zero-range pairing forces was implemented; 5. the localization functions of the HFB solution were implemented; 6. a MPI interface for large-scale mass table calculations was implemented. Nature of problem:HFBTHO is a physics computer code that is used to model the structure of the nucleus. It is an implementation of the energy density functional (EDF) approach to atomic nuclei, where the energy of the nucleus is obtained by integration over space of some phenomenological energy density, which is itself a functional of the neutron and proton

  20. Dirac-Fock atomic electronic structure calculations using different nuclear charge distributions

    NARCIS (Netherlands)

    Visscher, L; Dyall, KG

    1997-01-01

    Numerical Hartree-Fock calculations based on the Dirac-Coulomb Hamiltonian for the first 109 elements of the periodic table are presented. The results give the total electronic energy, as a function of the nuclear model that is used, for four different models of the nuclear charge distribution. The

  1. Pairing field and moments of inertia of superdeformed nuclei

    International Nuclear Information System (INIS)

    Chen Yongjing; Chen Yongshou; Xu Fuxin

    2002-01-01

    The authors have systematically analysed the dynamic moments of inertia of the experimental superdeformed (SD) bands observed in the A = 190, 150 and 60-80 mass regions as functions of rotational frequency. By combining the different mass regions, the dramatic features of the dynamic moments of inertia were found and explained based on the calculations of the pairing fields of SD nuclei with the anisotropic harmonic oscillator quadrupole pairing Hartree-Fock-Bogoliubov model

  2. Relativistic many-body perturbation-theory calculations based on Dirac-Fock-Breit wave functions

    International Nuclear Information System (INIS)

    Ishikawa, Y.; Quiney, H.M.

    1993-01-01

    A relativistic many-body perturbation theory based on the Dirac-Fock-Breit wave functions has been developed and implemented by employing analytic basis sets of Gaussian-type functions. The instantaneous Coulomb and low-frequency Breit interactions are treated using a unified formalism in both the construction of the Dirac-Fock-Breit self-consistent-field atomic potential and in the evaluation of many-body perturbation-theory diagrams. The relativistic many-body perturbation-theory calculations have been performed on the helium atom and ions of the helium isoelectronic sequence up to Z=50. The contribution of the low-frequency Breit interaction to the relativistic correlation energy is examined for the helium isoelectronic sequence

  3. Density functional theory of nuclei

    International Nuclear Information System (INIS)

    Terasaki, Jun

    2008-01-01

    The density functional theory of nuclei has come to draw attention of scientists in the field of nuclear structure because the theory is expected to provide reliable numerical data in wide range on the nuclear chart. This article is organized to present an overview of the theory to the people engaged in the theory of other fields as well as those people in the nuclear physics experiments. At first, the outline of the density functional theory widely used in the electronic systems (condensed matter, atoms, and molecules) was described starting from the Kohn-Sham equation derived on the variational principle. Then the theory used in the field of nuclear physics was presented. Hartree-Fock and Hartree-Fock-Bogolyubov approximation by using Skyrme interaction was explained. Comparison of the results of calculations and experiments of binding energies and ground state mean square charge radii of some magic number nuclei were shown. The similarity and dissimilarity between the two streams were summarized. Finally the activities of the international project of Universal Nuclear Energy Density Functional (UNEDF) which was started recently lead by US scientist was reported. This project is programmed for five years. One of the applications of the project is the calculation of the neutron capture cross section of nuclei on the r-process, which is absolutely necessary for the nucleosynthesis research. (S. Funahashi)

  4. Time independent mean-field theory

    International Nuclear Information System (INIS)

    Negele, J.W.

    1980-02-01

    The physical and theoretical motivations for the time-dependent mean-field theory are presented, and the successes and limitations of the time-dependent Hartree-Fock initial-vaue problem are reviewed. New theoretical developments are described in the treatment of two-body correlations and the formulation of a quantum mean-field theory of large-amplitude collective motion and tunneling decay. Finally, the mean-field theory is used to obtain new insights into the phenomenon of pion condensation in finite nuclei. 18 figures

  5. Effective interaction for relativistic mean-field theories of nuclear structure

    International Nuclear Information System (INIS)

    Ai, H.B.; Celenza, L.S.; Harindranath, A.; Shakin, C.M.

    1987-01-01

    We construct an effective interaction, which when treated in a relativistic Hartree-Fock approximation, reproduces rather accurately the nucleon self-energy in nuclear matter and the Migdal parameters obtained via relativistic Brueckner-Hartree-Fock calculations. This effective interaction is constructed by adding Born terms, describing the exchange of pseudoparticles, to the Born terms of the Dirac-Hartree-Fock analysis. The pseudoparticles have relatively large masses and either real or imaginary coupling constants. (For example, exchange of a pseudo-sigma with an imaginary coupling constant has the effect of reducing the scalar attraction arising from sigma exchange while exchange of a pseudo-omega with an imaginary coupling constant has the effect of reducing the repulsion arising from omega exchange. The terms beyond the Born term in the case of pion exchange are well simulated by pseudo-sigma exchange with a real coupling constant.) The effective interaction constructed here may be used for calculations of the properties of finite nuclei in a relativistic Hartree-Fock approximation

  6. Time-reversal-violating Schiff moment of 199Hg

    International Nuclear Information System (INIS)

    Jesus, J.H. de; Engel, J.

    2005-01-01

    We calculate the Schiff moment of the nucleus 199 Hg, created by πNN vertices that are odd under parity (P) and time-reversal (T). Our approach, formulated in diagrammatic perturbation theory with important core-polarization diagrams summed to all orders, gives a close approximation to the expectation value of the Schiff operator in the odd-A Hartree-Fock-Bogoliubov ground state generated by a Skyrme interaction and a weak P- and T-odd pion-exchange potential. To assess the uncertainty in the results, we carry out the calculation with several Skyrme interactions, the quality of which we test by checking predictions for the isoscalar-E1 strength distribution in 208 Pb, and estimate most of the important diagrams we omit

  7. Bose-Einstein condensation in atomic alkali gases

    Science.gov (United States)

    Dodd, Robert J.

    1998-05-01

    I present a review of the time-independent Gross-Pitaevskii (GP), Bogoliubov, and finite-temperature Hartree-Fock-Bogoliubov (HFB) mean-field theories used to study trapped, Bose-Einstein condensed alkali gases. Numerical solutions of the (zero-temperature) GP equation are presented for attractive (negative scattering length) and repulsive (positive scattering length) interactions. Comparison is made with the Thomas-Fermi and (variational) trial wavefunction appr oximations that are used in the literature to study condensed gases. Numerical calculations of the (zero-temperature) Bogoliubov quasi-particle excitation frequencies are found to be in excellent agreement with the experimental results. The finite-temperature properties of condensed gases are examined using the Popov approximation (of the HFB theory) and a simple two-gas model. Specific, quantitative comparisons are made with experimental results for finite-temperature excitation frequencies. Qualitative comparisons are made between the results of the Popov approximation, two-gas model, and other published models for condensate fraction and thermal density distribution. The time-independent mean-field theories are found to be in excellent agreement with experimental results at relatively low temperatures (high condensate fractions). However, at higher temperatures (and condensate fractions of less than 50%) there are significant discrepancies between experimental data and theoretical calculations. This work was undertaken at the University of Maryland at College Park and was supported in part by the National Science Foundation (PHY-9601261) and the U.S. Office of Naval Research.

  8. Nuclear-electronic orbital reduced explicitly correlated Hartree-Fock approach: Restricted basis sets and open-shell systems

    International Nuclear Information System (INIS)

    Brorsen, Kurt R.; Sirjoosingh, Andrew; Pak, Michael V.; Hammes-Schiffer, Sharon

    2015-01-01

    The nuclear electronic orbital (NEO) reduced explicitly correlated Hartree-Fock (RXCHF) approach couples select electronic orbitals to the nuclear orbital via Gaussian-type geminal functions. This approach is extended to enable the use of a restricted basis set for the explicitly correlated electronic orbitals and an open-shell treatment for the other electronic orbitals. The working equations are derived and the implementation is discussed for both extensions. The RXCHF method with a restricted basis set is applied to HCN and FHF − and is shown to agree quantitatively with results from RXCHF calculations with a full basis set. The number of many-particle integrals that must be calculated for these two molecules is reduced by over an order of magnitude with essentially no loss in accuracy, and the reduction factor will increase substantially for larger systems. Typically, the computational cost of RXCHF calculations with restricted basis sets will scale in terms of the number of basis functions centered on the quantum nucleus and the covalently bonded neighbor(s). In addition, the RXCHF method with an odd number of electrons that are not explicitly correlated to the nuclear orbital is implemented using a restricted open-shell formalism for these electrons. This method is applied to HCN + , and the nuclear densities are in qualitative agreement with grid-based calculations. Future work will focus on the significance of nonadiabatic effects in molecular systems and the further enhancement of the NEO-RXCHF approach to accurately describe such effects

  9. Nuclear-electronic orbital reduced explicitly correlated Hartree-Fock approach: Restricted basis sets and open-shell systems

    Energy Technology Data Exchange (ETDEWEB)

    Brorsen, Kurt R.; Sirjoosingh, Andrew; Pak, Michael V.; Hammes-Schiffer, Sharon, E-mail: shs3@illinois.edu [Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Ave., Urbana, Illinois 61801 (United States)

    2015-06-07

    The nuclear electronic orbital (NEO) reduced explicitly correlated Hartree-Fock (RXCHF) approach couples select electronic orbitals to the nuclear orbital via Gaussian-type geminal functions. This approach is extended to enable the use of a restricted basis set for the explicitly correlated electronic orbitals and an open-shell treatment for the other electronic orbitals. The working equations are derived and the implementation is discussed for both extensions. The RXCHF method with a restricted basis set is applied to HCN and FHF{sup −} and is shown to agree quantitatively with results from RXCHF calculations with a full basis set. The number of many-particle integrals that must be calculated for these two molecules is reduced by over an order of magnitude with essentially no loss in accuracy, and the reduction factor will increase substantially for larger systems. Typically, the computational cost of RXCHF calculations with restricted basis sets will scale in terms of the number of basis functions centered on the quantum nucleus and the covalently bonded neighbor(s). In addition, the RXCHF method with an odd number of electrons that are not explicitly correlated to the nuclear orbital is implemented using a restricted open-shell formalism for these electrons. This method is applied to HCN{sup +}, and the nuclear densities are in qualitative agreement with grid-based calculations. Future work will focus on the significance of nonadiabatic effects in molecular systems and the further enhancement of the NEO-RXCHF approach to accurately describe such effects.

  10. Fully discrete Galerkin schemes for the nonlinear and nonlocal Hartree equation

    Directory of Open Access Journals (Sweden)

    Walter H. Aschbacher

    2009-01-01

    Full Text Available We study the time dependent Hartree equation in the continuum, the semidiscrete, and the fully discrete setting. We prove existence-uniqueness, regularity, and approximation properties for the respective schemes, and set the stage for a controlled numerical computation of delicate nonlinear and nonlocal features of the Hartree dynamics in various physical applications.

  11. A importância do método de Hartree no ensino de química quântica

    Directory of Open Access Journals (Sweden)

    Silmar A. do Monte

    2011-01-01

    Full Text Available Hartree's original ideas are described. Its connection with electrostatics can be explored in order to decrease the gap between teaching of Physics and Chemistry. As a consequence of its simplicity and connection with electrostatics, it is suggested that Hartree's method should be presented before the Hartree-Fock method. Besides, since the fundamental concepts of indistinguishibility of electrons along with the antissimetry of the wave function are missing in the Hartree's product, the method itself can be used to introduce these concepts. Despite the fact that these features are not included in the trial wavefunction, important qualitatively correct results can be obtained.

  12. Few-particle quantum dynamics–comparing nonequilibrium Green functions with the generalized Kadanoff–Baym ansatz to density operator theory

    International Nuclear Information System (INIS)

    Hermanns, S; Bonitz, M; Balzer, K

    2013-01-01

    The nonequilibrium description of quantum systems requires, for more than two or three particles, the use of a reduced description to be numerically tractable. Two possible approaches are based on either reduced density matrices or nonequilibrium Green functions (NEGF). Both concepts are formulated in terms of hierarchies of coupled equations—the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy for the reduced density operators and the Martin-Schwinger-hierarchy (MS) for the Green functions, respectively. In both cases, similar approximations are introduced to decouple the hierarchy, yet still many questions regarding the correspondence of both approaches remain open. Here we analyze this correspondence by studying the generalized Kadanoff–Baym ansatz (GKBA) that reduces the NEGF to a single-time theory. Starting from the BBGKY-hierarchy we present the approximations that are necessary to recover the GKBA result both, with Hartree-Fock propagators (HF-GKBA) and propagators in second Born approximation. To test the quality of the HF-GKBA, we study the dynamics of a 4-electron Hubbard nanocluster starting from a strong nonequilibrium initial state and compare to exact results and the Wang-Cassing approximation to the BBGKY hierarchy presented recently by Akbari et al. [1].

  13. Quantities Ts[n] and Tc[n] in density-functional theory

    International Nuclear Information System (INIS)

    Zhao, Q.; Parr, R.G.

    1992-01-01

    Levy's constrained-search procedure [Proc. Natl. Acad. Sci. U.S, North 76, 6062 (1979)] is employed to show how to determine Kohn-Sham and Hartree-Fock-Kohn-Sham orbitals and kinetic energies T s and T c , for the two-electron, four-electron, and the general case starting from the electron density. Numerical results are presented for the species H - through F 7+ and the atom Be. The Pauli potential is also determined for Be. The small differences among Kohn-Sham, Hartree-Fock, and Hartree-Fock-Kohn-Sham orbitals suggest that determination of Kohn-Sham orbitals from the density in this way is an attractive procedure for getting an orbital description from an electron density

  14. Effects of pairing correlation on low-lying quasi-particle resonance in neutron drip-line nuclei

    OpenAIRE

    Kobayashi, Yoshihiko; Matsuo, Masayuki

    2015-01-01

    We discuss effects of pairing correlation on quasi-particle resonance. We analyze in detail how the width of low-lying quasi-particle resonance is governed by the pairing correlation in the neutron drip-line nuclei. We consider the 46Si + n system to discuss low-lying p wave quasi-particle resonance. Solving the Hartree-Fock-Bogoliubov equation in the coordinate space with scattering boundary condition, we calculate the phase shift, the elastic cross section, the resonance width and the reson...

  15. Bogoliubov quasiparticles in quantum universe

    International Nuclear Information System (INIS)

    Pawlowski, M.; Papoyan, V.; Pervushin, V.; Smirichinski, S.; )

    2000-01-01

    A powerful apparatus of the Bogoliubov transformations is used to get conserved quantum numbers of a set of free fields in the Friedmann-Robertson-Walker (FRW) metric with the back-reaction of the cosmic evolution. It is shown how the Bogoliubov vacuum of the Heisenberg equations of motion creates particles detected by an observer in the frame of reference at the present-day stage. The equations for coefficient of the Bogoliubov transformations reproduce the equations of states of the FRW classical cosmology in its conformal version [ru

  16. Nonlocal continuum field theories

    CERN Document Server

    2002-01-01

    Nonlocal continuum field theories are concerned with material bodies whose behavior at any interior point depends on the state of all other points in the body -- rather than only on an effective field resulting from these points -- in addition to its own state and the state of some calculable external field. Nonlocal field theory extends classical field theory by describing the responses of points within the medium by functionals rather than functions (the "constitutive relations" of classical field theory). Such considerations are already well known in solid-state physics, where the nonlocal interactions between the atoms are prevalent in determining the properties of the material. The tools developed for crystalline materials, however, do not lend themselves to analyzing amorphous materials, or materials in which imperfections are a major part of the structure. Nonlocal continuum theories, by contrast, can describe these materials faithfully at scales down to the lattice parameter. This book presents a unif...

  17. Construction of the Fock Matrix on a Grid-Based Molecular Orbital Basis Using GPGPUs.

    Science.gov (United States)

    Losilla, Sergio A; Watson, Mark A; Aspuru-Guzik, Alán; Sundholm, Dage

    2015-05-12

    We present a GPGPU implementation of the construction of the Fock matrix in the molecular orbital basis using the fully numerical, grid-based bubbles representation. For a test set of molecules containing up to 90 electrons, the total Hartree-Fock energies obtained from reference GTO-based calculations are reproduced within 10(-4) Eh to 10(-8) Eh for most of the molecules studied. Despite the very large number of arithmetic operations involved, the high performance obtained made the calculations possible on a single Nvidia Tesla K40 GPGPU card.

  18. Approximating the Shifted Hartree-Exchange-Correlation Potential in Direct Energy Kohn-Sham Theory.

    Science.gov (United States)

    Sharpe, Daniel J; Levy, Mel; Tozer, David J

    2018-02-13

    Levy and Zahariev [Phys. Rev. Lett. 113 113002 (2014)] have proposed a new approach for performing density functional theory calculations, termed direct energy Kohn-Sham (DEKS) theory. In this approach, the electronic energy equals the sum of orbital energies, obtained from Kohn-Sham-like orbital equations involving a shifted Hartree-exchange-correlation potential, which must be approximated. In the present study, density scaling homogeneity considerations are used to facilitate DEKS calculations on a series of atoms and molecules, leading to three nonlocal approximations to the shifted potential. The first two rely on preliminary Kohn-Sham calculations using a standard generalized gradient approximation (GGA) exchange-correlation functional and the results illustrate the benefit of describing the dominant Hartree component of the shift exactly. A uniform electron gas analysis is used to eliminate the need for these preliminary Kohn-Sham calculations, leading to a potential with an unconventional form that yields encouraging results, providing strong motivation for further research in DEKS theory.

  19. Some implications of the Hartree product treatment of the quantum nuclei in the ab initio nuclear–electronic orbital methodology

    Energy Technology Data Exchange (ETDEWEB)

    Gharabaghi, Masumeh [Faculty of Chemical and Petroleum Sciences, Shahid Beheshti University, G. C., Evin, Tehran, 19839, P.O. Box 19395-4716 (Iran, Islamic Republic of); Shahbazian, Shant, E-mail: chemist_shant@yahoo.com [Department of Physics, Shahid Beheshti University, G. C., Evin, Tehran, 19839, P.O. Box 19395-4716 (Iran, Islamic Republic of)

    2016-12-09

    In this letter the conceptual and computational implications of the Hartree product type nuclear wavefunction introduced recently within the context of the ab initio non-Born–Oppenheimer Nuclear–electronic orbital (NEO) methodology are considered. It is demonstrated that this wavefunction may imply a pseudo-adiabatic separation of the nuclei and electrons and each nucleus is conceived as a quantum oscillator while a non-Coulombic effective Hamiltonian is deduced for electrons. Using the variational principle this Hamiltonian is employed to derive a modified set of single-component Hartree–Fock equations which are equivalent to the multi-component version derived previously within the context of the NEO and, easy to be implemented computationally. - Highlights: • The Hartree product wavefunction is used for the quantum nuclei of a molecule. • With this wavefunction quantum nuclei may be conceived as quantum oscillators. • Using variational integral, non-Coulomb effective electronic Hamiltonian was derived. • A set of modified Hartree–Fock equations were derived from this Hamiltonian. • The derived equations are equivalent to the multi-component Hartree–Fock equations.

  20. Continuum regularized Yang-Mills theory

    International Nuclear Information System (INIS)

    Sadun, L.A.

    1987-01-01

    Using the machinery of stochastic quantization, Z. Bern, M. B. Halpern, C. Taubes and I recently proposed a continuum regularization technique for quantum field theory. This regularization may be implemented by applying a regulator to either the (d + 1)-dimensional Parisi-Wu Langevin equation or, equivalently, to the d-dimensional second order Schwinger-Dyson (SD) equations. This technique is non-perturbative, respects all gauge and Lorentz symmetries, and is consistent with a ghost-free gauge fixing (Zwanziger's). This thesis is a detailed study of this regulator, and of regularized Yang-Mills theory, using both perturbative and non-perturbative techniques. The perturbative analysis comes first. The mechanism of stochastic quantization is reviewed, and a perturbative expansion based on second-order SD equations is developed. A diagrammatic method (SD diagrams) for evaluating terms of this expansion is developed. We apply the continuum regulator to a scalar field theory. Using SD diagrams, we show that all Green functions can be rendered finite to all orders in perturbation theory. Even non-renormalizable theories can be regularized. The continuum regulator is then applied to Yang-Mills theory, in conjunction with Zwanziger's gauge fixing. A perturbative expansion of the regulator is incorporated into the diagrammatic method. It is hoped that the techniques discussed in this thesis will contribute to the construction of a renormalized Yang-Mills theory is 3 and 4 dimensions

  1. Actinide collisions for QED and superheavy elements with the time-dependent Hartree-Fock theory and the Balian-Vénéroni variational principle

    Directory of Open Access Journals (Sweden)

    Kedziora David J.

    2011-10-01

    Full Text Available Collisions of actinide nuclei form, during very short times of few zs (10−21 s, the heaviest ensembles of interacting nucleons available on Earth. Such collisions are used to produce super-strong electric fields by the huge number of interacting protons to test spontaneous positron-electron pair emission (vacuum decay predicted by the quantum electrodynamics (QED theory. Multi-nucleon transfer in actinide collisions could also be used as an alternative way to fusion in order to produce neutron-rich heavy and superheavy elements thanks to inverse quasifission mechanisms. Actinide collisions are studied in a dynamical quantum microscopic approach. The three-dimensional time-dependent Hartree-Fock (TDHF code tdhf3d is used with a full Skyrme energy density functional to investigate the time evolution of expectation values of one-body operators, such as fragment position and particle number. This code is also used to compute the dispersion of the particle numbers (e.g., widths of fragment mass and charge distributions from TDHF transfer probabilities, on the one hand, and using the BalianVeneroni variational principle, on the other hand. A first application to test QED is discussed. Collision times in 238U+238U are computed to determine the optimum energy for the observation of the vacuum decay. It is shown that the initial orientation strongly affects the collision times and reaction mechanism. The highest collision times predicted by TDHF in this reaction are of the order of ~ 4 zs at a center of mass energy of 1200 MeV. According to modern calculations based on the Dirac equation, the collision times at Ecm > 1 GeV are sufficient to allow spontaneous electron-positron pair emission from QED vacuum decay, in case of bare uranium ion collision. A second application of actinide collisions to produce neutron-rich transfermiums is discussed. A new inverse quasifission mechanism associated to a specific orientation of the nuclei is proposed to

  2. Anharmonic oscillator and Bogoliubov transformation

    International Nuclear Information System (INIS)

    Pattnayak, G.C.; Torasia, S.; Rath, B.

    1990-01-01

    The anharmonic oscillator occupies a cornerstone in many problems in physics. It was observed that none of the authors have tested Bogoliubov transformation to study anharmonic oscillator. The groundstate energy of the anharmonic oscillator is studied using Bogoliubov transformation and the results presented. (author)

  3. The molecular structure and vibrational spectra of N-(2,2-diphenylacetyl)- N'-(naphthalen-1yl)-thiourea by Hartree-Fock and density functional methods

    Science.gov (United States)

    Arslan, Hakan; Mansuroglu, Demet Sezgin; VanDerveer, Don; Binzet, Gun

    2009-04-01

    N-(2,2-Diphenylacetyl)- N'-(naphthalen-1yl)-thiourea (PANT) has been synthesized and characterized by elemental analysis, IR spectroscopy and 1H NMR spectroscopy. The crystal and molecular structure of the title compound has been determined from single crystal X-ray diffraction data. It crystallizes in the triclinic space group P-1, Z = 2 with a = 10.284(2) Å, b = 10.790(2) Å, c = 11.305(2) Å, α = 64.92(3)°, β = 89.88(3)°, γ = 62.99(3)°, V = 983.7(3) Å 3 and Dcalc = 1.339 Mg/m 3. The molecular structure, vibrational frequencies and infrared intensities of PANT were calculated by the Hartree-Fock and density functional theory methods (BLYP and B3LYP) using the 6-31G* basis set. The calculated geometric parameters were compared to the corresponding X-ray structure of the title compound. We obtained 22 stable conformers for the title compound; however Conformer 1 is approximately 9.53 kcal/mol more stable than Conformer 22. The comparison of the theoretical and experimental geometry of the title compound shows that the X-ray parameters fairly well reproduce the geometry of Conformer 17. The harmonic vibrations computed for this compound by the B3LYP/6-31G* method are in good agreement with the observed IR spectral data. Theoretical vibrational spectra of the title compound were interpreted by means of PEDs using the VEDA 4 program. A general better performance of the investigated methods was calculated by PAVF 1.0 program.

  4. Comparative study of the requantization of the time-dependent mean field for the dynamics of nuclear pairing

    Science.gov (United States)

    Ni, Fang; Nakatsukasa, Takashi

    2018-04-01

    To describe quantal collective phenomena, it is useful to requantize the time-dependent mean-field dynamics. We study the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory for the two-level pairing Hamiltonian, and compare results of different quantization methods. The one constructing microscopic wave functions, using the TDHFB trajectories fulfilling the Einstein-Brillouin-Keller quantization condition, turns out to be the most accurate. The method is based on the stationary-phase approximation to the path integral. We also examine the performance of the collective model which assumes that the pairing gap parameter is the collective coordinate. The applicability of the collective model is limited for the nuclear pairing with a small number of single-particle levels, because the pairing gap parameter represents only a half of the pairing collective space.

  5. Relativistic mean field calculations in neutron-rich nuclei

    Energy Technology Data Exchange (ETDEWEB)

    Gangopadhyay, G.; Bhattacharya, Madhubrata [Department of Physics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700 009 (India); Roy, Subinit [Saha Institute of Nuclear Physics, Block AF, Sector 1, Kolkata- 700 064 (India)

    2014-08-14

    Relativistic mean field calculations have been employed to study neutron rich nuclei. The Lagrange's equations have been solved in the co-ordinate space. The effect of the continuum has been effectively taken into account through the method of resonant continuum. It is found that BCS approximation performs as well as a more involved Relativistic Continuum Hartree Bogoliubov approach. Calculations reveal the possibility of modification of magic numbers in neutron rich nuclei. Calculation for low energy proton scattering cross sections shows that the present approach reproduces the density in very light neutron rich nuclei.

  6. Open-system Kohn-Sham density functional theory.

    Science.gov (United States)

    Zhou, Yongxi; Ernzerhof, Matthias

    2012-03-07

    A simple model for electron transport through molecules is provided by the source-sink potential (SSP) method [F. Goyer, M. Ernzerhof, and M. Zhuang, J. Chem. Phys. 126, 144104 (2007)]. In SSP, the boundary conditions of having an incoming and outgoing electron current are enforced through complex potentials that are added to the Hamiltonian. Depending on the sign of the imaginary part of the potentials, current density is generated or absorbed. In this way, a finite system can be used to model infinite molecular electronic devices. The SSP has originally been developed for the Hückel method and subsequently it has been extended [F. Goyer and M. Ernzerhof, J. Chem. Phys. 134, 174101 (2011)] to the Hubbard model. Here we present a step towards its generalization for first-principles electronic structure theory methods. In particular, drawing on our earlier work, we discuss a new generalized density functional theory for complex non-Hermitian Hamiltonians. This theory enables us to combine SSP and Kohn-Sham theory to obtain a method for the description of open systems that exchange current density with their environment. Similarly, the Hartree-Fock method is extended to the realm of non-Hermitian, SSP containing Hamiltonians. As a proof of principle, we present the first applications of complex-density functional theory (CODFT) as well as non-Hermitian Hartree-Fock theory to electron transport through molecules. © 2012 American Institute of Physics

  7. Heavy-ion reactions and new trends of nuclear Physics

    International Nuclear Information System (INIS)

    Bernas, M.

