WorldWideScience

Sample records for relativistic hartree approximation

  1. Toward a consistent random phase approximation based on the relativistic Hartree approximation

    International Nuclear Information System (INIS)

    Price, C.E.; Rost, E.; Shepard, J.R.; McNeil, J.A.

    1992-01-01

    We examine the random phase approximation (RPA) based on a relativistic Hartree approximation description for nuclear ground states. This model includes contributions from the negative energy sea at the one-loop level. We emphasize consistency between the treatment of the ground state and the RPA. This consistency is important in the description of low-lying collective levels but less important for the longitudinal (e,e') quasielastic response. We also study the effect of imposing a three-momentum cutoff on negative energy sea contributions. A cutoff of twice the nucleon mass improves agreement with observed spin-orbit splittings in nuclei compared to the standard infinite cutoff results, an effect traceable to the fact that imposing the cutoff reduces m * /m. Consistency is much more important than the cutoff in the description of low-lying collective levels. The cutoff model also provides excellent agreement with quasielastic (e,e') data

  2. 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

  3. 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.)

  4. 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)

  5. 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.

  6. 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.)

  7. 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

  8. 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)

  9. 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

  10. 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.

  11. 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

  12. 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.)

  13. Strong semiclassical approximation of Wigner functions for the Hartree dynamics

    KAUST Repository

    Athanassoulis, Agissilaos; Paul, Thierry; Pezzotti, Federica; Pulvirenti, Mario

    2011-01-01

    We consider the Wigner equation corresponding to a nonlinear Schrödinger evolution of the Hartree type in the semiclassical limit h → 0. Under appropriate assumptions on the initial data and the interaction potential, we show that the Wigner function is close in L 2 to its weak limit, the solution of the corresponding Vlasov equation. The strong approximation allows the construction of semiclassical operator-valued observables, approximating their quantum counterparts in Hilbert-Schmidt topology. The proof makes use of a pointwise-positivity manipulation, which seems necessary in working with the L 2 norm and the precise form of the nonlinearity. We employ the Husimi function as a pivot between the classical probability density and the Wigner function, which - as it is well known - is not pointwise positive in general.

  14. 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....

  15. 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

  16. Relativistic quasiparticle random phase approximation in deformed nuclei

    Energy Technology Data Exchange (ETDEWEB)

    Pena Arteaga, D.

    2007-06-25

    Covariant density functional theory is used to study the influence of electromagnetic radiation on deformed superfluid nuclei. The relativistic Hartree-Bogolyubov equations and the resulting diagonalization problem of the quasiparticle random phase approximation are solved for axially symmetric systems in a fully self-consistent way by a newly developed parallel code. Three different kinds of high precision energy functionals are investigated and special care is taken for the decoupling of the Goldstone modes. This allows the microscopic investigation of Pygmy and scissor resonances in electric and magnetic dipole fields. Excellent agreement with recent experiments is found and new types of modes are predicted for deformed systems with large neutron excess. (orig.)

  17. 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.)

  18. Local density approximations for relativistic exchange energies

    International Nuclear Information System (INIS)

    MacDonald, A.H.

    1986-01-01

    The use of local density approximations to approximate exchange interactions in relativistic electron systems is reviewed. Particular attention is paid to the physical content of these exchange energies by discussing results for the uniform relativistic electron gas from a new point of view. Work on applying these local density approximations in atoms and solids is reviewed and it is concluded that good accuracy is usually possible provided self-interaction corrections are applied. The local density approximations necessary for spin-polarized relativistic systems are discussed and some new results are presented

  19. Neutrino-nucleus reaction rates based on the relativistic quasiparticle random phase approximation

    International Nuclear Information System (INIS)

    Paar, N.; Vretenar, D.; Marketin, T.; Ring, P.