    1987-06-01

    On the chart of the nuclei, there are still areas which would deserve to be explored like the Nickel hole on the neutron rich side. We shall illustrate here the progress recently accomplished along this line and compare resulting datas with Hartree Fock Bogoliubov (H.F.B.) calculations performed on those isotopes. It is shown how well-known production reactions like quasi elastic transfer or neutron induced fission have been pushed toward their limits, thanks to improvements in experimental devices, to be usable further apart from stability

  8. Approximate angular momentum projection from cranked intrinsic states

    International Nuclear Information System (INIS)

    Goodman, A.L.

    1979-01-01

    High-spin spectra are determined by approximately projecting states of good angular momentum from cranked Hartree-Fock-Bogoliubov (CHFB) wave functions. For each J the projected energy is E/sub PROJ/ approx. = E/sub CHFB/ - (ΔJ) 2 /2 J/sub CHFB/, where the moment of inertia J and the fluctuation ΔJ are spin dependent. For /sup 168,170/Yb and 174 Hf the projected J is less than the CHFB value for all J. Consequently approximate projection increases all yrast excitation energies for these nuclei

  9. Roothaan approach in the thermodynamic limit

    Science.gov (United States)

    Gutierrez, G.; Plastino, A.

    1982-02-01

    A systematic method for the solution of the Hartree-Fock equations in the thermodynamic limit is presented. The approach is seen to be a natural extension of the one usually employed in the finite-fermion case, i.e., that developed by Roothaan. The new techniques developed here are applied, as an example, to neutron matter, employing the so-called V1 Bethe "homework" potential. The results obtained are, by far, superior to those that the ordinary plane-wave Hartree-Fock theory yields. NUCLEAR STRUCTURE Hartree-Fock approach; nuclear and neutron matter.

  10. Microscopic Theory of Fission

    International Nuclear Information System (INIS)

    Younes, W; Gogny, D

    2008-01-01

    In recent years, the microscopic method has been applied to the notoriously difficult problem of nuclear fission with unprecedented success. In this paper, we discuss some of the achievements and promise of the microscopic method, as embodied in the Hartree-Fock method using the Gogny finite-range effective interaction, and beyond-mean-field extensions to the theory. The nascent program to describe induced fission observables using this approach at the Lawrence Livermore National Laboratory is presented

  11. Tensor force effect on the evolution of single-particle energies in some isotopic chains in the relativistic Hartree-Fock approximation

    Science.gov (United States)

    López-Quelle, M.; Marcos, S.; Niembro, R.; Savushkin, L. N.

    2018-03-01

    Within a nonlinear relativistic Hartree-Fock approximation combined with the BCS method, we study the effect of the nucleon-nucleon tensor force of the π-exchange potential on the spin- and pseudospin-orbit doublets along the Ca and Sn isotopic chains. We show how the self-consistent tensor force effect modifies the splitting of both kinds of doublets in an interdependent form, leading, quite generally, to opposite effects in the accomplishment of the spin and pseudospin symmetries (the one is restored, the other one deteriorates and vice versa). The ordering of the single-particle energy levels is crucial to this respect. Also, we observe a mutual dependence on the evolution of the shell closure gap Z = 50 and the energy band outside the core, along the Sn chain, as due to the tensor force. In fact, when the shell gap is quenched the outside energy band is enlarged, and vice versa. A reduction of the strength of the pion tensor force with respect to its experimental value from the nucleon-nucleon scattering is needed to get results closer to the experiment. Pairing correlations act to some extent in the opposite direction of the tensor term of the one-pion-exchange force.

  12. Nonrelativistic theory of heavy-ion collisions

    International Nuclear Information System (INIS)

    Bertsch, G.

    1984-01-01

    A wide range of phenomena is observed in heavy-ion collisions, calling for a comprehensive theory based on fundamental principles of many-particle quantum mechanics. At low energies, the nuclear dynamics is controlled by the mean field, as we know from spectroscopic nuclear physics. We therefore expect the comprehensive theory of collisions to contain mean-field theory at low energies. The mean-field theory is the subject of the first lectures in this chapter. This theory can be studied quantum mechanically, in which form it is called TDHF (time-dependent Hartree-Fock), or classically, where the equation is called the Vlasov equation. 25 references, 14 figures

  13. A geometrical correction for the inter- and intra-molecular basis set superposition error in Hartree-Fock and density functional theory calculations for large systems

    Science.gov (United States)

    Kruse, Holger; Grimme, Stefan

    2012-04-01

    A semi-empirical counterpoise-type correction for basis set superposition error (BSSE) in molecular systems is presented. An atom pair-wise potential corrects for the inter- and intra-molecular BSSE in supermolecular Hartree-Fock (HF) or density functional theory (DFT) calculations. This geometrical counterpoise (gCP) denoted scheme depends only on the molecular geometry, i.e., no input from the electronic wave-function is required and hence is applicable to molecules with ten thousands of atoms. The four necessary parameters have been determined by a fit to standard Boys and Bernadi counterpoise corrections for Hobza's S66×8 set of non-covalently bound complexes (528 data points). The method's target are small basis sets (e.g., minimal, split-valence, 6-31G*), but reliable results are also obtained for larger triple-ζ sets. The intermolecular BSSE is calculated by gCP within a typical error of 10%-30% that proves sufficient in many practical applications. The approach is suggested as a quantitative correction in production work and can also be routinely applied to estimate the magnitude of the BSSE beforehand. The applicability for biomolecules as the primary target is tested for the crambin protein, where gCP removes intramolecular BSSE effectively and yields conformational energies comparable to def2-TZVP basis results. Good mutual agreement is also found with Jensen's ACP(4) scheme, estimating the intramolecular BSSE in the phenylalanine-glycine-phenylalanine tripeptide, for which also a relaxed rotational energy profile is presented. A variety of minimal and double-ζ basis sets combined with gCP and the dispersion corrections DFT-D3 and DFT-NL are successfully benchmarked on the S22 and S66 sets of non-covalent interactions. Outstanding performance with a mean absolute deviation (MAD) of 0.51 kcal/mol (0.38 kcal/mol after D3-refit) is obtained at the gCP-corrected HF-D3/(minimal basis) level for the S66 benchmark. The gCP-corrected B3LYP-D3/6-31G* model

  14. A geometrical correction for the inter- and intra-molecular basis set superposition error in Hartree-Fock and density functional theory calculations for large systems.

    Science.gov (United States)

    Kruse, Holger; Grimme, Stefan

    2012-04-21

    A semi-empirical counterpoise-type correction for basis set superposition error (BSSE) in molecular systems is presented. An atom pair-wise potential corrects for the inter- and intra-molecular BSSE in supermolecular Hartree-Fock (HF) or density functional theory (DFT) calculations. This geometrical counterpoise (gCP) denoted scheme depends only on the molecular geometry, i.e., no input from the electronic wave-function is required and hence is applicable to molecules with ten thousands of atoms. The four necessary parameters have been determined by a fit to standard Boys and Bernadi counterpoise corrections for Hobza's S66×8 set of non-covalently bound complexes (528 data points). The method's target are small basis sets (e.g., minimal, split-valence, 6-31G*), but reliable results are also obtained for larger triple-ζ sets. The intermolecular BSSE is calculated by gCP within a typical error of 10%-30% that proves sufficient in many practical applications. The approach is suggested as a quantitative correction in production work and can also be routinely applied to estimate the magnitude of the BSSE beforehand. The applicability for biomolecules as the primary target is tested for the crambin protein, where gCP removes intramolecular BSSE effectively and yields conformational energies comparable to def2-TZVP basis results. Good mutual agreement is also found with Jensen's ACP(4) scheme, estimating the intramolecular BSSE in the phenylalanine-glycine-phenylalanine tripeptide, for which also a relaxed rotational energy profile is presented. A variety of minimal and double-ζ basis sets combined with gCP and the dispersion corrections DFT-D3 and DFT-NL are successfully benchmarked on the S22 and S66 sets of non-covalent interactions. Outstanding performance with a mean absolute deviation (MAD) of 0.51 kcal/mol (0.38 kcal/mol after D3-refit) is obtained at the gCP-corrected HF-D3/(minimal basis) level for the S66 benchmark. The gCP-corrected B3LYP-D3/6-31G* model

  15. Open-ended response theory with polarizable embedding

    DEFF Research Database (Denmark)

    Steindal, Arnfinn Hykkerud; Beerepoot, Maarten T P; Ringholm, Magnus

    2016-01-01

    We present the theory and implementation of an open-ended framework for electric response properties at the level of Hartree-Fock and Kohn-Sham density functional theory that includes effects from the molecular environment modeled by the polarizable embedding (PE) model. With this new state......-of-the-art multiscale functionality, electric response properties to any order can be calculated for molecules embedded in polarizable atomistic molecular environments ranging from solvents to complex heterogeneous macromolecules such as proteins. In addition, environmental effects on multiphoton absorption (MPA...

  16. Superdeformed bands of odd nuclei in A=190 region in the quasiparticle picture

    International Nuclear Information System (INIS)

    Terasaki, J.; Flocard, H.; Heenen, P.H.; Bonche, P.

    1996-07-01

    Properties of the superdeformed (SD) bands of 195 Pb and 193 Hg have been studied by the cranked Hartree-Fock-Bogoliubov method. The calculations reproduce the flat behavior of the dynamical moment of inertia of two of the SD bands of 195 Pb measured recently. Possible configuration assignments for the observed bands 3 and 4 of 195 Pb are discussed. The two interacting SD bands of 193 Hg have also been calculated. The analysis confirms the superiority of a density-dependent pairing force over a seniority pairing interaction. (author)

  17. Condensation of bosons with Rashba-Dresselhaus spin-orbit coupling

    International Nuclear Information System (INIS)

    Baym, Gordon; Ozawa, Tomoki

    2014-01-01

    Cold atomic Bose-Einstein systems in the presence of simulated Rashba- Dresselhaus spin-orbit coupling exhibit novel physical features. With pure in-plane Rashba coupling the system is predicted in Bogoliubov-Hartree-Fock to have a stable Bose condensate below a critical temperature, even though the effective density of states is two-dimensional. In addition the system has a normal state at all temperatures. We review here the new physics when the system has such spin-orbit coupling, and discuss the nature of the finite temperature condensation phase transition from the normal to condensed phases.

  18. Microscopic structure of superdeformed states in Th, U, Pu and Cm isotopes with Gogny force

    International Nuclear Information System (INIS)

    Girod, M.; Delaroche, J.P.; Romain, P.; Libert, J.

    2002-01-01

    The structure properties of the even-even nuclei 226, 228, 230, 232, 234 Th, 230, 232, 234, 236, 238, 240 U, 240, 242, 244, 246 Pu, and 242, 244, 246, 248 Cm have been investigated at normal and superdeformed shapes in microscopic mean-field calculations based on Gogny force. Collective levels are predicted from constrained Hartree-Fock-Bogoliubov and configuration mixing calculations. Two quasiparticle states are also predicted from blocking calculations for neutron and proton configurations. Predictions are shown and compared with experimental data at superdeformed shapes. (orig.)

  19. Microscopic analysis of angular momentum projected HFB-states in terms of interacting bosons

    International Nuclear Information System (INIS)

    Ring, P.; Pannert, W.

    1984-12-01

    Angular momentum- and number-projected Hartree-Fock-Bogoliubov (HFB) wavefunctions for transitional and deformed Rare Earth nuclei are analyzed in terms of Fermion pairs coupled to angular momenta L = 0(S), 2(D), 4(G), ... The Fermion space is truncated to contain only S-D or S-D-G pairs. The variation is carried out before and after angular momentum projection and with different truncations. The influence of the truncation on physical quantities such as moments of inertia, quadrupole moments or pair transfer matrix elements is discussed. 21 references

  20. Angular momentum fuctuation energy in the cranking model

    International Nuclear Information System (INIS)

    Goodman, A.L.

    1979-01-01

    Angular momentum is approximately projected from Hartree-Fock-Bogoliubov cranked (HFBC) wave functions. At each J the projected energy is Esub(proj)approximately Esub(HFBC). The spin-dependent fluctuation ΔJ includes contributions from Jsub(y) and Jsub(z) as well as Jsub(x). There are no correlations in the three angular momentum components. Projected energies are calculated for 168 170 Yb and 174 Hf. When compared to experimental energies, the projected spectra are less compressed than the HFBC spectra. At low spins the projected and experimental energies are in good agreement. (Aut.)

  1. Test of a q-fractional V{sup (N-q)} Hartree-Fock potential for the calculation of double photoionization cross sections of neon

    Energy Technology Data Exchange (ETDEWEB)

    Kilin, V.A. [Tomsk Polytechnic University, Tomsk (Russian Federation); Lazarev, D.V.; Lazarev, Dm.A.; Zelichenko, V.M. [Tomsk Pedagogic University, Tomsk (Russian Federation); Amusia, M. Ya. [A.F. Ioffe Physico-Technical Institute, St. Petersburg (Russian Federation); Schartner, K.-H. [I Physikalisches Institut, Justus-Liebig-Universitaet, Giessen (Germany); Ehresmann, A.; Schmoranzer, H. [Fachbereich Physik, Universitaet Kaiserslautern, Kaiserslautern (Germany)

    2001-10-28

    The approach of a parametric V{sup (N-q)} Hartree-Fock potential with fractional q is developed and applied for the first time for the calculation of the double photoionization cross sections of Ne. A minimum of the squared difference between the length-form and velocity-form cross sections is used as a criterion for calculating the values of q. It is found that the minimization procedure leads to a practically exact equality of the length-form and velocity-form cross sections for the Ne III 2s{sup 2}2p{sup 4}[{sup 3}P,{sup 1}D,{sup 1}S], 2s{sup 1}2p{sup 5}[{sup 3}P,{sup 1}P] and 2s{sup 0}2p{sup 6}[{sup 1}S] states in the exciting-photon energy region from the double-ionization threshold up to 325 eV, if q is considered as a function of the exciting-photon energy. The calculated V{sup (N-q)} cross sections are in better agreement with the experimental data than those for the V{sup (N-1)} and V{sup (N-2)} potentials. (author)

  2. Hartree and Exchange in Ensemble Density Functional Theory: Avoiding the Nonuniqueness Disaster.

    Science.gov (United States)

    Gould, Tim; Pittalis, Stefano

    2017-12-15

    Ensemble density functional theory is a promising method for the efficient and accurate calculation of excitations of quantum systems, at least if useful functionals can be developed to broaden its domain of practical applicability. Here, we introduce a guaranteed single-valued "Hartree-exchange" ensemble density functional, E_{Hx}[n], in terms of the right derivative of the universal ensemble density functional with respect to the coupling constant at vanishing interaction. We show that E_{Hx}[n] is straightforwardly expressible using block eigenvalues of a simple matrix [Eq. (14)]. Specialized expressions for E_{Hx}[n] from the literature, including those involving superpositions of Slater determinants, can now be regarded as originating from the unifying picture presented here. We thus establish a clear and practical description for Hartree and exchange in ensemble systems.

  3. Symbolic computation of the Hartree-Fock energy from a chiral EFT three-nucleon interaction at N2LO

    International Nuclear Information System (INIS)

    Gebremariam, B.; Bogner, S.K.; Duguet, T.

    2010-01-01

    We present the first of a two-part Mathematica notebook collection that implements a symbolic approach for the application of the density matrix expansion (DME) to the Hartree-Fock (HF) energy from a chiral effective field theory (EFT) three-nucleon interaction at N 2 LO. The final output from the notebooks is a Skyrme-like energy density functional that provides a quasi-local approximation to the non-local HF energy. In this paper, we discuss the derivation of the HF energy and its simplification in terms of the scalar/vector-isoscalar/isovector parts of the one-body density matrix. Furthermore, a set of steps is described and illustrated on how to extend the approach to other three-nucleon interactions. Program summary: Program title: SymbHFNNN; Catalogue identifier: AEGC v 1 0 ; Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEGC_v1_0.html; Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland; Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html; No. of lines in distributed program, including test data, etc.: 96 666; No. of bytes in distributed program, including test data, etc.: 378 083; Distribution format: tar.gz; Programming language: Mathematica 7.1; Computer: Any computer running Mathematica 6.0 and later versions; Operating system: Windows Xp, Linux/Unix; RAM: 256 Mb; Classification: 5, 17.16, 17.22; Nature of problem: The calculation of the HF energy from the chiral EFT three-nucleon interaction at N 2 LO involves tremendous spin-isospin algebra. The problem is compounded by the need to eventually obtain a quasi-local approximation to the HF energy, which requires the HF energy to be expressed in terms of scalar/vector-isoscalar/isovector parts of the one-body density matrix. The Mathematica notebooks discussed in this paper solve the latter issue. Solution method: The HF energy from the chiral EFT three-nucleon interaction at N 2 LO is cast into a form suitable for an automatic

  4. Dependence of Excited State Potential Energy Surfaces on the Spatial Overlap of the Kohn-Sham Orbitals and the Amount of Nonlocal Hartree-Fock Exchange in Time-Dependent Density Functional Theory.

    Science.gov (United States)

    Plötner, Jürgen; Tozer, David J; Dreuw, Andreas

    2010-08-10

    Time-dependent density functional theory (TDDFT) with standard GGA or hybrid exchange-correlation functionals is not capable of describing the potential energy surface of the S1 state of Pigment Yellow 101 correctly; an additional local minimum is observed at a twisted geometry with substantial charge transfer (CT) character. To investigate the influence of nonlocal exact orbital (Hartree-Fock) exchange on the shape of the potential energy surface of the S1 state in detail, it has been computed along the twisting coordinate employing the standard BP86, B3LYP, and BHLYP xc-functionals as well as the long-range separated (LRS) exchange-correlation (xc)-functionals LC-BOP, ωB97X, ωPBE, and CAM-B3LYP and compared to RI-CC2 benchmark results. Additionally, a recently suggested Λ-parameter has been employed that measures the amount of CT in an excited state by calculating the spatial overlap of the occupied and virtual molecular orbitals involved in the transition. Here, the error in the calculated S1 potential energy curves at BP86, B3LYP, and BHLYP can be clearly related to the Λ-parameter, i.e., to the extent of charge transfer. Additionally, it is demonstrated that the CT problem is largely alleviated when the BHLYP xc-functional is employed, although it still exhibits a weak tendency to underestimate the energy of CT states. The situation improves drastically when LRS-functionals are employed within TDDFT excited state calculations. All tested LRS-functionals give qualitatively the correct potential energy curves of the energetically lowest excited states of P. Y. 101 along the twisting coordinate. While LC-BOP and ωB97X overcorrect the CT problem and now tend to give too large excitation energies compared to other non-CT states, ωPBE and CAM-B3LYP are in excellent agreement with the RI-CC2 results, with respect to both the correct shape of the potential energy curve as well as the absolute values of the calculated excitation energies.

  5. Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. VIII. Role of Coulomb exchange

    International Nuclear Information System (INIS)

    Goriely, S.; Pearson, J. M.

    2008-01-01

    Following suggestions that the energy associated with Coulomb correlations and a possible charge-symmetry breaking of nuclear forces might largely cancel the Coulomb-exchange term, we refit the HFB-14 mass model without the Coulomb-exchange term to essentially all the mass data. The resulting mass model, HFB-15, gives a better fit to the 2149 mass data, σ rms falling from 0.729 to 0.678 MeV. The improvement in the energy differences between mirror nuclei is particularly striking: the Nolen-Schiffer anomaly, which is strong for HFB-14, is essentially eliminated. As for the extrapolation to highly neutron-rich nuclei, the HFB-15 model differs significantly from HFB-14, with up to 15 MeV less binding being predicted. However, the differences in the predicted values of differential quantities such as the neutron-separation energies, β-decay energies and fission barriers are very much smaller

  6. Quantum versus classical statistical dynamics of an ultracold Bose gas

    International Nuclear Information System (INIS)

    Berges, Juergen; Gasenzer, Thomas

    2007-01-01

    We investigate the conditions under which quantum fluctuations are relevant for the quantitative interpretation of experiments with ultracold Bose gases. This requires to go beyond the description in terms of the Gross-Pitaevskii and Hartree-Fock-Bogoliubov mean-field theories, which can be obtained as classical (statistical) field-theory approximations of the quantum many-body problem. We employ functional-integral techniques based on the two-particle irreducible (2PI) effective action. The role of quantum fluctuations is studied within the nonperturbative 2PI 1/N expansion to next-to-leading order. At this accuracy level memory integrals enter the dynamic equations, which differ for quantum and classical statistical descriptions. This can be used to obtain a classicality condition for the many-body dynamics. We exemplify this condition by studying the nonequilibrium evolution of a one-dimensional Bose gas of sodium atoms, and discuss some distinctive properties of quantum versus classical statistical dynamics

  7. Field theory of large amplitude collective motion. A schematic model

    International Nuclear Information System (INIS)

    Reinhardt, H.

    1978-01-01

    By using path integral methods the equation for large amplitude collective motion for a schematic two-level model is derived. The original fermion theory is reformulated in terms of a collective (Bose) field. The classical equation of motion for the collective field coincides with the time-dependent Hartree-Fock equation. Its classical solution is quantized by means of the field-theoretical generalization of the WKB method. (author)

  8. Modeling molecule-plasmon interactions using quantized radiation fields within time-dependent electronic structure theory

    Energy Technology Data Exchange (ETDEWEB)

    Nascimento, Daniel R.; DePrince, A. Eugene, E-mail: deprince@chem.fsu.edu [Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390 (United States)

    2015-12-07

    We present a combined cavity quantum electrodynamics/ab initio electronic structure approach for simulating plasmon-molecule interactions in the time domain. The simple Jaynes-Cummings-type model Hamiltonian typically utilized in such simulations is replaced with one in which the molecular component of the coupled system is treated in a fully ab initio way, resulting in a computationally efficient description of general plasmon-molecule interactions. Mutual polarization effects are easily incorporated within a standard ground-state Hartree-Fock computation, and time-dependent simulations carry the same formal computational scaling as real-time time-dependent Hartree-Fock theory. As a proof of principle, we apply this generalized method to the emergence of a Fano-like resonance in coupled molecule-plasmon systems; this feature is quite sensitive to the nanoparticle-molecule separation and the orientation of the molecule relative to the polarization of the external electric field.

  9. A comparison between the adiabatic time dependent Hartree-Fock and the generator coordinate methods for the description of nuclear collective motion

    International Nuclear Information System (INIS)

    Villars, F.

    1975-01-01

    The objective of the work is to draw attention to the essential equivalence of the two apparently quite distinct ways of describing nuclear collective dyanmics, the adiabatic time-dependent Hartree-Fock method (ADTHF) on the one hand, and the Generator Coordinate (GC) method on the other hand. To demonstrate this relation, an analysis of the simplest case, in which collective motion is described by a single collective para- meter q(t) is presented. In the ATDHF approach, two self-consistency conditions are obtained; the resultant expressions for the collective potential and kinetic energies represent a special case of the more general results of Baranger and Veneroni. In the G.C. approach to the same system (with the same collective parameter q), the narrow overlap approximation must be made, as the counterpart of the adiabatic approximation in the TDHF method. In its conventional form, the G.C. method leads to a different expression for the collective kinetic energy. It is shown however, that a simple generalization of the G.C.-wave function leads to corrections determined by a variational principle. In leading order, the corrected expression for the collective kinetic energy is identical with the TDHF result In both cases, the collective inertia is determined by a self-consistent cranking formula

  10. Mechanism of equalization of proton and neutron radii and the Coulomb anomaly

    International Nuclear Information System (INIS)

    Caurier, E.; Poves, A.; Zuker, A.

    1980-01-01

    It is shown that a one parameter modification of the effective forces allows to resolve the Coulomb energy anomalies in the Ca region within the framework of Hartree Fock (HF) and isospin projected Hartree Fock (IPHF) theories. A simple microscopic mechanism of equalization of neutron and proton radii is invoked to produce results consistent with available data

  11. Molecular orbital theory. Spinor representation

    International Nuclear Information System (INIS)

    Aono, Shigeyuki

    2003-01-01

    The algebra representing electron is spinor. The many electron problem is investigated with the Nambu 2x2 spinor. Operators then are expressed 2x2 matrices. The electron-electron interaction is decomposed into couplings between various electron densities by using the Pauli spin matrices. The diagonal ones of them refer to the direct and exchange interactions and the off-diagonal terms to those for superconducting. The Roothaan theory is rewritten. The approximation beyond the Hartree-Fock is discussed. (author)

  12. Roothaan's approach to solve the Hartree-Fock equations for atoms confined by soft walls: Basis set with correct asymptotic behavior.

    Science.gov (United States)

    Rodriguez-Bautista, Mariano; Díaz-García, Cecilia; Navarrete-López, Alejandra M; Vargas, Rubicelia; Garza, Jorge

    2015-07-21

    In this report, we use a new basis set for Hartree-Fock calculations related to many-electron atoms confined by soft walls. One- and two-electron integrals were programmed in a code based in parallel programming techniques. The results obtained with this proposal for hydrogen and helium atoms were contrasted with other proposals to study just one and two electron confined atoms, where we have reproduced or improved the results previously reported. Usually, an atom enclosed by hard walls has been used as a model to study confinement effects on orbital energies, the main conclusion reached by this model is that orbital energies always go up when the confinement radius is reduced. However, such an observation is not necessarily valid for atoms confined by penetrable walls. The main reason behind this result is that for atoms with large polarizability, like beryllium or potassium, external orbitals are delocalized when the confinement is imposed and consequently, the internal orbitals behave as if they were in an ionized atom. Naturally, the shell structure of these atoms is modified drastically when they are confined. The delocalization was an argument proposed for atoms confined by hard walls, but it was never verified. In this work, the confinement imposed by soft walls allows to analyze the delocalization concept in many-electron atoms.

  13. Atomic effects of beta decay in astrophysics and in elementary particle physics

    International Nuclear Information System (INIS)

    Zonghua, Chen.