    2008-01-01

    Neutrino-nucleus cross sections are described in a novel theoretical framework where the weak interaction of leptons with hadrons is expressed in the standard current-current form, the nuclear ground state is described in the relativistic Hartree-Bogoliubov model, and the relevant transitions to excited states are calculated in the relativistic quasiparticle random phase approximation. The model is employed in studies of neutrino-nucleus reactions in several test cases

  20. 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

  1. 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)

  2. Random phase approximation in relativistic approach

    International Nuclear Information System (INIS)

    Ma Zhongyu; Yang Ding; Tian Yuan; Cao Ligang

    2009-01-01

    Some special issues of the random phase approximation(RPA) in the relativistic approach are reviewed. A full consistency and proper treatment of coupling to the continuum are responsible for the successful application of the RPA in the description of dynamical properties of finite nuclei. The fully consistent relativistic RPA(RRPA) requires that the relativistic mean filed (RMF) wave function of the nucleus and the RRPA correlations are calculated in a same effective Lagrangian and the consistent treatment of the Dirac sea of negative energy states. The proper treatment of the single particle continuum with scattering asymptotic conditions in the RMF and RRPA is discussed. The full continuum spectrum can be described by the single particle Green's function and the relativistic continuum RPA is established. A separable form of the paring force is introduced in the relativistic quasi-particle RPA. (authors)

  3. 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)

  4. 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.)

  5. 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.

  6. Intertwining solutions for magnetic relativistic Hartree type equations

    Science.gov (United States)

    Cingolani, Silvia; Secchi, Simone

    2018-05-01

    We consider the magnetic pseudo-relativistic Schrödinger equation where , m  >  0, is an external continuous scalar potential, is a continuous vector potential and is a convolution kernel, is a constant, , . We assume that A and V are symmetric with respect to a closed subgroup G of the group of orthogonal linear transformations of . If for any , the cardinality of the G-orbit of x is infinite, then we prove the existence of infinitely many intertwining solutions assuming that is either linear in x or uniformly bounded. The results are proved by means of a new local realization of the square root of the magnetic laplacian to a local elliptic operator with Neumann boundary condition on a half-space. Moreover we derive an existence result of a ground state intertwining solution for bounded vector potentials, if G admits a finite orbit.

  7. 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.)

  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. Electron correlation within the relativistic no-pair approximation

    Energy Technology Data Exchange (ETDEWEB)

    Almoukhalalati, Adel; Saue, Trond, E-mail: trond.saue@irsamc.ups-tlse.fr [Laboratoire de Chimie et Physique Quantique, UMR 5626 CNRS — Université Toulouse III-Paul Sabatier, 118 route de Narbonne, F-31062 Toulouse (France); Knecht, Stefan [ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich (Switzerland); Jensen, Hans Jørgen Aa. [Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense M (Denmark); Dyall, Kenneth G. [Dirac Solutions, 10527 NW Lost Park Drive, Portland, Oregon 97229 (United States)

    2016-08-21

    This paper addresses the definition of correlation energy within 4-component relativistic atomic and molecular calculations. In the nonrelativistic domain the correlation energy is defined as the difference between the exact eigenvalue of the electronic Hamiltonian and the Hartree-Fock energy. In practice, what is reported is the basis set correlation energy, where the “exact” value is provided by a full Configuration Interaction (CI) calculation with some specified one-particle basis. The extension of this definition to the relativistic domain is not straightforward since the corresponding electronic Hamiltonian, the Dirac-Coulomb Hamiltonian, has no bound solutions. Present-day relativistic calculations are carried out within the no-pair approximation, where the Dirac-Coulomb Hamiltonian is embedded by projectors eliminating the troublesome negative-energy solutions. Hartree-Fock calculations are carried out with the implicit use of such projectors and only positive-energy orbitals are retained at the correlated level, meaning that the Hartree-Fock projectors are frozen at the correlated level. We argue that the projection operators should be optimized also at the correlated level and that this is possible by full Multiconfigurational Self-Consistent Field (MCSCF) calculations, that is, MCSCF calculations using a no-pair full CI expansion, but including orbital relaxation from the negative-energy orbitals. We show by variational perturbation theory that the MCSCF correlation energy is a pure MP2-like correlation expression, whereas the corresponding CI correlation energy contains an additional relaxation term. We explore numerically our theoretical analysis by carrying out variational and perturbative calculations on the two-electron rare gas atoms with specially tailored basis sets. In particular, we show that the correlation energy obtained by the suggested MCSCF procedure is smaller than the no-pair full CI correlation energy, in accordance with the

  10. 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)

  11. Relativistic quasiparticle random phase approximation with a separable pairing force

    International Nuclear Information System (INIS)