    1988-01-01

    The thesis consists mainly of two parts. The first part is a study of the bound-state β decay of 187 Re and its application in Astrophysics. There existed an uncertainty in the ratio ρ b of bound-state to continuum β decay of 187 Re in both theory and experiment. A more definite theoretical result of ρ b ∼ 1% is obtained by using single-configuration and multi-configuration Hartree-Fock-Dirac approximations. The results obtained are close to those obtained by Williams, Fowler, and Koonin by a modified Thomas-Fermi model. The bound-state β decay of 187 Re at high temperatures is also studied. The second part of the thesis is a generalization of the Thomas-Fermi results of various energy contribution to the ground-state energy of a neutral atom. An analytical expression for the ratio of the electron-electron to electron-nuclear interaction is obtained by the corrected Thomas-Fermi result, the ratio obtained gives a better agreement with the Hartree-Fock numerical results

  14. Dynamical description of the fission process using the TD-BCS theory

    Energy Technology Data Exchange (ETDEWEB)

    Scamps, Guillaume, E-mail: scamps@nucl.phys.tohoku.ac.jp [Department of Physics, Tohoku University, Sendai 980-8578 (Japan); Simenel, Cédric [Department of Nuclear Physics, Research School of Physics and Engineering Australian National University, Canberra, Australian Capital Territory 2601 (Australia); Lacroix, Denis [Institut de Physique Nucléaire, IN2P3-CNRS, Université Paris-Sud, F-91406 Orsay Cedex (France)

    2015-10-15

    The description of fission remains a challenge for nuclear microscopic theories. The time-dependent Hartree-Fock approach with BCS pairing is applied to study the last stage of the fission process. A good agreement is found for the one-body observables: the total kinetic energy and the average mass asymmetry. The non-physical dependence of two-body observables with the initial shape is discussed.

  15. Hartree-type approximation applied to a phi4 field theory

    International Nuclear Information System (INIS)

    Chang, S.-J.

    1976-01-01

    Recently, there has been considerable interest in studying the relativistic field theories by means of nonperturbative method. These studies are partially motivated by the now fashionable physical picture that the hadrons are created from an 'abnormal vacuum state'. This abnormal vacuum state is the ground state associated with a spontaneously broken symmetry and is usually characterized by the non-vanishing expectation value of one or more scale fields. Presently, nearly all understandings of hadrons in the above description are based on semi-classical calculations. It is important to know how significant are the effects of the quantum corrections. Some results on the quantum fluctuations in a phi 4 field theory based in a self-consistent Hartree-type approximation are described. (Auth.)

  16. Norm overlap between many-body states: Uncorrelated overlap between arbitrary Bogoliubov product states

    Science.gov (United States)

    Bally, B.; Duguet, T.

    2018-02-01

    Background: State-of-the-art multi-reference energy density functional calculations require the computation of norm overlaps between different Bogoliubov quasiparticle many-body states. It is only recently that the efficient and unambiguous calculation of such norm kernels has become available under the form of Pfaffians [L. M. Robledo, Phys. Rev. C 79, 021302 (2009), 10.1103/PhysRevC.79.021302]. Recently developed particle-number-restored Bogoliubov coupled-cluster (PNR-BCC) and particle-number-restored Bogoliubov many-body perturbation (PNR-BMBPT) ab initio theories [T. Duguet and A. Signoracci, J. Phys. G 44, 015103 (2017), 10.1088/0954-3899/44/1/015103] make use of generalized norm kernels incorporating explicit many-body correlations. In PNR-BCC and PNR-BMBPT, the Bogoliubov states involved in the norm kernels differ specifically via a global gauge rotation. Purpose: The goal of this work is threefold. We wish (i) to propose and implement an alternative to the Pfaffian method to compute unambiguously the norm overlap between arbitrary Bogoliubov quasiparticle states, (ii) to extend the first point to explicitly correlated norm kernels, and (iii) to scrutinize the analytical content of the correlated norm kernels employed in PNR-BMBPT. Point (i) constitutes the purpose of the present paper while points (ii) and (iii) are addressed in a forthcoming paper. Methods: We generalize the method used in another work [T. Duguet and A. Signoracci, J. Phys. G 44, 015103 (2017), 10.1088/0954-3899/44/1/015103] in such a way that it is applicable to kernels involving arbitrary pairs of Bogoliubov states. The formalism is presently explicated in detail in the case of the uncorrelated overlap between arbitrary Bogoliubov states. The power of the method is numerically illustrated and benchmarked against known results on the basis of toy models of increasing complexity. Results: The norm overlap between arbitrary Bogoliubov product states is obtained under a closed

  17. Application of the weak-field asymptotic theory to the analysis of tunneling ionization of linear molecules

    DEFF Research Database (Denmark)

    Madsen, Lars Bojer; Tolstikhin, Oleg I.; Morishita, Toru

    2012-01-01

    The recently developed weak-field asymptotic theory [ Phys. Rev. A 84 053423 (2011)] is applied to the analysis of tunneling ionization of a molecular ion (H2+), several homonuclear (H2, N2, O2) and heteronuclear (CO, HF) diatomic molecules, and a linear triatomic molecule (CO2) in a static...... electric field. The dependence of the ionization rate on the angle between the molecular axis and the field is determined by a structure factor for the highest occupied molecular orbital. This factor is calculated using a virtually exact discrete variable representation wave function for H2+, very accurate...... Hartree-Fock wave functions for the diatomics, and a Hartree-Fock quantum chemistry wave function for CO2. The structure factors are expanded in terms of standard functions and the associated structure coefficients, allowing the determination of the ionization rate for any orientation of the molecule...

  18. Geometric continuum regularization of quantum field theory

    International Nuclear Information System (INIS)

    Halpern, M.B.

    1989-01-01

    An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs

  19. Stiffness-constant variation in nickel-based alloys: Experiment and theory

    International Nuclear Information System (INIS)

    Hennion, M.; Hennion, B.

    1979-01-01

    Recent measurements of the spin-wave stiffness constant in several nickel alloys at various concentrations are interpreted within a random-phase approximation, coherent-potential approximation (RPA-CPA) band model which uses the Hartree-Fock approximation to treat the intraatomic correlations. We give a theoretical description of the possible impurity states in the Hartree-Fock approximation. This allows the determination of the Hartree-Fock solutions which can account for the stiffness-constant behavior and the magnetic moment on the impurity for all the investigated alloys. For alloys such as NiCr, NiV, NiMo, and NiRu, the magnetizations of which deviate from the Slater-Pauling curve, our determination does not correspond to previous works and is consequently discussed. The limits of the model appear mainly due to local-environment effects; in the case of NiMn, it is found that a ternary-alloy model with some Mn atoms in the antiferromagnetic state can account for both stiffness-constant and magnetization behaviors

  20. Recent developments and applications of multi-configuration Hartree-Fock methods. NRCC proceedings No. 10

    Energy Technology Data Exchange (ETDEWEB)

    Dupuis, M. (ed.)

    1981-02-01

    Twenty-seven papers are included in four sessions titled: generalized Fock operator methods, annihilation of single excitations methods, second-order MCSCF methods, and applications of MCHF methods. Separate abstracts were prepared for eight papers; one of the remaining had been previously abstracted. (DLC)

  1. Recent developments and applications of multi-configuration Hartree-Fock methods. NRCC proceedings No. 10

    International Nuclear Information System (INIS)

    Dupuis, M.

    1981-02-01

    Twenty-seven papers are included in four sessions titled: generalized Fock operator methods, annihilation of single excitations methods, second-order MCSCF methods, and applications of MCHF methods. Separate abstracts were prepared for eight papers; one of the remaining had been previously abstracted

  2. Explicit polarization (X-Pol) potential using ab initio molecular orbital theory and density functional theory.

    Science.gov (United States)

    Song, Lingchun; Han, Jaebeom; Lin, Yen-lin; Xie, Wangshen; Gao, Jiali

    2009-10-29

    The explicit polarization (X-Pol) method has been examined using ab initio molecular orbital theory and density functional theory. The X-Pol potential was designed to provide a novel theoretical framework for developing next-generation force fields for biomolecular simulations. Importantly, the X-Pol potential is a general method, which can be employed with any level of electronic structure theory. The present study illustrates the implementation of the X-Pol method using ab initio Hartree-Fock theory and hybrid density functional theory. The computational results are illustrated by considering a set of bimolecular complexes of small organic molecules and ions with water. The computed interaction energies and hydrogen bond geometries are in good accord with CCSD(T) calculations and B3LYP/aug-cc-pVDZ optimizations.

  3. Analysis of the Bogoliubov free energy functional

    DEFF Research Database (Denmark)

    Reuvers, Robin

    In this thesis, we analyse a variational reformulation of the Bogoliubov approximation that is used to describe weakly-interacting translationally-invariant Bose gases. For the resulting model, the `Bogoliubov free energy functional', we demonstrate existence of minimizers as well as the presence...

  4. Diatomic interaction potential theory applications

    CERN Document Server

    Goodisman, Jerry

    2013-01-01

    Diatomic Interaction Potential Theory, Volume 2: Applications discusses the variety of applicable theoretical material and approaches in the calculations for diatomic systems in their ground states. The volume covers the descriptions and illustrations of modern calculations. Chapter I discusses the calculation of the interaction potential for large and small values of the internuclear distance R (separated and united atom limits). Chapter II covers the methods used for intermediate values of R, which in principle means any values of R. The Hartree-Fock and configuration interaction schemes des

  5. Z-dependent perturbation theory and its application to polyatomic molecules

    International Nuclear Information System (INIS)

    Galvan, D.H.

    1986-01-01

    Z-dependent perturbation theory is applied to study the ground states of simple diatomic and triatomic molecules in order to calculate the total third-order energies for these systems. The systems studied are H 2 + , H 2 , H 3 + , HeH +2 , HeH + , and HeH 2 +2 . The total energies are compared with exact energy values, as well as Hartree-Fock values, and the author's results are a considerable improvement over second-order energies for most internuclear distances, and consistently better than Hartree-Fock calculations for all internuclear distances. Compared with variational methods, this method is simpler and more efficient. In order to calculate total energies up to third order, the wave functions necessary will be two-center, one electron or one-center, two-electron wave functions, at most. Hence, the most complicated integrals that have to be performed are three-center, two-electron integrals, and four-center, one-electron integrals, no matter how complex the molecular system. More importantly, the results obtained for the one-electron diatomic molecular ion are directly incorporated into the calculations for polyatomic systems

  6. Study of the tensor correlation in a neutron-rich sd-shell region with the charge- and parity-projected Hartree-Fock method

    International Nuclear Information System (INIS)

    Sugimoto, Satoru; Toki, Hiroshi; Ikeda, Kiyomi

    2008-01-01

    We study the effect of the tensor force on nuclear structure with mean-field and beyond-mean-field methods. An important correlation induced by the tensor force is two-particle-two-hole (2p2h) correlation, which cannot be treated with a usual mean-filed method. To treat the 2p2h tensor correlation, we develop a new framework (charge- and parity-projected Hartree-Fock (CPPHF) method), which is a beyond-mean-field method. In the CPPHF method, we introduce single-particle states with parity and charge mixing. The parity and charge projections are performed on a total wave function before variation. We apply the CPPHF method to oxygen isotopes including neutron-rich ones. The potential energy from the tensor force has the same order of magnitude with that from the LS force and becomes smaller with neutron number, which indicates that excess neutrons do not contribute to the 2p2h tensor correlation significantly. We also study the effect of the tensor force on spin-orbit-splitting (ls-splitting) in a neutron-rich fluorine isotope 23 F. The tensor force reduces the ls-splitting for the proton d-orbits by about 3 MeV. This effect is important to reproduce the experimental value. We also find that the 2p2h tensor correlation does not affect the ls-splitting in 23 F

  7. Roothaan’s approach to solve the Hartree-Fock equations for atoms confined by soft walls: Basis set with correct asymptotic behavior

    Energy Technology Data Exchange (ETDEWEB)

    Rodriguez-Bautista, Mariano; Díaz-García, Cecilia; Navarrete-López, Alejandra M.; Vargas, Rubicelia; Garza, Jorge, E-mail: jgo@xanum.uam.mx [Departamento de Química, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Col. Vicentina, Iztapalapa C. P. 09340, México D. F., México (Mexico)

    2015-07-21

    In this report, we use a new basis set for Hartree-Fock calculations related to many-electron atoms confined by soft walls. One- and two-electron integrals were programmed in a code based in parallel programming techniques. The results obtained with this proposal for hydrogen and helium atoms were contrasted with other proposals to study just one and two electron confined atoms, where we have reproduced or improved the results previously reported. Usually, an atom enclosed by hard walls has been used as a model to study confinement effects on orbital energies, the main conclusion reached by this model is that orbital energies always go up when the confinement radius is reduced. However, such an observation is not necessarily valid for atoms confined by penetrable walls. The main reason behind this result is that for atoms with large polarizability, like beryllium or potassium, external orbitals are delocalized when the confinement is imposed and consequently, the internal orbitals behave as if they were in an ionized atom. Naturally, the shell structure of these atoms is modified drastically when they are confined. The delocalization was an argument proposed for atoms confined by hard walls, but it was never verified. In this work, the confinement imposed by soft walls allows to analyze the delocalization concept in many-electron atoms.

  8. Thouless-Valatin rotational moment of inertia from linear response theory

    Science.gov (United States)

    Petrík, Kristian; Kortelainen, Markus

    2018-03-01

    Spontaneous breaking of continuous symmetries of a nuclear many-body system results in the appearance of zero-energy restoration modes. These so-called spurious Nambu-Goldstone modes represent a special case of collective motion and are sources of important information about the Thouless-Valatin inertia. The main purpose of this work is to study the Thouless-Valatin rotational moment of inertia as extracted from the Nambu-Goldstone restoration mode that results from the zero-frequency response to the total-angular-momentum operator. We examine the role and effects of the pairing correlations on the rotational characteristics of heavy deformed nuclei in order to extend our understanding of superfluidity in general. We use the finite-amplitude method of the quasiparticle random-phase approximation on top of the Skyrme energy density functional framework with the Hartree-Fock-Bogoliubov theory. We have successfully extended this formalism and established a practical method for extracting the Thouless-Valatin rotational moment of inertia from the strength function calculated in the symmetry-restoration regime. Our results reveal the relation between the pairing correlations and the moment of inertia of axially deformed nuclei of rare-earth and actinide regions of the nuclear chart. We have also demonstrated the feasibility of the method for obtaining the moment of inertia for collective Hamiltonian models. We conclude that from the numerical and theoretical perspective, the finite-amplitude method can be widely used to effectively study rotational properties of deformed nuclei within modern density functional approaches.

  9. Vortex formation in a rotating two-component Fermi gas

    Energy Technology Data Exchange (ETDEWEB)

    Warringa, Harmen J.; Sedrakian, Armen [Institut fuer Theoretische Physik, Goethe-Universitaet Frankfurt am Main, Max-von-Laue-Strasse 1, D-60438 Frankfurt am Main (Germany)

    2011-08-15

    A two-component Fermi gas with attractive s-wave interactions forms a superfluid at low temperatures. When this gas is confined in a rotating trap, fermions can unpair at the edges of the gas and vortices can arise beyond certain critical rotation frequencies. We compute these critical rotation frequencies and construct the phase diagram in the plane of scattering length and rotation frequency for different total numbers of particles. We work at zero temperature and consider a cylindrically symmetric harmonic trapping potential. The calculations are performed in the Hartree-Fock-Bogoliubov approximation which implies that our results are quantitatively reliable for weak interactions.

  10. Shape mixing dynamics in the low-lying states of proton-rich Kr isotopes

    International Nuclear Information System (INIS)

    Sato, Koichi; Hinohara, Nobuo

    2011-01-01

    We study the oblate-prolate shape mixing in the low-lying states of proton-rich Kr isotopes using the five-dimensional quadrupole collective Hamiltonian. The collective Hamiltonian is derived microscopically by means of the CHFB (constrained Hartree-Fock-Bogoliubov) + Local QRPA (quasiparticle random phase approximation) method, which we have developed recently on the basis of the adiabatic self-consistent collective coordinate method. The results of the numerical calculation show the importance of large-amplitude collective vibrations in the triaxial shape degree of freedom and rotational effects on the oblate-prolate shape mixing dynamics in the low-lying states of these isotopes.

  11. Comparison of various HFB overlap formulae

    International Nuclear Information System (INIS)

    Oi, M.

    2015-01-01

    The nuclear many-body approach beyond the mean-field approximation demands overlap calculations of different many-body states. Norm overlaps between two different Hartree-Fock-Bogoliubov states can be calculated by means of the Onishi formula. However, the formula leaves the sign of the norm overlap undetermined. Several approaches have been proposed by Hara-Hayashi-Ring, Neergård-Wüst, and Robledo. In the present paper, the Neergård-Wüst formula is examined whether it is applicable to practical numerical calculations, although the formula was dismissed by many nuclear theoreticians so far for unknown reasons

  12. Low-energy coupling of individual and collective degrees of freedom: a general microscopic approach

    International Nuclear Information System (INIS)

    Quentin, P.; Meyer, M.

    1988-01-01

    A general microscopic approach of low energy coupling of individual and collective degrees of freedom is presented. The ingredients of a Bohr-Mottelson unified model description are determined consistently from the Skyrme SIII effective interaction, through the adiabatic limit of the time-dependent Hartree-Fock-Bogoliubov approximation. Three specific aspects will be mostly developed: i) the effect of pairing correlations on adiabatic mass parameters and collective dynamics; ii) a consistent coupling of collective and individual degrees of freedom to describe odd nuclei; iii) a study of spectroscopic data in odd-odd nuclei as a test of effective nucleon-nucleon interactions. (author)

  13. Stochastic TDHF and the Boltzman-Langevin equation

    International Nuclear Information System (INIS)

    Suraud, E.; Reinhard, P.G.

    1991-01-01

    Outgoing from a time-dependent theory of correlations, we present a stochastic differential equation for the propagation of ensembles of Slater determinants, called Stochastic Time-Dependent Hartree-Fock (Stochastic TDHF). These ensembles are allowed to develop large fluctuations in the Hartree-Fock mean fields. An alternative stochastic differential equation, the Boltzmann-Langevin equation, can be derived from Stochastic TDHF by averaging over subensembles with small fluctuations

  14. Bogoliubov coefficients for the twist operator in the D1D5 CFT

    Directory of Open Access Journals (Sweden)

    Zaq Carson

    2014-12-01

    Full Text Available The D1D5 CFT is a holographic dual of a near-extremal black hole in string theory. The interaction in this theory involves a twist operator which joins together different copies of a free CFT. Given a large number of D1 and D5 branes, the effective length of the circle on which the CFT lives is very large. We develop a technique to study the effect of the twist operator in the limit where the wavelengths of excitations are short compared to this effective length, which we call the ‘continuum limit’. The method uses Bogoliubov coefficients to compute the effect of the twist operator in this limit. For bosonic fields, we use the method to reproduce recent results describing the effect of the twist operator when it links together CFT copies with windings M and N, producing a copy of winding M+N. We also comment on possible generalizations of our results. The methods developed here may help in understanding the twist interaction at higher orders. This in turn should provide insight into the thermalization process in the D1D5 CFT, which gives a holographic description of black hole formation.

  15. Microscopic theory of dynamical subspace for large amplitude collective motion

    International Nuclear Information System (INIS)

    Sakata, Fumihiko; Marumori, Toshio; Ogura, Masanori.

    1986-01-01

    A full quantum theory appropriate for describing large amplitude collective motion is proposed by exploiting the basic idea of the semi-classical theory so far developed within the time-depedent Hartree-Fock theory. A central problem of the quantum theory is how to determine an optimal representation called a dynamical representation specific for the collective subspace where the large amplitude collective motion is replicated as precisely as possible. As an extension of the semi-classical theory where the concept of an approximate integral surface played an important role, the collective subspace is properly characterized by introducing a concept of an approximate invariant subspace of the Hamiltonian. (author)

  16. Electron impact ionization of heavy ions: some surprises

    International Nuclear Information System (INIS)

    Younger, S.M.

    1986-01-01

    This paper reports the results of calculations of electron impact ionization cross sections for a variety of heavy ions using a distorted wave Born-exchange approximation. The target is described by a Hartree-Fock wavefunction. The scattering matrix element is represented by a triple partial wave expansion over incident, scattered, and ejected (originally bound) continuum states. These partial waves are computed in the potentials associated with the initial target (incident and scattered waves) and the residual ion (ejected waves). A Gauss integration was performed over the distribution of energy between the two final state continuum electrons. For ionization of closed d- and f-subshells, the ejected f-waves were computed in frozen-core term-dependent Hartree-Fock potentials, which include the strong repulsive contribution in singlet terms which arises from the interaction of an excited orbital with an almost closed shell. Ground state correlation was included in some calculations of ionization of d 10 subshells

  17. Time-dependent restricted-active-space self-consistent-field theory for laser-driven many-electron dynamics

    DEFF Research Database (Denmark)

    Miyagi, Haruhide; Madsen, Lars Bojer

    2013-01-01

    We present the time-dependent restricted-active-space self-consistent-field (TD-RASSCF) theory as a framework for the time-dependent many-electron problem. The theory generalizes the multiconfigurational time-dependent Hartree-Fock (MCTDHF) theory by incorporating the restricted-active-space scheme...... well known in time-independent quantum chemistry. Optimization of the orbitals as well as the expansion coefficients at each time step makes it possible to construct the wave function accurately while using only a relatively small number of electronic configurations. In numerical calculations of high...

  18. Fractional Quantum Field Theory: From Lattice to Continuum

    Directory of Open Access Journals (Sweden)

    Vasily E. Tarasov

    2014-01-01

    Full Text Available An approach to formulate fractional field theories on unbounded lattice space-time is suggested. A fractional-order analog of the lattice quantum field theories is considered. Lattice analogs of the fractional-order 4-dimensional differential operators are proposed. We prove that continuum limit of the suggested lattice field theory gives a fractional field theory for the continuum 4-dimensional space-time. The fractional field equations, which are derived from equations for lattice space-time with long-range properties of power-law type, contain the Riesz type derivatives on noninteger orders with respect to space-time coordinates.

  19. Higher order alchemical derivatives from coupled perturbed self-consistent field theory.

    Science.gov (United States)

    Lesiuk, Michał; Balawender, Robert; Zachara, Janusz

    2012-01-21

    We present an analytical approach to treat higher order derivatives of Hartree-Fock (HF) and Kohn-Sham (KS) density functional theory energy in the Born-Oppenheimer approximation with respect to the nuclear charge distribution (so-called alchemical derivatives). Modified coupled perturbed self-consistent field theory is used to calculate molecular systems response to the applied perturbation. Working equations for the second and the third derivatives of HF/KS energy are derived. Similarly, analytical forms of the first and second derivatives of orbital energies are reported. The second derivative of Kohn-Sham energy and up to the third derivative of Hartree-Fock energy with respect to the nuclear charge distribution were calculated. Some issues of practical calculations, in particular the dependence of the basis set and Becke weighting functions on the perturbation, are considered. For selected series of isoelectronic molecules values of available alchemical derivatives were computed and Taylor series expansion was used to predict energies of the "surrounding" molecules. Predicted values of energies are in unexpectedly good agreement with the ones computed using HF/KS methods. Presented method allows one to predict orbital energies with the error less than 1% or even smaller for valence orbitals. © 2012 American Institute of Physics

  20. White noise calculus and Fock space

    CERN Document Server

    Obata, Nobuaki

    1994-01-01

    White Noise Calculus is a distribution theory on Gaussian space, proposed by T. Hida in 1975. This approach enables us to use pointwise defined creation and annihilation operators as well as the well-established theory of nuclear space.This self-contained monograph presents, for the first time, a systematic introduction to operator theory on fock space by means of white noise calculus. The goal is a comprehensive account of general expansion theory of Fock space operators and its applications. In particular,first order differential operators, Laplacians, rotation group, Fourier transform and their interrelations are discussed in detail w.r.t. harmonic analysis on Gaussian space. The mathematical formalism used here is based on distribution theory and functional analysis , prior knowledge of white noise calculus is not required.

  1. Continuum gauge theories

    International Nuclear Information System (INIS)

    Stora, R.

    1976-09-01

    The mathematics of gauge fields and some related concepts are discussed: some corrections on the principal fiber bundles emphasize the idea that the present formulation of continuum theories is incomplete. The main ingredients used through the construction of the renormalized perturbation series are then described: the Faddeev Popov argument, and the Faddeev Popov Lagrangian; the Slavnov symmetry and the nature of the Faddeev Popov ghost fields; the Slavnov identity, with an obstruction: the Adler Bardeen anomaly, and its generalization to the local cohomology of the gauge Lie algebra. Some smooth classical configurations of gauge fields which ought to play a prominent role in the evaluation of the functional integral describing the theory are also reviewed

  2. The Hartree product and the description of local and global quantities in atomic systems: A study within Kohn-Sham theory

    International Nuclear Information System (INIS)

    Garza, Jorge; Nichols, Jeffrey A.; Dixon, David A.

    2000-01-01

    The Hartree product is analyzed in the context of Kohn-Sham theory. The differential equations that emerge from this theory are solved with the optimized effective potential using the Krieger, Li, and Iafrate approximation, in order to get a local potential as required by the ordinary Kohn-Sham procedure. Because the diagonal terms of the exact exchange energy are included in Hartree theory, it is self-interaction free and the exchange potential has the proper asymptotic behavior. We have examined the impact of this correct asymptotic behavior on local and global properties using this simple model to approximate the exchange energy. Local quantities, such as the exchange potential and the average local electrostatic potential are used to examine whether the shell structure in an atom is revealed by this theory. Global quantities, such as the highest occupied orbital energy (related to the ionization potential) and the exchange energy are also calculated. These quantities are contrasted with those obtained from calculations with the local density approximation, the generalized gradient approximation, and the self-interaction correction approach proposed by Perdew and Zunger. We conclude that the main characteristics in an atomic system are preserved with the Hartree theory. In particular, the behavior of the exchange potential obtained in this theory is similar to those obtained within other Kohn-Sham approximations. (c) 2000 American Institute of Physics

  3. Constrained Hartree-Fock and beyond

    International Nuclear Information System (INIS)

    Berger, J.F.; Girod, M.; Gogny, D.

    1989-01-01

    Completely microscopic descriptions of the fission phenomenon based on the nuclear mean field theory and its extensions are reviewed. The basic ideas underlying this kind of approach and the way one can set up a consistent microscopic dynamical model of the low energy fission process are presented. The main difficulties encountered in earlier calculations when trying to reproduce experimental fission barriers and to account for scission are recalled. We describe the method by which these difficulties have been overcome and discuss recent results. They concern a proposed interpretation for the scission mechanism and 'cold fission' events. Other issues like adiabaticity in the descent from the second saddle to scission and odd-even effects in cold fission are also discussed. (orig.)

  4. Theoretical calculations of electron-impact and radiative processes in atoms

    International Nuclear Information System (INIS)

    Pindzola, M.S.

    1975-01-01

    Electron-impact and radiative processes in atoms are investigated with particular attention paid to the effects of electron correlations. Using the optical potential method, the cross section for the elastic scattering of electrons by the neutral argon atom is calculated from 0 to 300 eV. Corrections to the Hartree--Fock cross section are obtained from a many-particle perturbation expansion. The effects of electron correlations are found to be quite significant at low energy. The optical potential results are compared with a polarized orbital calculation, the Born approximation and experiment. The 2s and 2p excitation cross sections for electron scattering on hydrogen are calculated by two similar methods. The distorted wave method is applied and the effect of calculating the outgoing scattered electron in the potential of the initial or final state is investigated. The imaginary part of the optical potential is also calculated in lowest order by the use of many-body diagrams. The subshell photoionization cross sections in argon are calculated using the acceleration, length and velocity forms of the dipole operator. First order electron correlation corrections to the Hartree--Fock approximation are obtained through the use of many-body perturbation theory. Also investigated is the two photon ionization cross section for the neutral argon atom. A double perturbation expansion in the Coulomb correlations and the atom-radiation field interaction is made. Contributions from intermediate states are obtained by direct summation over Hartree--Fock bound and continuum single particle states. The effects of electron correlations and photon radiative corrections are investigated

  5. On the consistent solution of the gap-equation for spontaneously broken λΦ4-theory

    International Nuclear Information System (INIS)

    Nachbagauer, H.

    1994-10-01

    A self-consistent solution of the finite temperature gap-equation for λΦ 4 theory beyond the Hartree-Fock approximation is presented using a composite operator effective action. It was found that in a spontaneously broken theory not only the so-called daisy and super daisy graphs contribute to the re summed mass, but also re summed non-local diagrams are of the same order, thus altering the effective mass for small values of the latter. (author). 10 refs., 3 figs., 1 tab

  6. Molecular dynamics of a proguanil derivative | Muhammad | Bayero ...

    African Journals Online (AJOL)

    ... ab-initio Quantum chemical calculations at the Restricted Hatree-Fock (RHF) ... and 6-31++G basis sets were carried out for inclusion of electron correlation. ... The dipole moment of the Proguanil's derivative at both levels of theory is ... Keywords: Proguanil, Density Functional Theory, Restricted Hartree Fock, Gaussian ...

  7. Zitterbewegung in Bogoliubov's System

    International Nuclear Information System (INIS)

    Li Yan; Su Hong-Yi; Chen Jing-Ling; Zhang Fu-Lin; Wu Chun-Feng; Leong-Chuan Kwek

    2015-01-01

    We show that Bogoliubov's quasiparticle in superfluid 3 He-B undergoes the Zitterbewegung, as a free relativistic Dirac's electron does. The expectation value of position, as well as spin, of the quasiparticle is obtained and compared with that of the Dirac's electron. In particular, the Zitterbewegung of Bogoliubov's quasiparticle has a frequency approximately 10 5 lower than that of an electron, rendering a more promising experimental observation. (general)

  8. Continuum theory for nanotube piezoelectricity.

    Science.gov (United States)

    Michalski, P J; Sai, Na; Mele, E J

    2005-09-09

    We develop and solve a continuum theory for the piezoelectric response of one-dimensional nanotubes and nanowires, and apply the theory to study electromechanical effects in boron-nitride nanotubes. We find that the polarization of a nanotube depends on its aspect ratio, and a dimensionless constant specifying the ratio of the strengths of the elastic and electrostatic interactions. The solutions of the model as these two parameters are varied are discussed. The theory is applied to estimate the electric potential induced along the length of a boron-nitride nanotube in response to a uniaxial stress.

  9. Gauge-invariant variational methods for Hamiltonian lattice gauge theories

    International Nuclear Information System (INIS)

    Horn, D.; Weinstein, M.

    1982-01-01

    This paper develops variational methods for calculating the ground-state and excited-state spectrum of Hamiltonian lattice gauge theories defined in the A 0 = 0 gauge. The scheme introduced in this paper has the advantage of allowing one to convert more familiar tools such as mean-field, Hartree-Fock, and real-space renormalization-group approximation, which are by their very nature gauge-noninvariant methods, into fully gauge-invariant techniques. We show that these methods apply in the same way to both Abelian and non-Abelian theories, and that they are at least powerful enough to describe correctly the physics of periodic quantum electrodynamics (PQED) in (2+1) and (3+1) space-time dimensions. This paper formulates the problem for both Abelian and non-Abelian theories and shows how to reduce the Rayleigh-Ritz problem to that of computing the partition function of a classical spin system. We discuss the evaluation of the effective spin problem which one derives the PQED and then discuss ways of carrying out the evaluation of the partition function for the system equivalent to a non-Abelian theory. The explicit form of the effective partition function for the non-Abelian theory is derived, but because the evaluation of this function is considerably more complicated than the one derived in the Abelian theory no explicit evaluation of this function is presented. However, by comparing the gauge-projected Hartree-Fock wave function for PQED with that of the pure SU(2) gauge theory, we are able to show that extremely interesting differences emerge between these theories even at this simple level. We close with a discussion of fermions and a discussion of how one can extend these ideas to allow the computation of the glueball and hadron spectrum

  10. Baryonic forces and hyperons in nuclear matter from SU(3) chiral effective field theory

    Energy Technology Data Exchange (ETDEWEB)

    Petschauer, Stefan Karl

    2016-02-12

    In this work the baryon-baryon interaction is studied at next-to-leading order in SU(3) chiral effective field theory and applied to hyperon-nucleon scattering. The properties of hyperons in isospin-symmetric as well as asymmetric nuclear matter are calculated within the Bruecker-Hartree-Fock formalism. Moreover, the leading three-baryon interaction is derived and its low-energy constants are estimated from decuplet intermediate states. We conclude, that chiral effective field theory is a well-suited tool to describe the baryonic forces.

  11. Applicability of self-consistent mean-field theory

    International Nuclear Information System (INIS)

    Guo Lu; Sakata, Fumihiko; Zhao Enguang

    2005-01-01

    Within the constrained Hartree-Fock (CHF) theory, an analytic condition is derived to estimate whether a concept of the self-consistent mean field is realized in the level repulsive region. The derived condition states that an iterative calculation of the CHF equation does not converge when the quantum fluctuations coming from two-body residual interaction and quadrupole deformation become larger than a single-particle energy difference between two avoided crossing orbits. By means of numerical calculation, it is shown that the analytic condition works well for a realistic case

  12. Quantum stochastic calculus in Fock space: A review

    International Nuclear Information System (INIS)

    Hudson, R.L.

    1986-01-01

    This paper presents a survey of the recently developed theory of quantum stochastic calculus in Boson Fock space, together with its applications. The work focuses on a non-commutative generalization of the classical Ito stochastic calculus of Brownian motion, which exploits to the full the Wiener-Segal duality transformation identifying the L 2 space of Wiener measure with a Boson Fock space. This Fock space emerges as the natural home of not only Brownian motion but also classical Poisson processes, and even of Fermionic processes of the type developed by Barnett et al. The principle physical application of the theory to the construction and characterization of unitary dilations of quantum dynamical semigroups is also described

  13. Quantum theory of dynamical collective subspace for large-amplitude collective motion

    International Nuclear Information System (INIS)

    Sakata, Fumihiko; Marumori, Toshio; Ogura, Masanori.

    1986-03-01

    By placing emphasis on conceptual correspondence to the ''classical'' theory which has been developed within the framework of the time-dependent Hartree-Fock theory, a full quantum theory appropriate for describing large-amplitude collective motion is proposed. A central problem of the quantum theory is how to determine an optimal representation called a dynamical representation; the representation is specific for the collective subspace where the large-amplitude collective motion is replicated as satisfactorily as possible. As an extension of the classical theory where the concept of an approximate integral surface plays an important role, the dynamical representation is properly characterized by introducing a concept of an approximate invariant subspace of the Hamiltonian. (author)

  14. Self-consistent-field method and τ-functional method on group manifold in soliton theory. II. Laurent coefficients of soliton solutions for sln and for sun

    International Nuclear Information System (INIS)

    Nishiyama, Seiya; Providencia, Joao da; Komatsu, Takao

    2007-01-01

    To go beyond perturbative method in terms of variables of collective motion, using infinite-dimensional fermions, we have aimed to construct the self-consistent-field (SCF) theory, i.e., time dependent Hartree-Fock theory on associative affine Kac-Moody algebras along the soliton theory. In this paper, toward such an ultimate goal we will reconstruct a theoretical frame for a υ (external parameter)-dependent SCF method to describe more precisely the dynamics on the infinite-dimensional fermion Fock space. An infinite-dimensional fermion operator is introduced through Laurent expansion of finite-dimensional fermion operators with respect to degrees of freedom of the fermions related to a υ-dependent and a Υ-periodic potential. As an illustration, we derive explicit expressions for the Laurent coefficients of soliton solutions for sl n and for su n on infinite-dimensional Grassmannian. The associative affine Kac-Moody algebras play a crucial role to determine the dynamics on the infinite-dimensional fermion Fock space

  15. Alpha Decay of Even-Even Superheavy Nuclei

    International Nuclear Information System (INIS)

    Oudih, M.R.; Hamza, Y.; Fellah, M.; Allal, N.H.; Fellah, M.; Allal, N.H.

    2011-01-01

    Alpha decay properties of even-even superheavy nuclei with 112.Z.120 have been investigated using the Hartree-Fock-Bogoliubov approach. The method is based on the SkP Skyrme interaction and the Lipkin-Nogami prescription for treating the pairing correlations. The alpha decay energies are extracted from the binding energies and then used for the calculation of the decay half-lives using a formula similar to that of Viola-Seaborg. The parameters of the formula were obtained through a least square fit to even-even heavy nuclei taken from the tables of Audi- Wapstra and some more recent references. The results are compared with other theoretical evaluations.

  16. Microscopic structure of superdeformed states in Th, U, Pu and Cm isotopes with Gogny force

    Energy Technology Data Exchange (ETDEWEB)

    Girod, M.; Delaroche, J.P.; Romain, P. [CEA/DIF, DPTA/SPN, Boite Postale 12, 91680 Bruyeres-le-Chatel (France); Libert, J. [Institut de Physique Nucleaire Centre National de la Recherche Scientifique-IN2P3, F-91406 Orsay (France)

    2002-10-01

    The structure properties of the even-even nuclei {sup 226,} {sup 228,} {sup 230,} {sup 232,} {sup 234}Th, {sup 230,} {sup 232,} {sup 234,} {sup 236,} {sup 238,} {sup 240}U, {sup 240,} {sup 242,} {sup 244,} {sup 246}Pu, and {sup 242,} {sup 244,} {sup 246,} {sup 248}Cm have been investigated at normal and superdeformed shapes in microscopic mean-field calculations based on Gogny force. Collective levels are predicted from constrained Hartree-Fock-Bogoliubov and configuration mixing calculations. Two quasiparticle states are also predicted from blocking calculations for neutron and proton configurations. Predictions are shown and compared with experimental data at superdeformed shapes. (orig.)

  17. Evidence for a smooth onset of deformation in the neutron-rich Kr isotopes

    CERN Document Server

    Albers, M; Nomura, K; Blazhev, A; Jolie, J; Mucher, D; Bastin, B; Bauer, C; Bernards, C; Bettermann, L; Bildstein, V; Butterworth, J; Cappellazzo, M; Cederkall, J; Cline, D; Darby, I; Das Gupta, S; Daugas, J M; Davinson, T; De Witte, H; Diriken, J; Filipescu, D; Fiori, E; Fransen, C; Gaffney, L P; Georgiev, G; Gernhauser, R; Hackstein, M; Heinze, S; Hess, H; Huyse, M; Jenkins, D; Konki, J; Kowalczyk, M; Kroll, T; Krucken, R; Litzinger, J; Lutter, R; Marginean, N; Mihai, C; Moschner, K; Napiorkowski, P; Nara Singh, B S; Nowak, K; Otsuka, T; Pakarinen, J; Pfeiffer, M; Radeck, D; Reiter, P; Rigby, S; Robledo, L M; Rodriguez-Guzman, R; Rudigier, M; Sarriguren, P; Scheck, M; Seidlitz, M; Siebeck, B; Simpson, G; Thole, P; Thomas, T; Van de Walle, J; Van Duppen, P; Vermeulen, M; Voulot, D; Wadsworth, R; Wenander, F; Wimmer, K; Zell, K O; Zielinska, M

    2012-01-01

    The neutron-rich nuclei $^{94,96}$Kr were studied via projectile Coulomb excitation at the REX-ISOLDE facility at CERN. Level energies of the first excited 2$^{+}$ states and their absolute $E2$ transition strengths to the ground state are determined and discussed in the context of the $E(2^{+}_{1})$ and $B(E2;2^{+}_{1} \\rightarrow 0^{+}_{1})$ systematics of the krypton chain. Contrary to previously published results no sudden onset of deformation is observed. This experimental result is supported by a new proton-neutron interacting boson model calculation based on the constrained Hartree-Fock-Bogoliubov approach using the microscopic Gogny-D1M energy density functional.

  18. Recent development of relativistic molecular theory

    International Nuclear Information System (INIS)

    Takahito, Nakajima; Kimihiko, Hirao

    2005-01-01

    Today it is common knowledge that relativistic effects are important in the heavy-element chemistry. The continuing development of the relativistic molecular theory is opening up rows of the periodic table that are impossible to treat with the non-relativistic approach. The most straightforward way to treat relativistic effects on heavy-element systems is to use the four-component Dirac-Hartree-Fock approach and its electron-correlation methods based on the Dirac-Coulomb(-Breit) Hamiltonian. The Dirac-Hartree-Fock (DHF) or Dirac-Kohn-Sham (DKS) equation with the four-component spinors composed of the large- and small-components demands severe computational efforts to solve, and its applications to molecules including heavy elements have been limited to small- to medium-size systems. Recently, we have developed a very efficient algorithm for the four-component DHF and DKS approaches. As an alternative approach, several quasi-relativistic approximations have also been proposed instead of explicitly solving the four-component relativistic equation. We have developed the relativistic elimination of small components (RESC) and higher-order Douglas-Kroll (DK) Hamiltonians within the framework of the two-component quasi-relativistic approach. The developing four-component relativistic and approximate quasi-relativistic methods have been implemented into a program suite named REL4D. In this article, we will introduce the efficient relativistic molecular theories to treat heavy-atomic molecular systems accurately via the four-component relativistic and the two-component quasi-relativistic approaches. We will also show several chemical applications including heavy-element systems with our relativistic molecular approaches. (author)

  19. Spectroscopic criteria for identification of nuclear tetrahedral and octahedral symmetries: Illustration on a rare earth nucleus

    Science.gov (United States)

    Dudek, J.; Curien, D.; Dedes, I.; Mazurek, K.; Tagami, S.; Shimizu, Y. R.; Bhattacharjee, T.

    2018-02-01

    We formulate criteria for identification of the nuclear tetrahedral and octahedral symmetries and illustrate for the first time their possible realization in a rare earth nucleus 152Sm. We use realistic nuclear mean-field theory calculations with the phenomenological macroscopic-microscopic method, the Gogny-Hartree-Fock-Bogoliubov approach, and general point-group theory considerations to guide the experimental identification method as illustrated on published experimental data. Following group theory the examined symmetries imply the existence of exotic rotational bands on whose properties the spectroscopic identification criteria are based. These bands may contain simultaneously states of even and odd spins, of both parities and parity doublets at well-defined spins. In the exact-symmetry limit those bands involve no E 2 transitions. We show that coexistence of tetrahedral and octahedral deformations is essential when calculating the corresponding energy minima and surrounding barriers, and that it has a characteristic impact on the rotational bands. The symmetries in question imply the existence of long-lived shape isomers and, possibly, new waiting point nuclei—impacting the nucleosynthesis processes in astrophysics—and an existence of 16-fold degenerate particle-hole excitations. Specifically designed experiments which aim at strengthening the identification arguments are briefly discussed.

  20. Towards an improved continuum theory for phase transformations

    International Nuclear Information System (INIS)

    Tijssens, M.G.A.; James, R.D.

    2003-01-01

    We develop a continuum theory for martensitic phase transformations in which explicit use is made of atomistic calculations based on density functional theory. Following the work of Rabe and coworkers, branches of the phonon-dispersion relation with imaginary frequencies are selected to construct a localized basis tailored to the symmetry of the crystal lattice. This so-called Wannier basis helps to construct an effective Hamiltonian of a particularly simple form. We extend the methodology by incorporating finite deformations and passing the effective Hamiltonian fully to continuum level. The developments so far are implemented on the shape memory material NiTi

  1. Dirac-Fock-Breit-Gaunt calculations for tungsten hexacarbonyl W(CO)6.

    Science.gov (United States)

    Malli, Gulzari L

    2016-05-21

    The first all-electron fully relativistic Dirac-Fock-Breit-Gaunt (DFBG), Dirac-Fock (DF), and nonrelativistic (NR) Hartree-Fock (HF) calculations are reported for octahedral (Oh) tungsten hexacarbonyl W(CO)6. Our DF and NR HF calculations predict atomization energy of 73.76 and 70.33 eV, respectively. The relativistic contribution of ∼3.4 eV to the atomization energy of W(CO)6 is fairly significant. The DF and NR energy for the reaction W + 6CO → W(CO)6 is calculated as -7.90 and -8.86 eV, respectively. The mean bond energy predicted by our NR and DF calculations is 142.5 kJ/mol and 177.5 kJ/mol, respectively, and our predicted DF mean bond energy is in excellent agreement with the experimental value of 179 kJ/mol quoted in the literature. The relativistic effects contribute ∼35 kJ/mol to the mean bond energy and the calculated BSSE is 1.6 kcal/mol, which indicates that the triple zeta basis set used here is fairly good. The mean bond energy and the atomization energy calculated in our DFBG SCF calculations, which include variationally both the relativistic and magnetic Breit effects, is 157.4 kJ/mol and 68.84 eV, respectively. The magnetic Breit effects lead to a decrease of ∼20 kJ/mol and ∼4.9 eV for the mean bond energy and atomization energy, respectively, for W(CO)6. Our calculated magnetic Breit interaction energy of -9.79 eV for the energy of reaction (ΔE) for W + 6CO → W(CO)6 is lower by ∼1.90 eV as compared to the corresponding DF value (ΔE) and contributes significantly to the ΔE. A detailed discussion is presented of electronic structure, bonding, and molecular energy levels at various levels of theory for W(CO)6.

  2. Roothaan approach in the thermodynamic limit

    International Nuclear Information System (INIS)

    Gutierrez, G.; Plastino, A.

    1982-01-01

    A systematic method for the solution of the Hartree-Fock equations in the thermodynamic limit is presented. The approach is seen to be a natural extension of the one usually employed in the finite-fermion case, i.e., that developed by Roothaan. The new techniques developed here are applied, as an example, to neutron matter, employing the so-called V 1 Bethe homework potential. The results obtained are, by far, superior to those that the ordinary plane-wave Hartree-Fock theory yields

  3. Variational configuration interaction methods and comparison with perturbation theory

    International Nuclear Information System (INIS)

    Pople, J.A.; Seeger, R.; Krishnan, R.

    1977-01-01

    A configuration interaction (CI) procedure which includes all single and double substitutions from an unrestricted Hartree-Fock single determinant is described. This has the feature that Moller-Plesset perturbation results to second and third order are obtained in the first CI iterative cycle. The procedure also avoids the necessity of a full two-electron integral transformation. A simple expression for correcting the final CI energy for lack of size consistency is proposed. Finally, calculations on a series of small molecules are presented to compare these CI methods with perturbation theory

  4. An advanced kinetic theory for morphing continuum with inner structures

    Science.gov (United States)

    Chen, James

    2017-12-01

    Advanced kinetic theory with the Boltzmann-Curtiss equation provides a promising tool for polyatomic gas flows, especially for fluid flows containing inner structures, such as turbulence, polyatomic gas flows and others. Although a Hamiltonian-based distribution function was proposed for diatomic gas flow, a general distribution function for the generalized Boltzmann-Curtiss equations and polyatomic gas flow is still out of reach. With assistance from Boltzmann's entropy principle, a generalized Boltzmann-Curtiss distribution for polyatomic gas flow is introduced. The corresponding governing equations at equilibrium state are derived and compared with Eringen's morphing (micropolar) continuum theory derived under the framework of rational continuum thermomechanics. Although rational continuum thermomechanics has the advantages of mathematical rigor and simplicity, the presented statistical kinetic theory approach provides a clear physical picture for what the governing equations represent.

  5. SEACAS Theory Manuals: Part II. Nonlinear Continuum Mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.

    1998-09-01

    This report summarizes the key continuum mechanics concepts required for the systematic prescription and numerical solution of finite deformation solid mechanics problems. Topics surveyed include measures of deformation appropriate for media undergoing large deformations, stress measures appropriate for such problems, balance laws and their role in nonlinear continuum mechanics, the role of frame indifference in description of large deformation response, and the extension of these theories to encompass two dimensional idealizations, structural idealizations, and rigid body behavior. There are three companion reports that describe the problem formulation, constitutive modeling, and finite element technology for nonlinear continuum mechanics systems.

  6. The Calculation of Single-Nucleon Energies of Nuclei by Considering Two-Body Effective Interaction, n(k,ρ, and a Hartree-Fock Inspired Scheme

    Directory of Open Access Journals (Sweden)

    H. Mariji

    2016-01-01

    Full Text Available The nucleon single-particle energies (SPEs of the selected nuclei, that is, O16, Ca40, and Ni56, are obtained by using the diagonal matrix elements of two-body effective interaction, which generated through the lowest-order constrained variational (LOCV calculations for the symmetric nuclear matter with the Aυ18 phenomenological nucleon-nucleon potential. The SPEs at the major levels of nuclei are calculated by employing a Hartree-Fock inspired scheme in the spherical harmonic oscillator basis. In the scheme, the correlation influences are taken into account by imposing the nucleon effective mass factor on the radial wave functions of the major levels. Replacing the density-dependent one-body momentum distribution functions of nucleons, n(k,ρ, with the Heaviside functions, the role of n(k,ρ in the nucleon SPEs at the major levels of the selected closed shell nuclei is investigated. The best fit of spin-orbit splitting is taken into account when correcting the major levels of the nuclei by using the parameterized Wood-Saxon potential and the Aυ18 density-dependent mean field potential which is constructed by the LOCV method. Considering the point-like protons in the spherical Coulomb potential well, the single-proton energies are corrected. The results show the importance of including n(k,ρ, instead of the Heaviside functions, in the calculation of nucleon SPEs at the different levels, particularly the valence levels, of the closed shell nuclei.

  7. Analytically continued Fock space multi-reference coupled-cluster theory: Application to the shape resonance

    International Nuclear Information System (INIS)

    Pal, Sourav; Sajeev, Y.; Vaval, Nayana

    2006-01-01

    The Fock space multi-reference coupled-cluster (FSMRCC) method is used for the study of the shape resonance energy and width in an electron-atom/molecule collision. The procedure is based upon combining a complex absorbing potential (CAP) with FSMRCC theory. Accurate resonance parameters are obtained by solving a small non-Hermitian eigen-value problem. We study the shape resonances in e - -C 2 H 4 and e - -Mg

  8. Quantized Bogoliubov transformations

    International Nuclear Information System (INIS)

    Geyer, H.B.

    1984-01-01

    The boson mapping of single fermion operators in a situation dominated by the pairing force gives rise to a transformation that can be considered a quantized version of the Bogoliubov transformation. This transformation can also be obtained as an exact special case of operators constructed from an approximate treatment of particle number projection, suggesting a method of obtaining the boson mapping in cases more complicated than that of pairing force domination

  9. Theory of Kondo effect in superconductors, 2

    International Nuclear Information System (INIS)

    Ichinose, Shin-ichi

    1977-01-01

    Thermodynamic properties of superconducting alloys near the transition temperature are studied within the interpolation approximation which is constructed so as to coincide with theories in limiting cases. By the use of this approximation, the specific heat jump at the transition temperature is calculated in the case of the magnitude of the impurity spin being 1/2. The result shows a continuous change of the specific heat jump with T sub(K)/T sub(c0) from the Abrikosov-Gorkov value to essentially BCS-like behavior in contrast to the Mueller-Hartmann-Zittartz theory. One has an example of a cross over between a weak coupling situation at T sub(K)/T sub(c0) > 1. The Hartree-Fock theory is also discussed in connection with the present calculation. (auth.)

  10. Use of results from microscopic methods in optical model calculations

    International Nuclear Information System (INIS)

    Lagrange, C.

    1985-11-01

    A concept of vectorization for coupled-channel programs based upon conventional methods is first presented. This has been implanted in our program for its use on the CRAY-1 computer. In a second part we investigate the capabilities of a semi-microscopic optical model involving fewer adjustable parameters than phenomenological ones. The two main ingredients of our calculations are, for spherical or well-deformed nuclei, the microscopic optical-model calculations of Jeukenne, Lejeune and Mahaux and nuclear densities from Hartree-Fock-Bogoliubov calculations using the density-dependent force D1. For transitional nuclei deformation-dependent nuclear structure wave functions are employed to weigh the scattering potentials for different shapes and channels [fr

  11. Morphing continuum theory for turbulence: Theory, computation, and visualization

    Science.gov (United States)

    Chen, James

    2017-10-01

    A high order morphing continuum theory (MCT) is introduced to model highly compressible turbulence. The theory is formulated under the rigorous framework of rational continuum mechanics. A set of linear constitutive equations and balance laws are deduced and presented from the Coleman-Noll procedure and Onsager's reciprocal relations. The governing equations are then arranged in conservation form and solved through the finite volume method with a second-order Lax-Friedrichs scheme for shock preservation. A numerical example of transonic flow over a three-dimensional bump is presented using MCT and the finite volume method. The comparison shows that MCT-based direct numerical simulation (DNS) provides a better prediction than Navier-Stokes (NS)-based DNS with less than 10% of the mesh number when compared with experiments. A MCT-based and frame-indifferent Q criterion is also derived to show the coherent eddy structure of the downstream turbulence in the numerical example. It should be emphasized that unlike the NS-based Q criterion, the MCT-based Q criterion is objective without the limitation of Galilean invariance.

  12. Hole trapping at Al impurities in silica: A challenge for density functional theories

    DEFF Research Database (Denmark)

    Lægsgaard, Jesper; Stokbro, Kurt

    2001-01-01

    The atomic geometry and electronic structure around a neutral substitutional Al impurity in silica is investigated using either the unrestricted Hartree-Fock (UHF) approximation, or Beckes three-parameter hybrid functional (B3LYP). It is found that the B3LYP functional fails to describe...... the structural distortions around the Al impurity, while the UHF results are consistent with experimental information. We argue that the failure of the B3LYP functional is caused by the incomplete self-interaction cancellation usually present in density functional theories....

  13. Antieigenvalue analysis for continuum mechanics, economics, and number theory

    Directory of Open Access Journals (Sweden)

    Gustafson Karl

    2016-01-01

    Full Text Available My recent book Antieigenvalue Analysis, World-Scientific, 2012, presented the theory of antieigenvalues from its inception in 1966 up to 2010, and its applications within those forty-five years to Numerical Analysis, Wavelets, Statistics, Quantum Mechanics, Finance, and Optimization. Here I am able to offer three further areas of application: Continuum Mechanics, Economics, and Number Theory. In particular, the critical angle of repose in a continuum model of granular materials is shown to be exactly my matrix maximum turning angle of the stress tensor of the material. The important Sharpe ratio of the Capital Asset Pricing Model is now seen in terms of my antieigenvalue theory. Euclid’s Formula for Pythagorean triples becomes a special case of my operator trigonometry.

  14. Hankel transforms in generalized Fock spaces

    Directory of Open Access Journals (Sweden)

    John Schmeelk

    1994-01-01

    Full Text Available A classical Fock space consists of functions of the form,ϕ↔(ϕ0,ϕ1,…,ϕq,where ϕ0∈ℂ and ϕq∈Lp(ℝq, q≥1. We will replace the ϕq, q≥1 with test functions having Hankel transforms. This space is a natural generalization of a classical Fock space as seen by expanding functionals having abstract Taylor Series. The particular coefficients of such series are multilinear functionals having distributions as their domain. Convergence requirements set forth are somewhat in the spirit of ultra differentiable functions and ultra distribution theory. The Hankel transform oftentimes implemented in Cauchy problems will be introduced into this setting. A theorem will be proven relating the convergence of the transform to the inductive limit parameter, s, which sweeps out a scale of generalized Fock spaces.

  15. Gyromagnetic factors for high spin states in the actinides

    International Nuclear Information System (INIS)

    Ring, P.

    1984-01-01

    The cranked Hartree-Fock-Bogoliubov theory was used for a systematic investigation of gyromagnetic factors in the yrast states of even-even actinide nuclei. The theory used was the most simplified version with fixed deformation and gap parameters, that is, so-called rotating shell model. The gyromagnetic factor g and the contribution gsub(p) and gsub(n) were obtained for a large number of nuclei in the actinide region. The aligned angular momenta for protons and for neutrons are shown in the same actinide region. The general behaviour of g-factor was able to be understood in terms of simple rules: (i) For fixed proton number, neutron alignment becomes more difficult with increasing the neutron number, and vice versa. (ii) A sudden neutron alignment was observed for N=140 and N=146, and a sudden proton alignment was also observed for Z=94. The alignment between these critical numbers was smooth. The pattern obtained for the values of the aligned angular momentum was clearly reflected to the g-factor, and it provided an excellent tool to study the structure of level in the high spin region. (Asami, T.)

  16. Nuclear structure for the crust of neutron stars and exotic nuclei

    International Nuclear Information System (INIS)

    Goegelein, Peter

    2007-01-01

    In this work the Skyrme Hartree-Fock and Relativistic Hartree--Fock approaches have been considered to describe the structure of nuclear systems ranging from finite nuclei, structures in the crust of neutron stars to homogeneous matter. Effects of pairing correlations and finite temperature are also taken into account. The numerical procedure in the cubic box is described for the Skyrme Hartree-Fock as well as the relativistic Hartree-Fock approach. And finally, results for the crust of neutron stars and exotic nuclei are presented and discussed. (orig.)

  17. Nuclear structure for the crust of neutron stars and exotic nuclei

    Energy Technology Data Exchange (ETDEWEB)

    Goegelein, Peter

    2007-07-01

    In this work the Skyrme Hartree-Fock and Relativistic Hartree--Fock approaches have been considered to describe the structure of nuclear systems ranging from finite nuclei, structures in the crust of neutron stars to homogeneous matter. Effects of pairing correlations and finite temperature are also taken into account. The numerical procedure in the cubic box is described for the Skyrme Hartree-Fock as well as the relativistic Hartree-Fock approach. And finally, results for the crust of neutron stars and exotic nuclei are presented and discussed. (orig.)

  18. Functional approach to a time-dependent self-consistent field theory

    International Nuclear Information System (INIS)

    Reinhardt, H.

    1979-01-01

    The time-dependent Hartree-Fock approximation is formulated within the path integral approach. It is shown that by a suitable choice of the collective field the classical equation of motion of the collective field coincides with the time-dependent Hartree (TDH) equation. The consideration is restricted to the TDH equation, since the exchange terms do not appear in the functional approach on the same footing as the direct terms

  19. Asymptotic description of plasma turbulence: Krylov-Bogoliubov methods and quasi-particles

    International Nuclear Information System (INIS)

    Sosenko, P.P.; Bertrand, P.; Decyk, V.K.

    2001-01-01

    The asymptotic theory of charged particle motion in electromagnetic fields is developed for the general case of finite Larmor-radius effects by means of Krylov-Bogoliubov averaging method. The correspondence between the general asymptotic methods, elaborated by M. Krylov and M.Bogoliubov, the quasi-particle description and gyrokinetics is established. Such a comparison is used to shed more light on the physical sense of the reduced Poisson equation, introduced in gyrokinetics, and the particle polarization drift. It is shown that the modification of the Poisson equation in the asymptotic theory is due to the non-conservation of the magnetic moment and gyrophase trembling. it is shown that the second-order modification of the adiabatic invariant can determine the conditions of global plasma stability and introduces new nonlinear terms into the reduced Poisson equation. Such a modification is important for several plasma orderings, e.g. NHD type ordering. The feasibility of numerical simulation schemes in which the polarization drift is included into the quasi-particle equations of motion, and the Poisson equation remains unchanged is analyzed. A consistent asymptotic model is proposed in which the polarization drift is included into the quasi-particle equations of motion and the particle and quasi-particle velocities are equal. It is shown that in such models there are additional modifications of the reduced Poisson equation. The latter becomes even more complicated in contrast to earlier suggestions

  20. Superdeformation in Pb isotopes

    International Nuclear Information System (INIS)

    Naz, Tabassum; Ahmad, Shakeb

    2017-01-01

    The Relatvistic Hartree-Bogoliubov (RHB) theory is used to explore the structure of superdeformed (SD) 190,212 Pb isotopes using the non-linear NL3* and density dependent (DD-ME2, DD-PC1) interactions. We have studied the the excitation energy, the potential depth and the deformation of these Pb isotopes

  1. Straightening the Hierarchical Staircase for Basis Set Extrapolations: A Low-Cost Approach to High-Accuracy Computational Chemistry

    Science.gov (United States)

    Varandas, António J. C.

    2018-04-01

    Because the one-electron basis set limit is difficult to reach in correlated post-Hartree-Fock ab initio calculations, the low-cost route of using methods that extrapolate to the estimated basis set limit attracts immediate interest. The situation is somewhat more satisfactory at the Hartree-Fock level because numerical calculation of the energy is often affordable at nearly converged basis set levels. Still, extrapolation schemes for the Hartree-Fock energy are addressed here, although the focus is on the more slowly convergent and computationally demanding correlation energy. Because they are frequently based on the gold-standard coupled-cluster theory with single, double, and perturbative triple excitations [CCSD(T)], correlated calculations are often affordable only with the smallest basis sets, and hence single-level extrapolations from one raw energy could attain maximum usefulness. This possibility is examined. Whenever possible, this review uses raw data from second-order Møller-Plesset perturbation theory, as well as CCSD, CCSD(T), and multireference configuration interaction methods. Inescapably, the emphasis is on work done by the author's research group. Certain issues in need of further research or review are pinpointed.

  2. Some topics in continuum theory of liquid crystals

    Energy Technology Data Exchange (ETDEWEB)

    Anderson, Claire

    2000-07-01

    Since advancements by Ericksen and Leslie in the 1960's, interest in the continuum theory for liquid crystals has escalated. In this thesis, we present the well established continuum theory for nematics, and apply it to the simple Tsvetkov experiment. This analysis is further extended by studying a similar geometric setup which allows additional degrees of freedom. Steady state solutions are studied, and stable/unstable solutions discussed. The bulk of this thesis however, is concerned with the smectic continuum theory. The theory presented allows variable layer spacing, and hence goes beyond the scope of that proposed by Leslie, Stewart and Nakagawa in 1991. With this theory, we initially study a sample of SmA liquid crystal in the bookshelf geometry between two parallel plates, and subject to a strongly anchored pretilt at the boundaries. Weakly anchored solutions are also briefly discussed at the end of this chapter. This work is extended by considering the same problem with a SmC sample, and the distinct differences between the SmA and SmC solutions are highlighted. Symmetric chevron solutions of C1 and C2 type are discussed fully, and energy considerations are made to find the physically realistic configurations. Again, the last part of this chapter is dedicated to solutions subject to weak anchoring. Finally, we take a brief look at Freedericksz transitions when a magnetic field is applied across a cell containing a SmA sample in the bookshelf geometry. The Freedericksz thresholds for two possible deformations are obtained by linearising the appropriate equation, and solving the resulting eigenvalue problem. Numerical calculations finally show where the transitions occur, and confirm the accuracy of the threshold values obtained analytically. (author)

  3. Some topics in continuum theory of liquid crystals

    International Nuclear Information System (INIS)

    Anderson, Claire

    2000-01-01

    Since advancements by Ericksen and Leslie in the 1960's, interest in the continuum theory for liquid crystals has escalated. In this thesis, we present the well established continuum theory for nematics, and apply it to the simple Tsvetkov experiment. This analysis is further extended by studying a similar geometric setup which allows additional degrees of freedom. Steady state solutions are studied, and stable/unstable solutions discussed. The bulk of this thesis however, is concerned with the smectic continuum theory. The theory presented allows variable layer spacing, and hence goes beyond the scope of that proposed by Leslie, Stewart and Nakagawa in 1991. With this theory, we initially study a sample of SmA liquid crystal in the bookshelf geometry between two parallel plates, and subject to a strongly anchored pretilt at the boundaries. Weakly anchored solutions are also briefly discussed at the end of this chapter. This work is extended by considering the same problem with a SmC sample, and the distinct differences between the SmA and SmC solutions are highlighted. Symmetric chevron solutions of C1 and C2 type are discussed fully, and energy considerations are made to find the physically realistic configurations. Again, the last part of this chapter is dedicated to solutions subject to weak anchoring. Finally, we take a brief look at Freedericksz transitions when a magnetic field is applied across a cell containing a SmA sample in the bookshelf geometry. The Freedericksz thresholds for two possible deformations are obtained by linearising the appropriate equation, and solving the resulting eigenvalue problem. Numerical calculations finally show where the transitions occur, and confirm the accuracy of the threshold values obtained analytically. (author)

  4. BRST quantization of Yang-Mills theory: A purely Hamiltonian approach on Fock space

    Science.gov (United States)

    Öttinger, Hans Christian

    2018-04-01

    We develop the basic ideas and equations for the BRST quantization of Yang-Mills theories in an explicit Hamiltonian approach, without any reference to the Lagrangian approach at any stage of the development. We present a new representation of ghost fields that combines desirable self-adjointness properties with canonical anticommutation relations for ghost creation and annihilation operators, thus enabling us to characterize the physical states on a well-defined Fock space. The Hamiltonian is constructed by piecing together simple BRST invariant operators to obtain a minimal invariant extension of the free theory. It is verified that the evolution equations implied by the resulting minimal Hamiltonian provide a quantum version of the classical Yang-Mills equations. The modifications and requirements for the inclusion of matter are discussed in detail.

  5. Low-lying electric-dipole strengths of Ca, Ni, and Sn isotopes imprinted on total reaction cross sections

    Science.gov (United States)

    Horiuchi, W.; Hatakeyama, S.; Ebata, S.; Suzuki, Y.

    2017-08-01

    Low-lying electric-dipole (E 1 ) strength of a neutron-rich nucleus contains information on neutron-skin thickness, deformation, and shell evolution. We discuss the possibility of making use of total reaction cross sections on 40Ca, 120Sn, and 208Pb targets to probe the E 1 strength of neutron-rich Ca, Ni, and Sn isotopes. They exhibit large enhancement of the E 1 strength at neutron number N >28 , 50, and 82, respectively, due to a change of the single-particle orbits near the Fermi surface participating in the transitions. The density distributions and the electric-multipole strength functions of those isotopes are calculated by the Hartree-Fock+BCS and the canonical-basis-time-dependent-Hartree-Fock-Bogoliubov methods, respectively, using three kinds of Skyrme-type effective interaction. The nuclear and Coulomb breakup processes are respectively described with the Glauber model and the equivalent photon method in which the effect of finite-charge distribution is taken into account. The three Skyrme interactions give different results for the total reaction cross sections because of different Coulomb breakup contributions. The contribution of the low-lying E 1 strength is amplified when the low-incident energy is chosen. With an appropriate choice of the incident energy and target nucleus, the total reaction cross section can be complementary to the Coulomb excitation for analyzing the low-lying E 1 strength of unstable nuclei.

  6. Bogoliubov Angle, Particle-Hole Mixture and Angular Resolved Photoemission Spectroscopy in Superconductors

    Energy Technology Data Exchange (ETDEWEB)

    Balatsky, A.

    2010-05-04

    Superconducting excitations - Bogoliubov quasiparticles - are the quantum mechanical mixture of negatively charged electron (-e) and positively charged hole (+e). We propose a new observable for Angular Resolved Photoemission Spectroscopy (ARPES) studies that is the manifestation of the particle-hole entanglement of the superconducting quasiparticles. We call this observable a Bogoliubov angle. This angle measures the relative weight of particle and hole amplitude in the superconducting (Bogoliubov) quasiparticle. We show how this quantity can be measured by comparing the ratio of spectral intensities at positive and negative energies.

  7. Stability of thermal HFB and dissipative thermal RPA

    CERN Document Server

    Tanabe, K

    1999-01-01

    It is shown that, as for a Nilsson + pairing model, the extended stability condition of the thermal Hartree-Fock-Bogoliubov (THFB) solution coincides with the one of the thermal RPA (TRPA) solution unless the pairing constant G is too large. As possible extensions of the TRPA equation in alternative ways describing thermal fluctuation effect, the extended TRPA (ETRPA) and the dissipative TRPA (DTRPA) are discussed. Furthermore, the general microscopic framework of the TRPA predicts the saturation and decrease of giant resonance width in high temperature limit, i.e. the fragmentation width GAMMA sub f propor to(kT) sup ( sup - sup 3 sup ( sup 2 sup ) sup ) and the spreading width GAMMA suparrow down propor to(kT) sup ( sup - sup 1 sup ( sup 2 sup ) sup ).

  8. Microscopic description of low-energy nuclear collisions: review and perspective

    International Nuclear Information System (INIS)

    Bonche, Paul

    2000-01-01

    The primary goal of this lecture is a review of the microscopic approaches to nuclear reactions. Semi-phenomenological theories will not be discussed. First the Time-Dependent Hartree-Fock formalism is recalled. The effective nucleon-nucleon interactions used in TDHF calculations are discussed. Applications to collisions are presented in different approximation scheme, one-dimensional dynamics, approximate three-dimensional ones.... Finally two microscopic extensions beyond mean-field are reviewed: the variational principal of Balian and Veneroni and the implementation of residual two-body interactions in the Time-Dependent Density Matrix (TDDM) and the Extended Time-Dependent Hartree-Fock schemes (ET-DHF). (author)

  9. Calculation of the valence charge density and binding energy in a simple metal according to the neutral atom method: the Hartree-Fock ionic potential

    International Nuclear Information System (INIS)

    Dagens, L.

    1975-01-01

    The neutral atom method is generalized in order to deal with a Hartree-Fock nonlocal ionic potential. It is used to test the following metal potential, based upon a theoretical analysis due to Hedin and Lundquist. The true HF potential is used to describe the ionic part and a simple local density scheme (the Gaspar-Kohn-Sham approximation) is used for the valence part. The method is first applied to the calculation of the rigid neutral atom valence density of a few simple metals and the corresponding form factor n(q). The choice of the ionic potential (HF or GKS) is found to have a small but significant effect as far as n(q) is concerned. A comparison with experiment is made for Al and Be, using the available X-rays structure factor measurements. Good agreement is obtained for Al with the recent results of Raccah and Heinrich. No agreement is obtained with the Be results of Brown, although the general behavior of the observed and theoretical n(g) as function of g (reciprocal vector length) are found to be quite similar. The binding energy is calculated for Li, Be, Na, Mg and Al, using the Nozieres-Pines formula for the valence-valence correlation energy. The agreement with observed values is improved considerably when the present (HF+GKS) scheme is used, instead of the HFS completely local density scheme used in a previous work. The remaining discrepancies may be ascribed to the inaccuracy of the NP formula and to the neglect of the whole valence-core correlation energy [fr

  10. Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis.. (VII) HFODD (v2.49t): A new version of the program

    Science.gov (United States)

    Schunck, N.; Dobaczewski, J.; McDonnell, J.; Satuła, W.; Sheikh, J. A.; Staszczak, A.; Stoitsov, M.; Toivanen, P.

    2012-01-01

    We describe the new version (v2.49t) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite-temperature formalism for the HFB and HF + BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex-breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected. New version program summaryProgram title:HFODD (v2.49t) Catalogue identifier: ADFL_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFL_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public Licence v3 No. of lines in distributed program, including test data, etc.: 190 614 No. of bytes in distributed program, including test data, etc.: 985 898 Distribution

  11. Coupled state analysis of electron excitations in asymmetric collision systems

    International Nuclear Information System (INIS)

    Mehler, G.; Reus, T. de; Mueller, U.; Reinhardt, J.; Mueller, B.; Greiner, W.; Soff, G.

    1985-01-01

    A coupled channel formalism is presented, using relativistic basis states of the target atom. Screening effects are incorporated by means of an effective potential of Hartree-Fock-Slater type. Relativistic wave packets are employed for the description of the continuum. The impact parameter dependence of the K-hole production in p-Ag collisions is calculated, including quadrupole contributions of the projectile Coulomb potential. The results are compared with experimental data. (orig.)

  12. Ferromagnetism in the Hubbard model: a modified perturbation theory

    International Nuclear Information System (INIS)

    Gangadhar Reddy, G.; Ramakanth, A.; Nolting, W.

    2005-01-01

    We study the possibility of ferromagnetism in the Hubbard model using the modified perturbation theory. In this approach an Ansatz is made for the self-energy of the electron which contains the second order contribution developed around the Hartree-Fock solution and two parameters. The parameters are fixed by using a moment method. This self energy satisfies several known exact limiting cases. Using this self energy, the Curie temperature T c as a function of band filling n is investigated. It is found that T c falls off abruptly as n approaches half filling. The results are in qualitative agreement with earlier calculations using other approximation schemes. (author)

  13. Relativistic mean-field theory for unstable nuclei with non-linear σ and ω terms

    International Nuclear Information System (INIS)

    Sugahara, Y.; Toki, H.

    1994-01-01

    We search for a new parameter set for the description of stable as well as unstable nuclei in the wide mass range within the relativistic mean-field theory. We include a non-linear ω self-coupling term in addition to the non-linear σ self-coupling terms, the necessity of which is suggested by the relativistic Brueckner-Hartree-Fock (RBHF) theory of nuclear matter. We find two parameter sets, one of which is for nuclei above Z=20 and the other for nuclei below that. The calculated results agree very well with the existing data for finite nuclei. The parameter set for the heavy nuclei provides the equation of state of nuclear matter similar to the one of the RBHF theory. ((orig.))

  14. Continuum limit and improved action in lattice theories. Pt. 1

    International Nuclear Information System (INIS)

    Symanzik, K.

    1983-03-01

    Corrections to continuum theory results stemming from finite lattice-spacing can be diminished systematically by use of lattice actions that include also suitable irrelevant terms. We describe in detail the principles of such constructions at the example of PHI 4 theory. (orig.)

  15. Toroidal high-spin isomers in the nucleus 304120

    Science.gov (United States)

    Staszczak, A.; Wong, Cheuk-Yin; Kosior, A.

    2017-05-01

    Background: Strongly deformed oblate superheavy nuclei form an intriguing region where the toroidal nuclear structures may bifurcate from the oblate spheroidal shape. The bifurcation may be facilitated when the nucleus is endowed with a large angular moment about the symmetry axis with I =Iz . The toroidal high-K isomeric states at their local energy minima can be theoretically predicted using the cranked self-consistent Skyrme-Hartree-Fock method. Purpose: We use the cranked Skyrme-Hartree-Fock method to predict the properties of the toroidal high-spin isomers in the superheavy nucleus 120304184. Method: Our method consists of three steps: First, we use the deformation-constrained Skyrme-Hartree-Fock-Bogoliubov approach to search for the nuclear density distributions with toroidal shapes. Next, using these toroidal distributions as starting configurations, we apply an additional cranking constraint of a large angular momentum I =Iz about the symmetry z axis and search for the energy minima of the system as a function of the deformation. In the last step, if a local energy minimum with I =Iz is found, we perform at this point the cranked symmetry- and deformation-unconstrained Skyrme-Hartree-Fock calculations to locate a stable toroidal high-spin isomeric state in free convergence. Results: We have theoretically located two toroidal high-spin isomeric states of 120304184 with an angular momentum I =Iz=81 ℏ (proton 2p-2h, neutron 4p-4h excitation) and I =Iz=208 ℏ (proton 5p-5h, neutron 8p-8h) at the quadrupole moment deformations Q20=-297.7 b and Q20=-300.8 b with energies 79.2 and 101.6 MeV above the spherical ground state, respectively. The nuclear density distributions of the toroidal high-spin isomers 120304184(Iz=81 ℏ and 208 ℏ ) have the maximum density close to the nuclear matter density, 0.16 fm-3, and a torus major to minor radius aspect ratio R /d =3.25 . Conclusions: We demonstrate that aligned angular momenta of Iz=81 ℏ and 208 ℏ arising from

  16. Calculations of optical rotation: Influence of molecular structure

    Directory of Open Access Journals (Sweden)

    Yu Jia

    2012-01-01

    Full Text Available Ab initio Hartree-Fock (HF method and Density Functional Theory (DFT were used to calculate the optical rotation of 26 chiral compounds. The effects of theory and basis sets used for calculation, solvents influence on the geometry and values of calculated optical rotation were all discussed. The polarizable continuum model, included in the calculation, did not improve the accuracy effectively, but it was superior to γs. Optical rotation of five or sixmembered of cyclic compound has been calculated and 17 pyrrolidine or piperidine derivatives which were calculated by HF and DFT methods gave acceptable predictions. The nitrogen atom affects the calculation results dramatically, and it is necessary in the molecular structure in order to get an accurate computation result. Namely, when the nitrogen atom was substituted by oxygen atom in the ring, the calculation result deteriorated.

  17. Effect of side chain length on the stability and structural properties of 3

    African Journals Online (AJOL)

    thiophene (DOOPT) and their dimers studied by Hartree-Fock (HF) and Density Functional Theory (DFT) methods. The DFT calculations suggest that dimers of the dialkoxyphenylthiophenes with longer side chains are thermodynamically more ...

  18. Activities of the theoretical nuclear physics group of the Atomic Energy National Commission

    International Nuclear Information System (INIS)

    Reich, S.L.

    1982-01-01

    The theoretical studies that have been made in the Atomic Energy National Commission of Argentina about nuclear reactions, nuclear field theories, boson techniques and Hartree-Fock approximation, etc., are reported. (L.C.) [pt

  19. Coulomb displacement energies in relativistic and non-relativistic self-consistent models

    International Nuclear Information System (INIS)

    Marcos, S.; Savushkin, L.N.; Giai, N. van.

    1992-03-01

    Coulomb displacement energies in mirror nuclei are comparatively analyzed in Dirac-Hartree and Skyrme-Hartree-Fock models. Using a non-linear effective Lagrangian fitted on ground state properties of finite nuclei, it is found that the predictions of relativistic models are lower than those of Hartree-Fock calculations with Skyrme force. The main sources of reduction are the kinetic energy and the Coulomb-nuclear interference potential. The discrepancy with the data is larger than in the Skyrme-Hartree-Fock case. (author) 24 refs., 3 tabs

  20. Covariant density functional theory: The role of the pion

    International Nuclear Information System (INIS)

    Lalazissis, G. A.; Karatzikos, S.; Serra, M.; Otsuka, T.; Ring, P.

    2009-01-01

    We investigate the role of the pion in covariant density functional theory. Starting from conventional relativistic mean field (RMF) theory with a nonlinear coupling of the σ meson and without exchange terms we add pions with a pseudovector coupling to the nucleons in relativistic Hartree-Fock approximation. In order to take into account the change of the pion field in the nuclear medium the effective coupling constant of the pion is treated as a free parameter. It is found that the inclusion of the pion to this sort of density functionals does not destroy the overall description of the bulk properties by RMF. On the other hand, the noncentral contribution of the pion (tensor coupling) does have effects on single particle energies and on binding energies of certain nuclei.

  1. Universality and the approach to the continuum limit in lattice gauge theory

    CERN Document Server

    De Divitiis, G M; Guagnelli, M; Lüscher, Martin; Petronzio, Roberto; Sommer, Rainer; Weisz, P; Wolff, U; de Divitiis, G; Frezzotti, R; Guagnelli, M; Luescher, M; Petronzio, R; Sommer, R; Weisz, P; Wolff, U

    1995-01-01

    The universality of the continuum limit and the applicability of renormalized perturbation theory are tested in the SU(2) lattice gauge theory by computing two different non-perturbatively defined running couplings over a large range of energies. The lattice data (which were generated on the powerful APE computers at Rome II and DESY) are extrapolated to the continuum limit by simulating sequences of lattices with decreasing spacings. Our results confirm the expected universality at all energies to a precision of a few percent. We find, however, that perturbation theory must be used with care when matching different renormalized couplings at high energies.

  2. Hartree–Fock many-body perturbation theory for nuclear ground-states

    Directory of Open Access Journals (Sweden)

    Alexander Tichai

    2016-05-01

    Full Text Available We investigate the order-by-order convergence behavior of many-body perturbation theory (MBPT as a simple and efficient tool to approximate the ground-state energy of closed-shell nuclei. To address the convergence properties directly, we explore perturbative corrections up to 30th order and highlight the role of the partitioning for convergence. The use of a simple Hartree–Fock solution for the unperturbed basis leads to a convergent MBPT series for soft interactions, in contrast to the divergent MBPT series obtained with a harmonic oscillator basis. For larger model spaces and heavier nuclei, where a direct high-order MBPT calculation is not feasible, we perform third-order calculations and compare to advanced ab initio coupled-cluster results for the same interactions and model spaces. We demonstrate that third-order MBPT provides ground-state energies for nuclei up into the tin isotopic chain in excellent agreement with the best available coupled-cluster calculations at a fraction of the computational cost.

  3. Hartree–Fock many-body perturbation theory for nuclear ground-states

    Energy Technology Data Exchange (ETDEWEB)

    Tichai, Alexander, E-mail: alexander.tichai@physik.tu-darmstadt.de [Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt (Germany); Langhammer, Joachim [Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt (Germany); Binder, Sven [Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996 (United States); Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States); Roth, Robert, E-mail: robert.roth@physik.tu-darmstadt.de [Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt (Germany)

    2016-05-10

    We investigate the order-by-order convergence behavior of many-body perturbation theory (MBPT) as a simple and efficient tool to approximate the ground-state energy of closed-shell nuclei. To address the convergence properties directly, we explore perturbative corrections up to 30th order and highlight the role of the partitioning for convergence. The use of a simple Hartree–Fock solution for the unperturbed basis leads to a convergent MBPT series for soft interactions, in contrast to the divergent MBPT series obtained with a harmonic oscillator basis. For larger model spaces and heavier nuclei, where a direct high-order MBPT calculation is not feasible, we perform third-order calculations and compare to advanced ab initio coupled-cluster results for the same interactions and model spaces. We demonstrate that third-order MBPT provides ground-state energies for nuclei up into the tin isotopic chain in excellent agreement with the best available coupled-cluster calculations at a fraction of the computational cost.

  4. Mean-field theory of nuclear structure and dynamics

    International Nuclear Information System (INIS)

    Negele, J.W.

    1982-01-01

    The physical and theoretical foundations are presented for the mean-field theory of nuclear structure and dynamics. Salient features of the many-body theory of stationary states are reviewed to motivate the time-dependent mean-field approximation. The time-dependent Hartree-Fock approximation and its limitations are discussed and general theoretical formulations are presented which yield time-dependent mean-field equations in lowest approximation and provide suitable frameworks for overcoming various conceptual and practical limitations of the mean-field theory. Particular emphasis is placed on recent developments utilizing functional integral techniques to obtain a quantum mean-field theory applicable to quantized eigenstates, spontaneous fission, the nuclear partition function, and scattering problems. Applications to a number of simple, idealized systems are presented to verify the approximations for solvable problems and to elucidate the essential features of mean-field dynamics. Finally, calculations utilizing moderately realistic geometries and interactions are reviewed which address heavy-ion collisions, fusion, strongly damped collisions, and fission

  5. Ab initio calculations and modelling of atomic cluster structure

    DEFF Research Database (Denmark)

    Solov'yov, Ilia; Lyalin, Andrey G.; Solov'yov, Andrey V.

    2004-01-01

    The optimized structure and electronic properties of small sodium and magnesium clusters have been investigated using it ab initio theoretical methods based on density-functional theory and post-Hartree-Fock many-body perturbation theory accounting for all electrons in the system. A new theoretical...

  6. Quantum electrodynamics and the relativistic theory of many-electron atoms

    International Nuclear Information System (INIS)

    Sucher, J.

    1981-01-01

    The development of relativistic theories of many-electron atoms is reviewed, with emphasis on the fact that the Dirac-Coulomb Hamiltonian H/sub DC/ has no bound states. This fact implies that neither the Dirac-Hartree-Fock (DHF) equations nor the DHF wavefunction chi have a simple theoretical interpretation. A no-pair hamiltonian H/sub +/ is defined which does not have the fatal flaw of H/sub DC/ and hence can serve as a starting point for a systematic study of relativistic effects in many-electron atoms which can go beyond central-field approximations. H/sub +/ differs from H/sub DC/ by the presence of external-field positive-energy projection operators in the electron-electron interaction terms. Unlike H/sub DC/, H/sub +/ and its eigenfunctions psi have a clear-cut field-theoretic meaning, which is described. Similar remarks hold for a simpler no-pair Hamiltonian h/sub +/, which involves free positive-energy projection operators and for related Hamiltonians H/sub +/' and h/sup +/' which include the Breit operator. Relativistic Hartree-Fock equations are obtained from H/sub +/ and the relation between their solutions psi and the DHF solutions chi is discussed. The DHF equations may be reinterpreted as approximations to the new HF-type equations; this provides a rationale for their success in applications. It is argued that the Breit operator ought to be included even in the original DHF equations

  7. Thermal quasiparticle correlations and continuum coupling in nuclei far from stability

    International Nuclear Information System (INIS)

    Dang, Nguyen Dinh; Arima, Akito

    2003-01-01

    The contributions of quasiparticle correlations and continuum coupling upon the superfluid properties of neutron-rich Ni isotopes are studied within the modified BCS approximation at finite temperature. The effect of quasiparticle correlations is included using a secondary Bogoliubov transformation explicitly involving the quasiparticle occupation numbers at temperature T. The effect of continuum coupling is taken in to account via the finite widths of the single-particle resonant states. It is shown that the combination of these effects washes out the sharp superfluid-normal phase transition given by the standard finite-temperature BCS calculations. It is also found that the two-neutron separation energy for 84 Ni drops to zero at T congruent with 0.8 MeV

  8. Theoretical investigation of pressure-induced structural transitions in americium using GGA+U and hybrid density functional theory methods

    DEFF Research Database (Denmark)

    Verma, Ashok K.; Modak, P.; Sharma, Surinder M.

    2013-01-01

    First-principles calculations have been performed for americium (Am) metal using the generalized gradient approximation + orbital-dependent onsite Coulomb repulsion via Hubbard interaction (GGA+U) and hybrid density functional theory (HYB-DFT) methods to investigate various ground state properties......-I to Am-II transition. Good agreement was found between calculated and experimental equations of states for all phases, but the first three phases need larger U (α) parameters (where α represents the fraction of Hartree-Fock exchange energy replacing the DFT exchange energy) than the fourth phase in order...

  9. Density functional theory study of vibrational spectra, and ...

    Indian Academy of Sciences (India)

    The FTIR and FT Raman spectra of dacarbazine were recorded in the regions 4000-400 and 3500-100 cm-1, respectively. The optimized geometry, wavenumber, polarizability and several thermodynamic properties of dacarbazine were studied using ab initio Hartree-Fock, MP2 and DFT methods. A complete vibrational ...

  10. Theoretical study of the properties of BH3NH3

    International Nuclear Information System (INIS)

    Binkley, J.S.; Thorne, L.R.

    1983-01-01

    Borane monoammoniate (BH 3 NH 3 ) has been studied using several ab initio electronic structure methods and Gaussian basis sets. Equilibrium geometries have been computed at the Hartree--Fock level and, using the electron-correlated Moller--Plesset perturbation method, carried out to third order (MP3) with double-zeta polarized quality basis sets. The computed MP3 geometry is in close agreement with recent microwave data; electron correlation is found to be necessary for a proper description of the B--N distance. Hartree--Fock dipole moments and harmonic vibrational frequencies are presented and discussed. Moller--Plesset perturbation theory carried out to fourth order with triple-zeta plus polarization basis sets is used to compute a B--N dissociation energy of 34.7 kcal mol -1 and a (Hartree--Fock zero-point corrected) rotational barrier of 2.065 kcal mol -1 , which is in excellent agreement with the experimental value. Analysis of the dissociation energy as a function of perturbation order indicates that terms involving triple and quadruple substitutions are required in the dissociation energy

  11. Bogoliubov-de Gennes method and its applications

    CERN Document Server

    Zhu, Jian-Xin

    2016-01-01

    The purpose of this book is to provide an elementary yet systematic description of the Bogoliubov-de Gennes (BdG) equations, their unique symmetry properties and their relation to Green’s function theory. Specifically, it introduces readers to the supercell technique for the solutions of the BdG equations, as well as other related techniques for more rapidly solving the equations in practical applications. The BdG equations are derived from a microscopic model Hamiltonian with an effective pairing interaction and fully capture the local electronic structure through self-consistent solutions via exact diagonalization. This approach has been successfully generalized to study many aspects of conventional and unconventional superconductors with inhomogeneities – including defects, disorder or the presence of a magnetic field – and becomes an even more attractive choice when the first-principles information of a typical superconductor is incorporated via the construction of a low-energy tight-binding model. ...

  12. Elementary quantum chemistry

    CERN Document Server

    Pilar, Frank L

    2003-01-01

    Useful introductory course and reference covers origins of quantum theory, Schrödinger wave equation, quantum mechanics of simple systems, electron spin, quantum states of atoms, Hartree-Fock self-consistent field method, more. 1990 edition.

  13. Constraints on effective interactions imposed by antisymmetry and charge independence

    Energy Technology Data Exchange (ETDEWEB)

    Stringari, S [Trento Univ. (Italy). Dipartimento di Matematica e Fisica; Brink, D M [Oxford Univ. (UK). Dept. of Theoretical Physics

    1978-07-24

    Restrictions on the form of the energy functional following antisymmetry and charge independence have been investigated for a Hartree-Fock theory based on effective interactions. These restrictions impose severe constraints on density dependent effective interactions.

  14. Self-consistent RPA and the time-dependent density matrix approach

    Energy Technology Data Exchange (ETDEWEB)

    Schuck, P. [Institut de Physique Nucleaire, Orsay (France); CNRS et Universite Joseph Fourier, Laboratoire de Physique et Modelisation des Milieux Condenses, Grenoble (France); Tohyama, M. [Kyorin University School of Medicine, Mitaka, Tokyo (Japan)

    2016-10-15

    The time-dependent density matrix (TDDM) or BBGKY (Bogoliubov, Born, Green, Kirkwood, Yvon) approach is decoupled and closed at the three-body level in finding a natural representation of the latter in terms of a quadratic form of two-body correlation functions. In the small amplitude limit an extended RPA coupled to an also extended second RPA is obtained. Since including two-body correlations means that the ground state cannot be a Hartree-Fock state, naturally the corresponding RPA is upgraded to Self-Consistent RPA (SCRPA) which was introduced independently earlier and which is built on a correlated ground state. SCRPA conserves all the properties of standard RPA. Applications to the exactly solvable Lipkin and the 1D Hubbard models show good performances of SCRPA and TDDM. (orig.)

  15. Shell model Monte Carlo investigation of rare earth nuclei

    International Nuclear Information System (INIS)

    White, J. A.; Koonin, S. E.; Dean, D. J.

    2000-01-01

    We utilize the shell model Monte Carlo method to study the structure of rare earth nuclei. This work demonstrates the first systematic full oscillator shell with intruder calculations in such heavy nuclei. Exact solutions of a pairing plus quadrupole Hamiltonian are compared with the static path approximation in several dysprosium isotopes from A=152 to 162, including the odd mass A=153. Some comparisons are also made with Hartree-Fock-Bogoliubov results from Baranger and Kumar. Basic properties of these nuclei at various temperatures and spin are explored. These include energy, deformation, moments of inertia, pairing channel strengths, band crossing, and evolution of shell model occupation numbers. Exact level densities are also calculated and, in the case of 162 Dy, compared with experimental data. (c) 2000 The American Physical Society

  16. Magnetizability and rotational g tensors for density fitted local second-order Møller-Plesset perturbation theory using gauge-including atomic orbitals

    International Nuclear Information System (INIS)

    Loibl, Stefan; Schütz, Martin

    2014-01-01

    In this paper, we present theory and implementation of an efficient program for calculating magnetizabilities and rotational g tensors of closed-shell molecules at the level of local second-order Møller-Plesset perturbation theory (MP2) using London orbitals. Density fitting is employed to factorize the electron repulsion integrals with ordinary Gaussians as fitting functions. The presented program for the calculation of magnetizabilities and rotational g tensors is based on a previous implementation of NMR shielding tensors reported by S. Loibl and M. Schütz [J. Chem. Phys. 137, 084107 (2012)]. Extensive test calculations show (i) that the errors introduced by density fitting are negligible, and (ii) that the errors of the local approximation are still rather small, although larger than for nuclear magnetic resonance (NMR) shielding tensors. Electron correlation effects for magnetizabilities are tiny for most of the molecules considered here. MP2 appears to overestimate the correlation contribution of magnetizabilities such that it does not constitute an improvement over Hartree-Fock (when comparing to higher-order methods like CCSD(T)). For rotational g tensors the situation is different and MP2 provides a significant improvement in accuracy over Hartree-Fock. The computational performance of the new program was tested for two extended systems, the larger comprising about 2200 basis functions. It turns out that a magnetizability (or rotational g tensor) calculation takes about 1.5 times longer than a corresponding NMR shielding tensor calculation

  17. Microscopically-constrained Fock energy density functionals from chiral effective field theory. I. Two-nucleon interactions

    International Nuclear Information System (INIS)

    Gebremariam, B.; Bogner, S.K.; Duguet, T.

    2011-01-01

    The density matrix expansion (DME) of Negele and Vautherin is a convenient tool to map finite-range physics associated with vacuum two- and three-nucleon interactions into the form of a Skyrme-like energy density functional (EDF) with density-dependent couplings. In this work, we apply the improved formulation of the DME proposed recently in (arXiv:0910.4979) by Gebremariam et al. to the non-local Fock energy obtained from chiral effective field theory (EFT) two-nucleon (NN) interactions at next-to-next-to-leading-order (N 2 LO). The structure of the chiral interactions is such that each coupling in the DME Fock functional can be decomposed into a coupling constant arising from zero-range contact interactions and a coupling function of the density arising from the universal long-range pion exchanges. This motivates a new microscopically-guided Skyrme phenomenology where the density-dependent couplings associated with the underlying pion-exchange interactions are added to standard empirical Skyrme functionals, and the density-independent Skyrme parameters subsequently refit to data. A link to a downloadable Mathematica notebook containing the novel density-dependent couplings is provided.

  18. On the physical origin for the geometric theory of continuum mechanics

    International Nuclear Information System (INIS)

    Guenther, H.

    1984-01-01

    It is explained, that the basic notion for a geometric picture of the continuum mechanics is a four dimensional material manifold. The four dimensional mechanical affinity is then the unified field for any defect distribution in the general time dependent case. The minimal number of geometric relations being valid for any continuum is formulated as a set of pure affine relations. The state variables of the theory are additional tensor fields as e.g. deformation defining a metric. A material with a well defined deformation has a Newton-Cartan structure. Only if defects are included into the dynamical determination by additional equilibrium conditions, the theory has a pseudo relativistic structure. (author)

  19. Self-consistent theory of finite Fermi systems and radii of nuclei

    International Nuclear Information System (INIS)

    Saperstein, E. E.; Tolokonnikov, S. V.

    2011-01-01

    Present-day self-consistent approaches in nuclear theory were analyzed from the point of view of describing distributions of nuclear densities. The generalized method of the energy density functional due to Fayans and his coauthors (this is the most successful version of the self-consistent theory of finite Fermi systems) was the first among the approaches under comparison. The second was the most successful version of the Skyrme-Hartree-Fock method with the HFB-17 functional due to Goriely and his coauthors. Charge radii of spherical nuclei were analyzed in detail. Several isotopic chains of deformed nuclei were also considered. Charge-density distributions ρ ch (r) were calculated for several spherical nuclei. They were compared with model-independent data extracted from an analysis of elastic electron scattering on nuclei.

  20. Static and dynamic continuum theory liquid crystals a mathematical introduction

    CERN Document Server

    Stewart, Iain W

    2004-01-01

    Providing a rigorous, clear and accessible text for graduate students regardless of scientific background, this text introduces the basic continuum theory for nematic liquid crystals in equilibria, and details its various simple applications.

  1. Toward the fundamental theory of nuclear matter physics: The microscopic theory of nuclear collective dynamics

    International Nuclear Information System (INIS)

    Sakata, F.; Marumori, T.; Hashimoto, Y.; Tsukuma, H.; Yamamoto, Y.; Terasaki, J.; Iwasawa, Y.; Itabashi, H.

    1992-01-01

    Since the research field of nuclear physics is expanding rapidly, it is becoming more imperative to develop the microscopie theory of nuclear matter physics which provides us with a unified understanding of diverse phenomena exhibited by nuclei. An estabishment of various stable mean-fields in nuclei allows us to develop the microscopie theory of nuclear collective dynamics within the mean-field approximation. The classical-level theory of nuclear collective dynamics is developed by exploiting the symplectic structure of the timedependent Hartree-Fock (TDHF)-manifold. The importance of exploring the single-particle dynamics, e.g. the level-crossing dynamics in connection with the classical order-to-chaos transition mechanism is pointed out. Since the classical-level theory os directly related to the full quantum mechanical boson expansion theory via the symplectic structure of the TDHF-manifold, the quantum theory of nuclear collective dynamics is developed at the dictation of what os developed on the classical-level theory. The quantum theory thus formulated enables us to introduce the quantum integrability and quantum chaoticity for individual eigenstates. The inter-relationship between the classical-level and quantum theories of nuclear collective dynamics might play a decisive role in developing the quantum theory of many-body problems. (orig.)

  2. Quantal theory of heavy ion scattering in a three-dimensional TDHF model

    International Nuclear Information System (INIS)

    Cusson, R.Y.

    1977-01-01

    The fast Fourier transform and the predictor corrector method are used to solve the time-dependent Hartree-Fock equations. The equations are then used to calculate the electric scattering of heavy ions, concentrating on 16 O + 16 O and 14 N + 12 C

  3. IUTAM-Symposium on The Generalized Cosserat Continuum and the Continuum Theory of Dislocations with Applications

    CERN Document Server

    1968-01-01

    5 The symposium was held in Freudenstadt from 28\\h to 31 \\ ofAugust st nd 1967 and in Stuttgart from 1 to 2 of September 1967. The proposal to hold this symposium originated with the German Society of Applied Mathematics and Mechanics (GAMM) late in 1964 and was examined by a committee of IUTAM especially appointed for this purpose. The basis of this examination was a report in which the present situation in the field and the possible aims of the symposium were surveyed. Briefly, the aims of the symposium were stated to be 1. the unification of the various approaches developed in recent years with the aim of penetrating into the microscopic world of matter by means of continuum theories; 2. the bridging of the gap between microscopic (or atomic) research on mechanics on one hand, and the phenomenological (or continuum mechanical) approach on the other hand; 3. the physical interpretation and the relation to actual material behaviour of the quantities and laws introduced into the new theories, together with ap...

  4. Bogoliubov condensation of gluons and spontaneous gauge symmetry breaking in QCD

    International Nuclear Information System (INIS)

    Pervushin, V.N.; Roepke, G.; Volkov, M.K.; Blaschke, D.; Pavel, H.P.; Litvin, A.

    1995-08-01

    The ''squeezed'' representation of commutation relations for gluon fields in QCD is formulated as the mathematical tool for the description of the gluon condensate. We first consider λφ 4 theory and show that the ''squeezed'' Bogoliubov condensate can lead to the spontaneous appearance of a mass. Using the ''squeezed'' representation, we show that in the non-Abelian theory spontaneous gauge symmetry breaking (SGSB) and the appearance of a constituent mass of gluons can be described. We construct a projector onto the oscillator - like variables, for which the ''squeezed'' representation is valid, by using the formal solution of the Gauss equation instead of fixing a gauge. We discuss the effects of the SGSB and present as an application of the approach the calculation of the gluon mass from the difference of the η' and the η - meson masses. (author). 27 refs

  5. Iterative scheme for electronic systems: using one-electron Green's functions

    International Nuclear Information System (INIS)

    Hyslop, J.; Rees, D.

    1976-01-01

    An iterative generalization of the minimum principle proposed for electronic systems by Hall, Hyslop, and Rees is investigated. It is shown that this generalization still retains the advantage of using members of a larger class of trial wave functions, for example those with discontinuities, as initial approximations to the wave functions. This scheme has the advantage that, at each stage of iteration, an upper bound is obtained which is at least as good as that obtained previously. The theory is first applied to the hydrogen atom. It is then adapted to estimate the Hartree--Fock energy of the helium atom, the Hartree--Fock limit being obtained after a relatively small number of iterations

  6. Optimized Hypernetted-Chain Solutions for Helium -4 Surfaces and Metal Surfaces

    Science.gov (United States)

    Qian, Guo-Xin

    This thesis is a study of inhomogeneous Bose systems such as liquid ('4)He slabs and inhomogeneous Fermi systems such as the electron gas in metal films, at zero temperature. Using a Jastrow-type many-body wavefunction, the ground state energy is expressed by means of Bogoliubov-Born-Green-Kirkwood -Yvon and Hypernetted-Chain techniques. For Bose systems, Euler-Lagrange equations are derived for the one- and two -body functions and systematic approximation methods are physically motivated. It is shown that the optimized variational method includes a self-consistent summation of ladder- and ring-diagrams of conventional many-body theory. For Fermi systems, a linear potential model is adopted to generate the optimized Hartree-Fock basis. Euler-Lagrange equations are derived for the two-body correlations which serve to screen the strong bare Coulomb interaction. The optimization of the pair correlation leads to an expression of correlation energy in which the state averaged RPA part is separated. Numerical applications are presented for the density profile and pair distribution function for both ('4)He surfaces and metal surfaces. Both the bulk and surface energies are calculated in good agreement with experiments.

  7. Analytic calculations of hyper-Raman spectra from density functional theory hyperpolarizability gradients

    Energy Technology Data Exchange (ETDEWEB)

    Ringholm, Magnus; Ruud, Kenneth [Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø – The Arctic University of Norway, 9037 Tromsø (Norway); Bast, Radovan [Theoretical Chemistry and Biology, School of Biotechnology, Royal Institute of Technology, AlbaNova University Center, S-10691 Stockholm (Sweden); PDC Center for High Performance Computing, Royal Institute of Technology, S-10044 Stockholm (Sweden); Oggioni, Luca [Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø – The Arctic University of Norway, 9037 Tromsø (Norway); Department of Physics G. Occhialini, University of Milano Bicocca, Piazza della scienza 3, 20126 Milan (Italy); Ekström, Ulf [Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, 0315 Oslo (Norway)

    2014-10-07

    We present the first analytic calculations of the geometrical gradients of the first hyperpolarizability tensors at the density-functional theory (DFT) level. We use the analytically calculated hyperpolarizability gradients to explore the importance of electron correlation effects, as described by DFT, on hyper-Raman spectra. In particular, we calculate the hyper-Raman spectra of the all-trans and 11-cis isomers of retinal at the Hartree-Fock (HF) and density-functional levels of theory, also allowing us to explore the sensitivity of the hyper-Raman spectra on the geometrical characteristics of these structurally related molecules. We show that the HF results, using B3LYP-calculated vibrational frequencies and force fields, reproduce the experimental data for all-trans-retinal well, and that electron correlation effects are of minor importance for the hyper-Raman intensities.

  8. Importance of dispersion and electron correlation in ab initio protein folding.

    Science.gov (United States)

    He, Xiao; Fusti-Molnar, Laszlo; Cui, Guanglei; Merz, Kenneth M

    2009-04-16

    Dispersion is well-known to be important in biological systems, but the effect of electron correlation in such systems remains unclear. In order to assess the relationship between the structure of a protein and its electron correlation energy, we employed both full system Hartree-Fock (HF) and second-order Møller-Plesset perturbation (MP2) calculations in conjunction with the Polarizable Continuum Model (PCM) on the native structures of two proteins and their corresponding computer-generated decoy sets. Because of the expense of the MP2 calculation, we have utilized the fragment molecular orbital method (FMO) in this study. We show that the sum of the Hartree-Fock (HF) energy and force field (LJ6)-derived dispersion energy (HF + LJ6) is well correlated with the energies obtained using second-order Møller-Plesset perturbation (MP2) theory. In one of the two examples studied, the correlation energy as well as the empirical dispersive energy term was able to discriminate between native and decoy structures. On the other hand, for the second protein we studied, neither the correlation energy nor dispersion energy showed discrimination capabilities; however, the ab initio MP2 energy and the HF+LJ6 both ranked the native structure correctly. Furthermore, when we randomly scrambled the Lennard-Jones parameters, the correlation between the MP2 energy and the sum of the HF energy and dispersive energy (HF+LJ6) significantly drops, which indicates that the choice of Lennard-Jones parameters is important.

  9. Superheavy nuclei in the relativistic mean-field theory

    International Nuclear Information System (INIS)

    Lalazissis, G.A.; Ring, P.; Gambhir, Y.K.

    1996-01-01

    We have carried out a study of superheavy nuclei in the framework of the relativistic mean-field theory. Relativistic Hartree-Bogoliubov (RHB) calculations have been performed for nuclei with large proton and neutron numbers. A finite-range pairing force of Gogny type has been used in the RHB calculations. The ground-state properties of very heavy nuclei with atomic numbers Z=100-114 and neutron numbers N=154-190 have been obtained. The results show that in addition to N=184 the neutron numbers N=160 and N=166 exhibit an extra stability as compared to their neighbors. For the case of protons the atomic number Z=106 is shown to demonstrate a closed-shell behavior in the region of well deformed nuclei about N=160. The proton number Z=114 also indicates a shell closure. Indications for a doubly magic character at Z=106 and N=160 are observed. Implications of shell closures on a possible synthesis of superheavy nuclei are discussed. (orig.)

  10. Physical Fock space of tensionless strings

    CERN Document Server

    Antoniadis, Ignatios; Antoniadis, Ignatios; Savvidy, George

    2004-01-01

    We study the physical Fock space of the tensionless string theory with perimeter action which has pure massless spectrum. The states are classified by the Wigner's little group for massless particles. The ground state contains infinite many massless fields of fixed helicity, the excitation levels realize CSR representations. We demonstrate that the first and the second excitation levels are physical null states.

  11. Ab initio theory of magnetic interactions at surfaces

    Energy Technology Data Exchange (ETDEWEB)

    Sousa, C [Departament de Quimica Fisica i Centre de Recerca en Quimica Teorica, Universitat de Barcelona i Parc Cientific de Barcelona, C/ MartI i Franques 1, E-08028 Barcelona (Spain); Graaf, C de [Departament de Quimica Fisica i Inorganica, Universitat Rovira i Virgili, P. Imperial Tarraco 1, E-43005 Tarragona (Spain); Lopez, N [Departament de Quimica Fisica i Centre de Recerca en Quimica Teorica, Universitat de Barcelona i Parc Cientific de Barcelona, C/ Marti i Franques 1, E-08028 Barcelona (Spain); Harrison, N M [Department of Chemistry, Imperial College of Science, Technology and Medicine, London SW7 2AY (United Kingdom); Illas, F [Departament de Quimica Fisica i Centre de Recerca en Quimica Teorica, Universitat de Barcelona i Parc Cientific de Barcelona, C/ Marti i Franques 1, E-08028 Barcelona (Spain)

    2004-07-07

    The low to high spin energy transition of Ni adsorbed on regular and defective sites of MgO(100) and the relative strengths of bulk and surface magnetic coupling constants of first row transition metal oxides (MnO, FeO, CoO, NiO and CuO) are taken as examples to illustrate some deficiencies of density functional theory (DFT). For these ionic systems a cluster/periodic comparison within the same computational method (either DFT or Hartree-Fock) is used to establish that embedded cluster models provide an adequate representation. The cluster model approach is then used to obtain accurate values for the magnetic properties of interest by using explicitly correlated wavefunction methods which handle the electronic open shell rigorously as spin eigenfunctions.

  12. Ab initio theory of magnetic interactions at surfaces

    International Nuclear Information System (INIS)

    Sousa, C; Graaf, C de; Lopez, N; Harrison, N M; Illas, F

    2004-01-01

    The low to high spin energy transition of Ni adsorbed on regular and defective sites of MgO(100) and the relative strengths of bulk and surface magnetic coupling constants of first row transition metal oxides (MnO, FeO, CoO, NiO and CuO) are taken as examples to illustrate some deficiencies of density functional theory (DFT). For these ionic systems a cluster/periodic comparison within the same computational method (either DFT or Hartree-Fock) is used to establish that embedded cluster models provide an adequate representation. The cluster model approach is then used to obtain accurate values for the magnetic properties of interest by using explicitly correlated wavefunction methods which handle the electronic open shell rigorously as spin eigenfunctions

  13. Variational continuum multiphase poroelasticity theory and applications

    CERN Document Server

    Serpieri, Roberto

    2017-01-01

    This book collects the theoretical derivation of a recently presented general variational macroscopic continuum theory of multiphase poroelasticity (VMTPM), together with its applications to consolidation and stress partitioning problems of interest in several applicative engineering contexts, such as in geomechanics and biomechanics. The theory is derived based on a purely-variational deduction, rooted in the least-Action principle, by considering a minimal set of kinematic descriptors. The treatment herein considered keeps a specific focus on the derivation of most general medium-independent governing equations. It is shown that VMTPM recovers paradigms of consolidated use in multiphase poroelasticity such as Terzaghi's stress partitioning principle and Biot's equations for wave propagation. In particular, the variational treatment permits the derivation of a general medium-independent stress partitioning law, and the proposed variational theory predicts that the external stress, the fluid pressure, and the...

  14. Bogoliubov transformation for quantum fields in (S1)d x RD-d topology and applications to the Casimir effect

    International Nuclear Information System (INIS)

    Khanna, F C; Malbouisson, J M C; Santana, A E

    2009-01-01

    A Bogoliubov transformation accounting simultaneously for spatial compactifica-tion and thermal effects is introduced. The fields are described in a Γ D d = S 1 1 x ... x S 1 d x R D-d topology, and the Bogoliubov transformation is derived by a generalization of the thermofield dynamics formalism, a real-time finite-temperature quantum field theory. We consider the Casimir effect for Maxwell and Dirac fields and for a non-interacting massless QCD at finite temperature. For the fermion sector in a cubic box, we analyze the temperature at which the Casimir pressure changes its sign from attractive to repulsive. This critical temperature is approximately 200 MeV when the edge of the cube is of the order of the confining lengths (∼ 1 : fm) for quarks in baryons.

  15. Comparison of self-consistent calculations of the static polarizability of atoms and molecules

    International Nuclear Information System (INIS)

    Moullet, I.; Martins, J.L.

    1990-01-01

    The static dipole polarizabilities and other ground-state properties of H, H 2 , He, Na, and Na 2 are calculated using five different self-consistent schemes: Hartree--Fock, local spin density approximation, Hartree--Fock plus local density correlation, self-interaction-corrected local spin density approximation, and Hartree--Fock plus self-interaction-corrected local density correlation. The inclusion of the self-interaction corrected local spin density approximation in the Hartree--Fock method improves dramatically the calculated dissociation energies of molecules but has a small effect on the calculated polarizabilities. Correcting the local spin density calculations for self-interaction effects improves the calculated polarizability in the cases where the local spin density results are mediocre, and has only a small effect in the cases where the local spin density values are in reasonable agreement with experiment

  16. Quantum corrections to potential energy surfaces and their influence on barriers

    International Nuclear Information System (INIS)

    Reinhard, P.G.; Goeke, K.W.; Bonn Univ.

    1980-01-01

    A microscopic theory suitable for the description of fission processes and other large-amplitude collective phenomena is presented. The approach makes use of an optimal collective path, which is constructed by means of adiabatic time-dependent Hartree-Fock (TDHF) techniques as to show maximal de-coupling of collective and non-collective degrees of freedom. Although this involves a classical concept, the theory fully incorporates quantum effects associated with extracting a collective Schroedinger equation from adiabatic time-dependent Hartree-Fock theories (ATDHF). The quantum corrections are discussed extensively, and calculations in the two-centre shell model show, e.g. that they reduce the second barrier by 2 MeV and the life-time by a factor of 10 -7 . The relationships of the presented quantized ATDHF approach to the random-phase approximation (RPA) and a generalized dynamic generator co-ordinate method are investigated. For the construction of the optimal fission path, simple step-by-step methods are suggested. (author)

  17. Mean field theory of nuclei and shell model. Present status and future outlook

    International Nuclear Information System (INIS)

    Nakada, Hitoshi

    2003-01-01

    Many of the recent topics of the nuclear structure are concerned on the problems of unstable nuclei. It has been revealed experimentally that the nuclear halos and the neutron skins as well as the cluster structures or the molecule-like structures can be present in the unstable nuclei, and the magic numbers well established in the stable nuclei disappear occasionally while new ones appear. The shell model based on the mean field approximation has been successfully applied to stable nuclei to explain the nuclear structure as the finite many body system quantitatively and it is considered as the standard model at present. If the unstable nuclei will be understood on the same model basis or not is a matter related to fundamental principle of nuclear structure theories. In this lecture, the fundamental concept and the framework of the theory of nuclear structure based on the mean field theory and the shell model are presented to make clear the problems and to suggest directions for future researches. At first fundamental properties of nuclei are described under the subtitles: saturation and magic numbers, nuclear force and effective interactions, nuclear matter, and LS splitting. Then the mean field theory is presented under subtitles: the potential model, the mean field theory, Hartree-Fock approximation for nuclear matter, density dependent force, semiclassical mean field theory, mean field theory and symmetry, Skyrme interaction and density functional, density matrix expansion, finite range interactions, effective masses, and motion of center of mass. The subsequent section is devoted to the shell model with the subtitles: beyond the mean field approximation, core polarization, effective interaction of shell model, one-particle wave function, nuclear deformation and shell model, and shell model of cross shell. Finally structure of unstable nuclei is discussed with the subtitles: general remark on the study of unstable nuclear structure, asymptotic behavior of wave

  18. effect of side chain length on the stability and structural properties of 3

    African Journals Online (AJOL)

    Preferred Customer

    We report on the effect of the alkoxy chain length on the thermodynamic ... studied by Hartree-Fock (HF) and Density Functional Theory (DFT) methods. ..... with longer alkoxy substituents on the phenyl ring have lesser value of change in Gibbs ...

  19. Gaussian-3 theory using scaled energies

    International Nuclear Information System (INIS)

    Curtiss, Larry A.; Raghavachari, Krishnan; Redfern, Paul C.; Pople, John A.

    2000-01-01

    A modification of Guassian-3 (G3) theory using multiplicative scale factors, instead of the additive higher level correction, is presented. In this method, referred to as G3S, the correlation energy is scaled by five parameters and the Hartree-Fock energy by one parameter. The six parameters are fitted to the G2/97 test set of 299 energies and the resulting mean absolute deviation from experiment is 0.99 kcal/mol compared to 1.01 kcal/mol for G3 theory. The G3S method has the advantage compared to G3 theory in that it can be used for studying potential energy surfaces where the products and reactants have a different number of paired electrons. In addition, versions of the computationally less intensive G3(MP3) and G3(MP2) methods that use scaled energies are also presented. These methods, referred to as G3S(MP3) and G3S(MP2), have mean absolute deviations of 1.16 and 1.35 kcal/mol, respectively. (c) 2000 American Institute of Physics

  20. One-Body Potential Theory of Molecules and Solids Modified Semiempirically for Electron Correlation

    International Nuclear Information System (INIS)

    March, N.H.

    2010-08-01

    The study of Cordero, March and Alonso (CMA) for four spherical atoms, Be,Ne,Mg and Ar, semiempirically fine-tunes the Hartree-Fock (HF) ground-state electron density by inserting the experimentally determined ionization potentials. The present Letter, first of all, relates this approach to the very recent work of Bartlett 'towards an exact correlated orbital theory for electrons'. Both methods relax the requirement of standard DFT that a one-body potential shall generate the exact ground-state density, though both work with high quality approximations. Unlike DFT, the CMA theory uses a modified HF non-local potential. It is finally stressed that this potential generates also an idempotent Dirac density matrix. The CMA approach is thereby demonstrated to relate, albeit approximately, to the DFT exchange-correlation potential. (author)

  1. Gauge origin independent calculations of molecular magnetisabilities in relativistic four-component theory

    DEFF Research Database (Denmark)

    Iliaš, M.; Jensen, Hans Jørgen Aagaard; Bast, R.

    2013-01-01

    of the four-component relativistic linear response method at the self-consistent field single reference level. Benefits of employing the London atomic orbitals in relativistic calculations are illustrated with Hartree-Fock wave functions on the XF3 (X = N, P, As, Sb, Bi) series of molecules. Significantly...

  2. Towards quantifying the role of exact exchange in the prediction hydrogen bond spin-spin coupling constants involving fluorine

    Energy Technology Data Exchange (ETDEWEB)

    San Fabián, J.; Omar, S.; García de la Vega, J. M., E-mail: garcia.delavega@uam.es [Departamento de Química Física Aplicada, Facultad de Ciencias, Universidad Autónoma de Madrid, Madrid (Spain)

    2016-08-28

    The effect of a fraction of Hartree-Fock exchange on the calculated spin-spin coupling constants involving fluorine through a hydrogen bond is analyzed in detail. Coupling constants calculated using wavefunction methods are revisited in order to get high-level calculations using the same basis set. Accurate MCSCF results are obtained using an additive approach. These constants and their contributions are used as a reference for density functional calculations. Within the density functional theory, the Hartree-Fock exchange functional is split in short- and long-range using a modified version of the Coulomb-attenuating method with the SLYP functional as well as with the original B3LYP. Results support the difficulties for calculating hydrogen bond coupling constants using density functional methods when fluorine nuclei are involved. Coupling constants are very sensitive to the Hartree-Fock exchange and it seems that, contrary to other properties, it is important to include this exchange for short-range interactions. Best functionals are tested in two different groups of complexes: those related with anionic clusters of type [F(HF){sub n}]{sup −} and those formed by difluoroacetylene and either one or two hydrogen fluoride molecules.

  3. New numerical methods for quantum field theories on the continuum

    Energy Technology Data Exchange (ETDEWEB)

    Emirdag, P.; Easter, R.; Guralnik, G.S.; Hahn, S.C

    2000-03-01

    The Source Galerkin Method is a new numerical technique that is being developed to solve Quantum Field Theories on the continuum. It is not based on Monte Carlo techniques and has a measure to evaluate relative errors. It promises to increase the accuracy and speed of calculations, and takes full advantage of symmetries of the theory. The application of this method to the non-linear {sigma} model is outlined.

  4. Theory of Nernst effect in layered superconductors

    International Nuclear Information System (INIS)

    Tinh, B D; Rosenstein, B

    2009-01-01

    We calculate, using the time-dependent Ginzburg-Landau (TDGL) equation with thermal noise, the transverse thermoelectric conductivity α xy , describing the Nernst effect, in type-II superconductor in the vortex-liquid regime. The method is an elaboration of the Hartree-Fock. An often made in analytical calculations additional assumption that only the lowest Landau level significantly contributes to α xy in the high field limit is lifted by including all the Landau levels. The resulting values in two dimensions (2D) are significantly lower than the numerical simulation data of the same model, but are in reasonably good quantitative agreement with experimental data on La 2 SrCuO 4 above the irreversibility line (below the irreversibility line at which α xy diverges and theory should be modified by including pinning effects).

  5. Yrast-yrare interaction strength and bandcrossing frequency

    International Nuclear Information System (INIS)

    Wu, C.S.; Zeng, J.Y.

    1991-01-01

    Accurate particle-number-conserving calculation shows that in a single-j model the yrast-yrare interaction V is always strong and no periodic oscillation of V with the degree of shell filling is found, in contrast to the results obtained by the Hartree-Fock-Bogoliubov approximation. To understand the behavior of V and bandcrossing frequency ω c , the spin-alignment, seniority structure, configuration structure, and ''quasiparticle structure'' of the yrast and yrare bands are analyzed in detail. Calculation in a two-j model (high-j intruder orbits plus normal orbits of opposite parity) was also carried out to illustrate schematically that a weak yrast-yrare interaction may occur for certain single-particle level scheme. The coexistence of normal low-j orbits with high-j intruder orbits is indispensible for a sharp backbending observed in some realistic nuclei

  6. Spin-orbit ZORA and four-component Dirac-Coulomb estimation of relativistic corrections to isotropic nuclear shieldings and chemical shifts of noble gas dimers

    DEFF Research Database (Denmark)

    Jankowska, Marzena; Kupka, Teobald; Stobiński, Leszek

    2016-01-01

    Hartree-Fock and density functional theory with the hybrid B3LYP and general gradient KT2 exchange-correlation functionals were used for non-relativistic and relativistic nuclear magnetic shielding calculations of helium, neon, argon, krypton and xenon dimers and free atoms. Relativistic...

  7. Difficulties in applying pure Kohn-Sham density functional theory electronic structure methods to protein molecules

    Science.gov (United States)

    Rudberg, Elias

    2012-02-01

    Self-consistency-based Kohn-Sham density functional theory (KS-DFT) electronic structure calculations with Gaussian basis sets are reported for a set of 17 protein-like molecules with geometries obtained from the Protein Data Bank. It is found that in many cases such calculations do not converge due to vanishing HOMO-LUMO gaps. A sequence of polyproline I helix molecules is also studied and it is found that self-consistency calculations using pure functionals fail to converge for helices longer than six proline units. Since the computed gap is strongly correlated to the fraction of Hartree-Fock exchange, test calculations using both pure and hybrid density functionals are reported. The tested methods include the pure functionals BLYP, PBE and LDA, as well as Hartree-Fock and the hybrid functionals BHandHLYP, B3LYP and PBE0. The effect of including solvent molecules in the calculations is studied, and it is found that the inclusion of explicit solvent molecules around the protein fragment in many cases gives a larger gap, but that convergence problems due to vanishing gaps still occur in calculations with pure functionals. In order to achieve converged results, some modeling of the charge distribution of solvent water molecules outside the electronic structure calculation is needed. Representing solvent water molecules by a simple point charge distribution is found to give non-vanishing HOMO-LUMO gaps for the tested protein-like systems also for pure functionals.

  8. Difficulties in applying pure Kohn-Sham density functional theory electronic structure methods to protein molecules

    International Nuclear Information System (INIS)

    Rudberg, Elias

    2012-01-01

    Self-consistency-based Kohn-Sham density functional theory (KS-DFT) electronic structure calculations with Gaussian basis sets are reported for a set of 17 protein-like molecules with geometries obtained from the Protein Data Bank. It is found that in many cases such calculations do not converge due to vanishing HOMO-LUMO gaps. A sequence of polyproline I helix molecules is also studied and it is found that self-consistency calculations using pure functionals fail to converge for helices longer than six proline units. Since the computed gap is strongly correlated to the fraction of Hartree-Fock exchange, test calculations using both pure and hybrid density functionals are reported. The tested methods include the pure functionals BLYP, PBE and LDA, as well as Hartree-Fock and the hybrid functionals BHandHLYP, B3LYP and PBE0. The effect of including solvent molecules in the calculations is studied, and it is found that the inclusion of explicit solvent molecules around the protein fragment in many cases gives a larger gap, but that convergence problems due to vanishing gaps still occur in calculations with pure functionals. In order to achieve converged results, some modeling of the charge distribution of solvent water molecules outside the electronic structure calculation is needed. Representing solvent water molecules by a simple point charge distribution is found to give non-vanishing HOMO-LUMO gaps for the tested protein-like systems also for pure functionals. (fast track communication)

  9. RHF and DFT study of the optimized molecular structure and atomic ...

    African Journals Online (AJOL)

    Restricted HartreeFock (RHF) and Density Functional Theory (DFT) studies were carried out on the organic semi conductor material Pentacene. 6-31G and 6-31G* basis sets were used to optimize the molecule and compute the charge distribution at both levels of theory. The results show that the Carbon-Hydrogen bonds in ...

  10. Equations-of-motion approach to a quantum theory of large-amplitude collective motion

    International Nuclear Information System (INIS)

    Klein, A.

    1984-01-01

    The equations-of-motion approach to large-amplitude collective motion is implemented both for systems of coupled bosons, also studied in a previous paper, and for systems of coupled fermions. For the fermion case, the underlying formulation is that provided by the generalized Hartree-Fock approximation (or generalized density matrix method). To obtain results valid in the semi-classical limit, as in most previous work, we compute the Wigner transform of quantum matrices in the representation in which collective coordinates are diagonal and keep only the leading contributions. Higher-order contributions can be retained, however, and, in any case, there is no ambiguity of requantization. The semi-classical limit is seen to comprise the dynamics of time-dependent Hartree-Fock theory (TDHF) and a classical canonicity condition. By utilizing a well-known parametrization of the manifold of Slater determinants in terms of classical canonical variables, we are able to derive and understand the equations of the adiabatic limit in full parallelism with the boson case. As in the previous paper, we can thus show: (i) to zero and first order in the adiabatic limit the physics is contained in Villar's equations; (ii) to second order there is consistency and no new conditions. The structure of the solution space (discussed thoroughly in the previous paper) is summarized. A discussion of associated variational principles is given. A form of the theory equivalent to self-consistent cranking is described. A method of solution is illustrated by working out several elementary examples. The relationship to previsous work, especially that of Zelevinsky and Marumori and coworkers is discussed briefly. Three appendices deal respectively with the equations-of-motion method, with useful properties of Slater determinants, and with some technical details associated with the fermion equations of motion. (orig.)

  11. Photons in Fock space and beyond

    CERN Document Server

    Honegger, Reinhard

    2015-01-01

    The three-volume major reference "Photons in Fock Space and Beyond" undertakes a new mathematical and conceptual foundation of the theory of light emphasizing mesoscopic radiation systems. The quantum optical notions are generalized beyond Fock representations where the richness of an infinite dimensional quantum field system, with its mathematical difficulties and theoretical possibilities, is fully taken into account. It aims at a microscopic formulation of a mesoscopic model class which covers in principle all stages of the generation and propagation of light within a unified and well-defined conceptual frame. The dynamics of the interacting systems is founded — according to original works of the authors — on convergent perturbation series and describes the developments of the quantized microscopic as well as the classical collective degrees of freedom at the same time. The achieved theoretical unification fits especially to laser and microwave applications inheriting objective information over quantu...

  12. Evidence against the continuum structure underlying motivation measures derived from self-determination theory.

    Science.gov (United States)

    Chemolli, Emanuela; Gagné, Marylène

    2014-06-01

    Self-determination theory (SDT) proposes a multidimensional conceptualization of motivation in which the different regulations are said to fall along a continuum of self-determination. The continuum has been used as a basis for using a relative autonomy index as a means to create motivational scores. Rasch analysis was used to verify the continuum structure of the Multidimensional Work Motivation Scale and of the Academic Motivation Scale. We discuss the concept of continuum against SDT's conceptualization of motivation and argue against the use of the relative autonomy index on the grounds that evidence for a continuum structure underlying the regulations is weak and because the index is statistically problematic. We suggest exploiting the full richness of SDT's multidimensional conceptualization of motivation through the use of alternative scoring methods when investigating motivational dynamics across life domains.

  13. Entanglement in the Bogoliubov vacuum

    DEFF Research Database (Denmark)

    Poulsen, Uffe Vestergaard; Meyer, T.; Lewenstein, M.

    2005-01-01

    We analyze the entanglement properties of the Bogoliubov vacuum, which is obtained as a second-order approximation to the ground state of an interacting Bose-Einstein condensate. We work in one- and two-dimensional lattices and study the entanglement between two groups of sites as a function...... of the geometry of the configuration and the strength of the interactions. As our measure of entanglement we use the logarithmic negativity, supplemented by an algorithmic check for bound entanglement where appropiate. The short-range entanglement is found to grow approximately linearly with the group sizes...

  14. Realistic nuclear shell theory and the doubly-magic 132Sn region

    International Nuclear Information System (INIS)

    Vary, J.P.

    1978-01-01

    After an introduction discussing the motivation and interest in results obtained with isotope separators, the fundamental problem in realistic nuclear shell theory is posed in the context of renormalization theory. Then some of the important developments that have occurred over the last fifteen years in the derivation of the effective Hamiltonian and application of realistic nuclear shell theory are briefly reviewed. Doubly magic regions of the periodic table and the unique advantages of the 132 Sn region are described. Then results are shown for the ground-state properties of 132 Sn as calculated from the density-dependent Hartree-Fock approach with the Skyrme Hamiltonian. A single theoretical Hamiltonian for all nuclei from doubly magic 132 Sn to doubly magic 208 Pb is presented; single-particle energies are graphed. Finally, predictions of shell-model level-density distributions obtained with spectral distribution methods are discussed; calculated level densities are shown for 136 Xe. 10 figures

  15. Ab Initio Calculations of Oxosulfatovanadates

    DEFF Research Database (Denmark)

    Frøberg, Torben; Johansen, Helge

    1996-01-01

    Restricted Hartree-Fock and multi-configurational self-consistent-field calculations together with secondorder perturbation theory have been used to study the geometry, the electron density, and the electronicspectrum of (VO2SO4)-. A bidentate sulphate attachment to vanadium was found to be stabl...

  16. 68 - 75 Galadanchi et al.c

    African Journals Online (AJOL)

    User

    Restricted HartreeFock (RHF) and Density Functional Theory (DFT) studies were carried out on the organic semi ... arrays), organic light emitting diodes (OLEDs), solar cells and low-cost devices (Kitamura,Arakawa, 2008;. Hwan et al.2004; Byoungnan,2008). Organic semiconductors are materials with semiconducting.

  17. Linear response at the 4-component relativistic level

    DEFF Research Database (Denmark)

    Saue, T.; Jensen, Hans Jørgen Aagaard

    2003-01-01

    The theory, implementation, and application of linear response at the 4-component relativistic closed-shell Hartree-Fock level based on the concept of quasienergy and time averaging are reported. As such, an efficient AO-driven algorithm is obtained by assigning specific Hermiticity and time...

  18. Reaction Kinetics of Acetone Peroxide Formation and Structure Investigations Using Raman Spectroscopy and X-ray Diffraction

    DEFF Research Database (Denmark)

    Jensen, Lars; Mortensen, Peter Mølgaard; Trane, Rasmus

    2009-01-01

    functional theory (DFT)/Hartree-Fock approach. It was not possible from this to assess with certainty which intermediate products formed most extensively in an acetone/hydrogen peroxide mixture. However, it was concluded that the most likely reaction mixture is a mixture of the different intermediate...

  19. Journal of Chemical Sciences | Indian Academy of Sciences

    Indian Academy of Sciences (India)

    Abstract. The structure and coordination chemistry of boron porphyrin complexes B2OX2 (TYPP) (X = OH, F; Y = Cl, CH3) in connection with its chemical reactivity are analyzed at ab initio density functional theory B3LYP/6-31G∗ and restricted Hartree-Fock RHF/6-31G∗ levels of theory. Global reactivity and local selectivity ...

  20. Self-consistent collective-coordinate method for ''maximally-decoupled'' collective subspace and its boson mapping: Quantum theory of ''maximally-decoupled'' collective motion

    International Nuclear Information System (INIS)

    Marumori, T.; Sakata, F.; Maskawa, T.; Une, T.; Hashimoto, Y.

    1983-01-01

    The main purpose of this paper is to develop a full quantum theory, which is capable by itself of determining a ''maximally-decoupled'' collective motion. The paper is divided into two parts. In the first part, the motivation and basic idea of the theory are explained, and the ''maximal-decoupling condition'' on the collective motion is formulated within the framework of the time-dependent Hartree-Fock theory, in a general form called the invariance principle of the (time-dependent) Schrodinger equation. In the second part, it is shown that when the author positively utilize the invariance principle, we can construct a full quantum theory of the ''maximally-decoupled'' collective motion. This quantum theory is shown to be a generalization of the kinematical boson-mapping theories so far developed, in such a way that the dynamical ''maximal-decoupling condition'' on the collective motion is automatically satisfied

  1. Cross-sections for neutrino-nucleus interactions on $^{12}C$ and $^{16}O$

    CERN Document Server

    Jachowicz, N; Heyde, Kris L G

    1998-01-01

    We calculate cross sections for neutral current quasi-elastic neutrino-nucleus scattering within a continuum RPA model, based on a Green's function approach. As residual interaction a Skyrme force is used. The unperturbed single particle wave functions are generated using either a Woods-Saxon potential or a Hartree-Fock calculation. These calculations have interesting applications. Neutrinos play an important role in supernova nucleosynthesis. To obtain more information about these processes, cross sections are folded with a Fermi-Dirac distribution with temperatures of approximately 10 9 K.

  2. Cross-sections for neutral-current neutrino-nucleus interactions applications for $^{12}$C and $^{16}$O

    CERN Document Server

    Jachowicz, N; Heyde, Kris L G; Ryckebusch, J

    1999-01-01

    We calculate cross sections for neutral current quasi-elastic neutrino-nucleus scattering within a continuum RPA model, based on a Green's function approach. As residual interaction a Skyrme force is used. The unperturbed single particle wave functions are generated using either a Woods-Saxon potential or a Hartree-Fock calculation. These calculations have interesting applications. Neutrinos play an important role in supernova nucleosynthesis. To obtain more information about these processes, cross sections are folded with a Fermi-Dirac distribution with temperatures of approximately 10$^9$ K.

  3. Natural excitation orbitals from linear response theories : Time-dependent density functional theory, time-dependent Hartree-Fock, and time-dependent natural orbital functional theory

    NARCIS (Netherlands)

    Van Meer, R.; Gritsenko, O. V.; Baerends, E. J.

    2017-01-01

    Straightforward interpretation of excitations is possible if they can be described as simple single orbital-to-orbital (or double, etc.) transitions. In linear response time-dependent density functional theory (LR-TDDFT), the (ground state) Kohn-Sham orbitals prove to be such an orbital basis. In

  4. Test of atomic theory by photoelectron spectrometry with synchrotron radiation

    International Nuclear Information System (INIS)

    Krause, M.O.

    1984-01-01

    The successful combination of synchrotron radiation with electron spectrometry, accomplished at Daresbury, England and Orsay, France, made it possible to investigate sigma/sub x/ and β/sub x/ continuously over the very soft x-ray or the uv range of photon energies. The detailed and highly differentiated data resulting from this advanced experimentation put theory to a stringent test. In the interplay between theory and experiment, sophisticated Hartree Fock (HF) based models were developed which included both relativistic and many-electron effects. These theoretical models have provided us with a better insight than previously possible into the physics of the photon-atom interaction and the electronic structure and dynamics of atoms. However, critical experiments continue to be important for further improvements of theory. A number of such experiments are discussed in this presentation. The dynamic properties determined in these studies include in addition to sigma/sub x/ and β/sub x/ the spin polarization parameters. As a result the comparison between theory and experiment becomes rigorous, detailed and comprehensive. 46 references, 6 figures

  5. A study on the multiple solutions of the Martree-Fock-Roothaan equation for closed shell systems

    International Nuclear Information System (INIS)

    Malbouisson, L.A.C.

    1985-01-01

    An analysis of the multiple solutions of the Hartree-Fock-Roothaan equation for closed shell systems is done. The meaning of these solutions is discussed as self-consistent solutions of the pseudo-eingen-value equation and a general method for obtaining them is proposed. It is developed a criterion of stability for classifying the solutions depending on the type of the extremum point of the electronic energy function that the solution represent. It is also shown the existence of a correspondence between the multiple solutions and the several ordering rules that can be introduced for the usual iterative procedure of resolution of the equation. All the analysis and procedures developed are applied to the systems LiH, BH, Be and He. (author) [pt

  6. Molecular-crystal approach to accounting of correlation corrections in the chemical bond theory in crystals: electronic structure of Ti2O3 crystal

    International Nuclear Information System (INIS)

    Ehvarestov, R.A.; Panin, A.I.

    2000-01-01

    The problem on the possibility of partial accounting for the electron correlation effects within the frames of the Hartree-Fock unlimited method (HF). The local characteristic of the electron structure of the molecular systems for the case of the multi-determinant wave functions, configurational interaction methods and multiconfigurational self-consistent field (MCSCF) are determined. The molecular-crystalline approach is applied to studies on the electron correlation effects in the Ti 2 O 3 crystal. It is shown on the basis of the [Ti 2 O 9 ] 12- cluster electron structure calculation, that the Hartree-Fock unlimited method accounts in a number of cases for an essential part of statistical correlation effects. The energy values and local characteristics of the [Ti 2 O 9 ] 12- cluster, calculated through the HF and MCSCF methods, are presented [ru

  7. Kohn's theorem in a superfluid Fermi gas with a Feshbach resonance

    International Nuclear Information System (INIS)

    Ohashi, Y.

    2004-01-01

    We investigate the dipole mode in a superfluid gas of Fermi atoms trapped in a harmonic potential. According to Kohn's theorem, the frequency of this collective mode is not affected by an interaction between the atoms and is always equal to the trap frequency. This remarkable property, however, does not necessarily hold in an approximate theory. We explicitly prove that the Hartree-Fock-Bogoliubov generalized random phase approximation (HFB-GRPA), including a coupling between fluctuations in the density and Cooper channels, is consistent with both Kohn's theorem as well as Goldstone's theorem. This proof can be immediately extended to the strong-coupling superfluid theory developed by Nozieres and Schmitt-Rink (NSR), where the effect of superfluid fluctuations is included within the Gaussian level. As a result, the NSR-GRPA formalism can be used to study collective modes in the BCS-BEC crossover region in a manner which is consistent with Kohn's theorem. We also include the effect of a Feshbach resonance and a condensate of the associated molecular bound states. A detailed discussion is given of the unusual nature of the Kohn mode eigenfunctions in a Fermi superfluid, in the presence and absence of a Feshbach resonance. When the molecular bosons feel a different trap frequency from the Fermi atoms, the dipole frequency is shown to depend on the strength of effective interaction associated with the Feshbach resonance

  8. The effect of basis set and exchange-correlation functional on time-dependent density functional theory calculations within the Tamm-Dancoff approximation of the x-ray emission spectroscopy of transition metal complexes.

    Science.gov (United States)

    Roper, Ian P E; Besley, Nicholas A

    2016-03-21

    The simulation of X-ray emission spectra of transition metal complexes with time-dependent density functional theory (TDDFT) is investigated. X-ray emission spectra can be computed within TDDFT in conjunction with the Tamm-Dancoff approximation by using a reference determinant with a vacancy in the relevant core orbital, and these calculations can be performed using the frozen orbital approximation or with the relaxation of the orbitals of the intermediate core-ionised state included. Both standard exchange-correlation functionals and functionals specifically designed for X-ray emission spectroscopy are studied, and it is shown that the computed spectral band profiles are sensitive to the exchange-correlation functional used. The computed intensities of the spectral bands can be rationalised by considering the metal p orbital character of the valence molecular orbitals. To compute X-ray emission spectra with the correct energy scale allowing a direct comparison with experiment requires the relaxation of the core-ionised state to be included and the use of specifically designed functionals with increased amounts of Hartree-Fock exchange in conjunction with high quality basis sets. A range-corrected functional with increased Hartree-Fock exchange in the short range provides transition energies close to experiment and spectral band profiles that have a similar accuracy to those from standard functionals.

  9. Fourth nuclear theory workshop 'clusters in nuclei'

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    2005-07-01

    This document gathers the slides of 3 lectures: 1) the R-matrix method, 2) from realistic NN-interactions to cluster structures in nuclei - in this part the unitary correlation operator method (UCOM) is applied to 3 domains: the fermionic molecular dynamics, the Hartree-Fock approximation, and the no-core shell model -, and 3) the shell model point of view on cluster states.

  10. Simulations and analysis of the Raman scattering and differential Raman scattering/Raman optical activity (ROA) spectra of amino acids, peptides and proteins in aqueous solution

    DEFF Research Database (Denmark)

    Jalkanen, Karl J.; Nieminen, R. M.; Bohr, Jakob

    2000-01-01

    The Raman and Raman optical activity (ROA) spectra of amino acids and small peptides in aqueous solution have been simulated by density functional theory and restricted Hartree/Fock methods. The treatment of the aqueous environment in treated in two ways. The water molecules in the first hydratio...

  11. Polarizable Density Embedding Coupled Cluster Method

    DEFF Research Database (Denmark)

    Hršak, Dalibor; Olsen, Jógvan Magnus Haugaard; Kongsted, Jacob

    2018-01-01

    by an embedding potential consisting of a set of fragment densities obtained from calculations on isolated fragments with a quantum-chemistry method such as Hartree-Fock (HF) or Kohn-Sham density functional theory (KS-DFT) and dressed with a set of atom-centered anisotropic dipole-dipole polarizabilities...

  12. Extended Møller-Plesset perturbation theory for dynamical and static correlations

    International Nuclear Information System (INIS)

    Tsuchimochi, Takashi; Van Voorhis, Troy

    2014-01-01

    We present a novel method that appropriately handles both dynamical and static electron correlations in a balanced manner, using a perturbation theory on a spin-extended Hartree-Fock (EHF) wave function reference. While EHF is a suitable candidate for degenerate systems where static correlation is ubiquitous, it is known that most of dynamical correlation is neglected in EHF. In this work, we derive a perturbative correction to a fully spin-projected self-consistent wave function based on second-order Møller-Plesset perturbation theory (MP2). The proposed method efficiently captures the ability of EHF to describe static correlation in degeneracy, combined with MP2's ability to treat dynamical correlation effects. We demonstrate drastic improvements on molecular ground state and excited state potential energy curves and singlet-triplet splitting energies over both EHF and MP2 with similar computational effort to the latter

  13. A J matrix engine for density functional theory calculations

    International Nuclear Information System (INIS)

    White, C.A.; Head-Gordon, M.

    1996-01-01

    We introduce a new method for the formation of the J matrix (Coulomb interaction matrix) within a basis of Cartesian Gaussian functions, as needed in density functional theory and Hartree endash Fock calculations. By summing the density matrix into the underlying Gaussian integral formulas, we have developed a J matrix open-quote open-quote engine close-quote close-quote which forms the exact J matrix without explicitly forming the full set of two electron integral intermediates. Several precomputable quantities have been identified, substantially reducing the number of floating point operations and memory accesses needed in a J matrix calculation. Initial timings indicate a speedup of greater than four times for the (pp parallel pp) class of integrals with speedups increasing to over ten times for (ff parallel ff) integrals. copyright 1996 American Institute of Physics

  14. Positive semidefinite tensor factorizations of the two-electron integral matrix for low-scaling ab initio electronic structure.

    Science.gov (United States)

    Hoy, Erik P; Mazziotti, David A

    2015-08-14

    Tensor factorization of the 2-electron integral matrix is a well-known technique for reducing the computational scaling of ab initio electronic structure methods toward that of Hartree-Fock and density functional theories. The simplest factorization that maintains the positive semidefinite character of the 2-electron integral matrix is the Cholesky factorization. In this paper, we introduce a family of positive semidefinite factorizations that generalize the Cholesky factorization. Using an implementation of the factorization within the parametric 2-RDM method [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)], we study several inorganic molecules, alkane chains, and potential energy curves and find that this generalized factorization retains the accuracy and size extensivity of the Cholesky factorization, even in the presence of multi-reference correlation. The generalized family of positive semidefinite factorizations has potential applications to low-scaling ab initio electronic structure methods that treat electron correlation with a computational cost approaching that of the Hartree-Fock method or density functional theory.

  15. Positive semidefinite tensor factorizations of the two-electron integral matrix for low-scaling ab initio electronic structure

    Energy Technology Data Exchange (ETDEWEB)

    Hoy, Erik P.; Mazziotti, David A., E-mail: damazz@uchicago.edu [Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 (United States)

    2015-08-14

    Tensor factorization of the 2-electron integral matrix is a well-known technique for reducing the computational scaling of ab initio electronic structure methods toward that of Hartree-Fock and density functional theories. The simplest factorization that maintains the positive semidefinite character of the 2-electron integral matrix is the Cholesky factorization. In this paper, we introduce a family of positive semidefinite factorizations that generalize the Cholesky factorization. Using an implementation of the factorization within the parametric 2-RDM method [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)], we study several inorganic molecules, alkane chains, and potential energy curves and find that this generalized factorization retains the accuracy and size extensivity of the Cholesky factorization, even in the presence of multi-reference correlation. The generalized family of positive semidefinite factorizations has potential applications to low-scaling ab initio electronic structure methods that treat electron correlation with a computational cost approaching that of the Hartree-Fock method or density functional theory.

  16. Comparative studies of atomic independent-particle potentials

    International Nuclear Information System (INIS)

    Talman, J.D.; Ganas, P.S.; Green, A.E.S.

    1979-01-01

    A number of atomic properties are compared in various independent-particle models for atoms. The models studied are the Hartree-Fock method, a variationally optimized potential model, a parametrized analytic form of the same model, parametrized analytic models constructed to fit atomic energy levels, the so-called Hartree-Fock-Slater model, and the Xα model. The physical properties compared are single-particle energy levels, total energies, and dipole polarizabilities. The extent to which the virial theorem is satisfied in the different models is also considered. The atoms Be, Ne, Ar, Kr, and Xe and ions O v and Al iv hav been compared. The results show that the experimental properties can be well represented by several of the independent-particle models. Since it has been shown that the optimized potential models yield wavefunctions that are almost the same as Hartree-Fock wavefunctions, they provide a natural solution to the problem of extending the Hartree-Fock method to excited states

  17. Inner-shell correlations and Sturm expansions in coupled perturbation calculations of atomic systems

    International Nuclear Information System (INIS)

    Sherstyuk, A.I.; Solov'eva, G.S.

    1995-01-01

    It is shown that virtual Hartree-Fock orbitals in Sturm-type expansions can be used to calculate the response of atomic systems to an external field within the framework of the coupled perturbation theory with allowance for correlation effects. The corrected electron-electron interaction in a system with field-distorted orbitals is considered by adding a nonlocal potential to a one-electron Hartree-Fock operator within each group of equivalent elections. The remaining correlation effects are calculated by solving a system of equations for corrections to the radial functions. The system is solved iteratively, with each subsequent iteration corresponding to a correction of an increasingly higher order in the electron--electron interaction. The explicit expression derived for the polarizability contains one-and two-particle radial integrals of the Sturm functions

  18. Physical Origin of Density Dependent Force of the Skyrme Type within the Quark Meson Coupling Model

    International Nuclear Information System (INIS)

    Pierre Guichon; Hrayr Matevosyan; N. Sandulescu; Anthony Thomas

    2006-01-01

    A density dependent, effective nucleon-nucleon force of the Skyrme type is derived from the quark-meson coupling model--a self-consistent, relativistic quark level description of nuclear matter. This new formulation requires no assumption that the mean scalar field is small and hence constitutes a significant advance over earlier work. The similarity of the effective interaction to the widely used SkM* force encourages us to apply it to a wide range of nuclear problems, beginning with the binding energies and charge distributions of doubly magic nuclei. Finding impressive results in this conventional arena, we apply the same effective interaction, within the Hartree-Fock-Bogoliubov approach, to the properties of nuclei far from stability. The resulting two neutron drip lines and shell quenching are quite satisfactory. Finally, we apply the relativistic formulation to the properties of dense nuclear matter in anticipation of future application to the properties of neutron stars

  19. On the continuum limit of a Z4 lattice gauge theory

    International Nuclear Information System (INIS)

    Pena, A.; Socolovsky, M.

    1983-01-01

    The continuum limit of a Z 4 gauge plus matter lattice theory is identified with massless scalar and vector fields with quartic self-interactions phi 4 and (AμAμ) 2 , respectively. The analysis is based on the mean field approximation after gauge fixing. (orig.)

  20. Microscopic approach to subthreshold pion production in heavy-ion collisions

    International Nuclear Information System (INIS)

    Tohyama, M.; Kaps, R.; Masak, D.; Mosel, U.

    1985-01-01

    A microscopic approach to subthreshold pion production in heavy-ion collisions is proposed, in which the wave function of the nucleon system is approximated in the time-dependent Hartree-Fock theory and an effective interaction for the pion-production process is taken from (p,π) reaction theories. The model is applied to pion production in 16 O + 16 O collisions. (orig.)

  1. The temperature dependence of giant resonances in high-excited nucleus

    International Nuclear Information System (INIS)

    Li Ming; Song Hongqiu

    1991-01-01

    The Hartree-Fock equation and the linear response theory in finite temperature are used to calculate the positions and transition strenghths of the giant resonances of high-excited nucleus Pb 208 . The result shows a downward shift and a broadening of the giant resonance energies as temperatrue increases

  2. Ab initio benchmark study for the oxidative addition of CH4 to Pd: importance of basis-set flexibility and polarization

    NARCIS (Netherlands)

    de Jong, G.T.; Sola, M.; Visscher, L.; Bickelhaupt, F.M.

    2004-01-01

    To obtain a state-of-the-art benchmark potential energy surface (PES) for the archetypal oxidative addition of the methane C-H bond to the palladium atom, we have explored this PES using a hierarchical series of ab initio methods (Hartree-Fock, second-order Møller-Plesset perturbation theory,

  3. Theoretical studies of atomic transitions. Progress report, March 15, 1985-March 14, 1986

    International Nuclear Information System (INIS)

    Fischer, C.F.

    1986-01-01

    A brief description of the research program for atomic studies is given. The program includes an effort to combine the Multi-Configuration Hartree-Fock (MCHF) method with Many-Body Perturbation Theory and the development of a database system for atomic data generated by the atomic structure package. 6 refs

  4. Multiconfiguration hartree-fock theory for pseudorelativistic systems: The time-dependent case

    KAUST Repository

    Hajaiej, Hichem; Markowich, Peter A.; Trabelsi, Saber

    2014-01-01

    to the underlying system under technical assumptions on the energy of the initial data and the charge of the nucleus. Moreover, we prove that the result can be extended to the case of neutron stars when the number of electrons is less than a critical number N cr

  5. Hartree-Fock and density functional theory study of alpha-cyclodextrin conformers.

    Science.gov (United States)

    Jiménez, Verónica; Alderete, Joel B

    2008-01-31

    Herein, we report the geometry optimization of four conformers of alpha-cyclodextrin (alpha-CD) by means of PM3, HF/STO-3G, HF/3-21G, HF/6-31G(d), B3LYP/6-31G(d), and X3LYP/6-31G(d) calculations. The analysis of several geometrical parameters indicates that all conformers possess bond lengths, angles, and dihedrals that agree fairly well with the crystalline structure of alpha-CD. However, only three of them (1-3) resemble the polar character of CDs and show intramolecular hydrogen-bonding patterns that agree with experimental NMR data. Among them, conformer 3 appears to be the most stable species both in the gas phase and in solution; therefore, it is expected to be the most suitable representative structure for alpha-CD conformation. The purpose of selecting such a species is to identify an appropriate structure to be employed as a starting point for reliable computational studies on complexation phenomena. Our results indicate that the choice of a particular alpha-CD conformer should affect the results of ab initio computational studies on the inclusion complexation with this cyclodextrin since both the direction and the magnitude of the dipole moment depend strongly on the conformation of alpha-CD.

  6. A single-electron picture based on the multiconfiguration time-dependent Hartree-Fock method: application to the anisotropic ionization and subsequent high-harmonic generation of the CO molecule

    Science.gov (United States)

    Ohmura, S.; Kato, T.; Oyamada, T.; Koseki, S.; Ohmura, H.; Kono, H.

    2018-02-01

    The mechanisms of anisotropic near-IR tunnel ionization and high-order harmonic generation (HHG) in a CO molecule are theoretically investigated by using the multiconfiguration time-dependent Hartree-Fock (MCTDHF) method developed for the simulation of multielectron dynamics of molecules. The multielectron dynamics obtained by numerically solving the equations of motion (EOMs) in the MCTDHF method is converted to a single orbital picture in the natural orbital representation where the first-order reduced density matrix is diagonalized. The ionization through each natural orbital is examined and the process of HHG is classified into different optical paths designated by a combinations of initial, intermediate and final natural orbitals. The EOMs for natural spin-orbitals are also derived within the framework of the MCTDHF, which maintains the first-order reduced density matrix to be a diagonal one throughout the time propagation of a many-electron wave function. The orbital dependent, time-dependent effective potentials that govern the dynamics of respective time-dependent natural orbitals are deduced from the derived EOMs, of which the temporal variation can be used to interpret the motion of the electron density associated with each natural spin-orbital. The roles of the orbital shape, multiorbital ionization, linear Stark effect and multielectron interaction in the ionization and HHG of a CO molecule are revealed by the effective potentials obtained. When the laser electric field points to the nucleus O from C, tunnel ionization from the C atom side is enhanced; a hump structure originating from multielectron interaction is then formed on the top of the field-induced distorted barrier of the HOMO effective potential. This hump formation, responsible for the directional anisotropy of tunnel ionization, restrains the influence of the linear Stark effect on the energy shifts of bound states.

  7. A microscopic study of giant resonances in nuclei near drip lines

    CERN Document Server

    Sagawa, H; Zhang, X Z

    1999-01-01

    We study giant resonances using the self-consistent Hartree-Fock calculation plus the random phase approximation with Skyrme interactions. Including simultaneously both the isoscalar and the isovector correlation the RPA response function is calculated in the coordinate space so as to take properly into account the continuum effect. Giant monopole states are discussed in relation with the nuclear compression modulus of the nuclear matter K sub n sub m. The core polarization charges are also discussed in comparison with recent empirical data in sup 1 sup 0 sup 0 Sn region.

  8. Nuclear vorticity and the low-energy nuclear response. Towards the neutron drip line

    International Nuclear Information System (INIS)

    Papakonstantinou, P.; Athens Univ.; Wambach, J.; Ponomarev, V.Y.; Mavrommatis, E.

    2004-01-01

    The transition density and current provide valuable insight into the nature of nuclear vibrations. Nuclear vorticity is a quantity related to the transverse transition current. In this work, we study the evolution of the strength distribution, related to density fluctuations, and the vorticity strength distribution, as the neutron drip line is approached. Our results on the isoscalar, natural-parity multipole response of Ni isotopes, obtained by using a self-consistent Skyrme-Hartree-Fock+continuum RPA model, indicate that, close to the drip line, the low-energy response is dominated by L > 1 vortical transitions. (orig.)

  9. Estudo QSPR sobre os coeficientes de partição: descritores mecânico-quânticos e análise multivariada QSPR study on partition coefficients: quantum-mechanical descriptors and multivariate analysis

    Directory of Open Access Journals (Sweden)

    Edilson Grünheidt Borges

    2002-12-01

    Full Text Available Quantum chemistry and multivariate analysis were used to estimate the partition coefficients between n-octanol and water for a serie of 188 compounds, with the values of the q 2 until 0.86 for crossvalidation test. The quantum-mechanical descriptors are obtained with ab initio calculation, using the solvation effects of the Polarizable Continuum Method. Two different Hartree-Fock bases were used, and two different ways for simulating solvent cavity formation. The results for each of the cases were analised, and each methodology proposed is indicated for particular case.

  10. Correlation Matrix Renormalization Theory: Improving Accuracy with Two-Electron Density-Matrix Sum Rules.

    Science.gov (United States)

    Liu, C; Liu, J; Yao, Y X; Wu, P; Wang, C Z; Ho, K M

    2016-10-11

    We recently proposed the correlation matrix renormalization (CMR) theory to treat the electronic correlation effects [Phys. Rev. B 2014, 89, 045131 and Sci. Rep. 2015, 5, 13478] in ground state total energy calculations of molecular systems using the Gutzwiller variational wave function (GWF). By adopting a number of approximations, the computational effort of the CMR can be reduced to a level similar to Hartree-Fock calculations. This paper reports our recent progress in minimizing the error originating from some of these approximations. We introduce a novel sum-rule correction to obtain a more accurate description of the intersite electron correlation effects in total energy calculations. Benchmark calculations are performed on a set of molecules to show the reasonable accuracy of the method.

  11. Geometry and time scales of self-consistent orbits in a modified SU(2) model

    International Nuclear Information System (INIS)

    Jezek, D.M.; Hernandez, E.S.; Solari, H.G.

    1986-01-01

    We investigate the time-dependent Hartree-Fock flow pattern of a two-level many fermion system interacting via a two-body interaction which does not preserve the parity symmetry of standard SU(2) models. The geometrical features of the time-dependent Hartree-Fock energy surface are analyzed and a phase instability is clearly recognized. The time evolution of one-body observables along self-consistent and exact trajectories are examined together with the overlaps between both orbits. Typical time scales for the determinantal motion can be set and the validity of the time-dependent Hartree-Fock approach in the various regions of quasispin phase space is discussed

  12. Global hybrids from the semiclassical atom theory satisfying the local density linear response.

    Science.gov (United States)

    Fabiano, Eduardo; Constantin, Lucian A; Cortona, Pietro; Della Sala, Fabio

    2015-01-13

    We propose global hybrid approximations of the exchange-correlation (XC) energy functional which reproduce well the modified fourth-order gradient expansion of the exchange energy in the semiclassical limit of many-electron neutral atoms and recover the full local density approximation (LDA) linear response. These XC functionals represent the hybrid versions of the APBE functional [Phys. Rev. Lett. 2011, 106, 186406] yet employing an additional correlation functional which uses the localization concept of the correlation energy density to improve the compatibility with the Hartree-Fock exchange as well as the coupling-constant-resolved XC potential energy. Broad energetic and structural testing, including thermochemistry and geometry, transition metal complexes, noncovalent interactions, gold clusters and small gold-molecule interfaces, as well as an analysis of the hybrid parameters, show that our construction is quite robust. In particular, our testing shows that the resulting hybrid, including 20% of Hartree-Fock exchange and named hAPBE, performs remarkably well for a broad palette of systems and properties, being generally better than popular hybrids (PBE0 and B3LYP). Semiempirical dispersion corrections are also provided.

  13. Single-photon double ionization: renormalized-natural-orbital theory versus multi-configurational Hartree–Fock

    International Nuclear Information System (INIS)

    Brics, M; Rapp, J; Bauer, D

    2017-01-01

    The N -particle wavefunction has too many dimensions for a direct time propagation of a many-body system according to the time-dependent Schrödinger equation (TDSE). On the other hand, time-dependent density functional theory (TDDFT) tells us that the single-particle density is, in principle, sufficient. However, a practicable equation of motion for the accurate time evolution of the single-particle density is unknown. It is thus an obvious idea to propagate a quantity which is not as reduced as the single-particle density but less dimensional than the N -body wavefunction. Recently, we have introduced time-dependent renormalized-natural-orbital theory (TDRNOT). TDRNOT is based on the propagation of the eigenfunctions of the one-body reduced density matrix, the so-called natural orbitals. In this paper we demonstrate how TDRNOT is related to the multi-configurational time-dependent Hartree–Fock (MCTDHF) approach. We also compare the performance of MCTDHF and TDRNOT versus the TDSE for single-photon double ionization (SPDI) of a 1D helium model atom. SPDI is one of the effects where TDDFT does not work in practice, especially if one is interested in correlated photoelectron spectra, for which no explicit density functional is known. (paper)

  14. Microscopic theory of nuclear collective dynamics

    International Nuclear Information System (INIS)

    Sakata, Fumihiko; Marumori, Toshio; Hashimoto, Yukio; Tsukuma, Hidehiko; Yamamoto, Yoshifumi; Iwasawa, Kazuo.

    1990-10-01

    A recent development of the INS-TSUKUBA joint research project on large-amplitude collective motion is summarized by putting special emphasis on an inter-relationship between quantum chaos and nuclear spectroscopy. Aiming at introducing various concepts used in this lecture, we start with recapitulating the semi-classical theory of nuclear collective dynamics formulated within the time-dependent Hartree-Fock (TDHF) theory. The central part of the semi-classical theory is provided by the self-consistent collective coordinate (SCC) method which has been developed to properly take account of the non-linear dynamics specific for the finite many-body quantum system. A decisive role of the level crossing dynamics on the order-to-chaos transition of collective motion is discussed in detail. Extending the basic idea of the semi-classical theory, we discuss a full quantum theory of nuclear collective dynamics which allows us to properly define a concept of the quantum integrability as well as the quantum chaoticity for each eigenfunction. The lecture is arranged so as to clearly show the similar structure between the semi-classical and quantum theories of nuclear collective dynamics. Using numerical calculations, we illustrate what the quantum chaos for each eigenfunction means and relate it to the usual definition of quantum chaos for nearest neighbor level spacing statistics based on the random matrix theory. (author)

  15. Communication: Orbital instabilities and triplet states from time-dependent density functional theory and long-range corrected functionals

    Science.gov (United States)

    Sears, John S.; Koerzdoerfer, Thomas; Zhang, Cai-Rong; Brédas, Jean-Luc

    2011-10-01

    Long-range corrected hybrids represent an increasingly popular class of functionals for density functional theory (DFT) that have proven to be very successful for a wide range of chemical applications. In this Communication, we examine the performance of these functionals for time-dependent (TD)DFT descriptions of triplet excited states. Our results reveal that the triplet energies are particularly sensitive to the range-separation parameter; this sensitivity can be traced back to triplet instabilities in the ground state coming from the large effective amounts of Hartree-Fock exchange included in these functionals. As such, the use of standard long-range corrected functionals for the description of triplet states at the TDDFT level is not recommended.

  16. Finite-field evaluation of the Lennard-Jones atom-wall interaction constant C3 for alkali-metal atoms

    International Nuclear Information System (INIS)

    Johnson, W.R.; Dzuba, V.A.; Safronova, U.I.; Safronova, M.S.

    2004-01-01

    A finite-field scaling method is applied to evaluate the Lennard-Jones interaction constant C 3 for alkali-metal atoms. The calculations are based on the relativistic single-double approximation in which single and double excitations of Dirac-Hartree-Fock wave functions are included to all orders in perturbation theory

  17. Comment on "Density functional theory is straying from the path toward the exact functional"

    DEFF Research Database (Denmark)

    Kepp, Kasper Planeta

    2017-01-01

    Medvedev et al (Reports, 6 January 2017, p. 49) argue that recent density functionals stray from the path toward exactness. This conclusion rests on very compact 1s2 and 1s22s2 systems favored by the Hartree-Fock picture. Comparison to actual energies for the same systems indicates that the "stra...

  18. The light-cone Fock state expansion and hadron physics phenomenology

    International Nuclear Information System (INIS)

    Brodsky, S.J.

    1997-06-01

    The light-cone Fock expansion is defined in the following way: one first constructs the light-cone time evolution operator and the invariant mass operator in light-cone gauge from the QCD Lagrangian. The total longitudinal momentum and transverse momenta are conserved, i.e. are independent of the interactions. The matrix elements of the invariant mass operator on the complete orthonormal basis of the free theory can then be constructed. The matrix elements connect Fock states differing by 0, 1, or 2 quark or gluon quanta, and they include the instantaneous quark and gluon contributions imposed by eliminating dependent degrees of freedom in light-cone gauge. Applications of light-cone methods to QCD phenomenology are briefly described

  19. Coulomb correlations in many-electron systems on the level of self-consistent fields

    International Nuclear Information System (INIS)

    Warken, M.

    1991-06-01

    It was the aim of this thesis to show means and ways, in order to regard Coulomb correlation already on the SCF level. As mean to facilitate this general averaged fields should serve. For this first in chapter I was shown, how by means of suitable gauge fixings terms into effective potentials of the Hartree-Fock or g-Hartree type are introduced, which permit an interpretation as correlation density or as effective coupling constant. The following considerations were exemplarily performed on the cases g-Hartree (in Coulomb gauge) and on f-Hartree-Fock. (orig./HSI) [de

  20. Relativistic approach to nuclear structure

    International Nuclear Information System (INIS)

    Nguyen Van Giai; Bouyssy, A.

    1987-03-01

    Some recent works related with relativistic models of nuclear structure are briefly reviewed. The Dirac-Hartree-Fock and Dirac-Brueckner-Hartree-Fock are recalled and illustrated by some examples. The problem of isoscalar current and magnetic moments of odd nuclei is discussed. The application of the relativistic model to the nuclear response function is examined