    Tian Yuan; Ma Zhongyu; Ring Peter

    2009-01-01

    In our previous work, we introduced a separable pairing force for relativistic Hartree-Bogoliubov calculations. This force was adjusted to reproduce the pairing properties of the Gogny force in nuclear matter. By using the well known techniques of Talmi and Moshinsky it can be expanded in a series of separable terms and converges quickly after a few terms. It was found that the pairing properties can be depicted on almost the same footing as the original pairing interaction, not only in nuclear matter, but also in finite nuclei. In this study, we construct a relativistic quasiparticle random phase approximation (RQRPA) with this separable pairing interaction and calculate the excitation energies of the first excited 2 + states and reduced B(E2; 0 + →2 + ) transition rates for a chain of Sn isotopes in RQRPA. Compared with the results of the full Gogny force, we find that this simple separable pairing interaction can describe the pairing properties of the excited vibrational states as well as the original pairing interaction. (authors)

  12. Separable pairing force for relativistic quasiparticle random-phase approximation

    International Nuclear Information System (INIS)

    Tian Yuan; Ma Zhongyu; Ring, Peter

    2009-01-01

    We have introduced a separable pairing force, which was adjusted to reproduce the pairing properties of the Gogny force in nuclear matter. This separable pairing force is able to describe in relativistic Hartree-Bogoliubov (RHB) calculations the pairing properties in the ground state of finite nuclei on almost the same footing as the original Gogny interaction. In this work we investigate excited states using the Relativistic Quasiparticle Random-Phase Approximation (RQRPA) with the same separable pairing force. For consistency the Goldstone modes and the convergence with various cutoff parameters in this version of RQRPA are studied. The first excited 2 + states for the chain of Sn isotopes with Z=50 and the chain of isotones with N=82 isotones are calculated in RQRPA together with the 3 - states of Sn isotopes. By comparing our results with experimental data and with the results of the original Gogny force we find that this simple separable pairing interaction is very successful in depicting the pairing properties of vibrational excitations.

  13. 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

  14. Development of the relativistic impulse approximation

    International Nuclear Information System (INIS)

    Wallace, S.J.

    1985-01-01

    This talk contains three parts. Part I reviews the developments which led to the relativistic impulse approximation for proton-nucleus scattering. In Part II, problems with the impulse approximation in its original form - principally the low energy problem - are discussed and traced to pionic contributions. Use of pseudovector covariants in place of pseudoscalar ones in the NN amplitude provides more satisfactory low energy results, however, the difference between pseudovector and pseudoscalar results is ambiguous in the sense that it is not controlled by NN data. Only with further theoretical input can the ambiguity be removed. Part III of the talk presents a new development of the relativistic impulse approximation which is the result of work done in the past year and a half in collaboration with J.A. Tjon. A complete NN amplitude representation is developed and a complete set of Lorentz invariant amplitudes are calculated based on a one-meson exchange model and appropriate integral equations. A meson theoretical basis for the important pair contributions to proton-nucleus scattering is established by the new developments. 28 references

  15. Well-posedness for Semi-relativistic Hartree Equations of Critical Type

    International Nuclear Information System (INIS)

    Lenzmann, Enno

    2007-01-01

    We prove local and global well-posedness for semi-relativistic, nonlinear Schroedinger equations with initial data in H s (R 3 ). Here F(u) is a critical Hartree nonlinearity that corresponds to Coulomb or Yukawa type self-interactions. For focusing F(u), which arise in the quantum theory of boson stars, we derive global-in-time existence for small initial data, where the smallness condition is expressed in terms of the L 2 -norm of solitary wave ground states. Our proof of well-posedness does not rely on Strichartz type estimates. As a major benefit from this, our method enables us to consider external potentials of a quite general class

  16. Approximate relativistic corrections to atomic radial wave functions

    International Nuclear Information System (INIS)

    Cowan, R.D.; Griffin, D.C.

    1976-01-01

    The mass-velocity and Darwin terms of the one-electron-atom Pauli equation have been added to the Hartree-Fock differential equations by using the HX formula to calculate a local central field potential for use in these terms. Introduction of the quantum number j is avoided by omitting the spin-orbit term of the Pauli equation. The major relativistic effects, both direct and indirect, are thereby incorporated into the wave functions, while allowing retention of the commonly used nonrelativistic formulation of energy level calculations. The improvement afforded in calculated total binding energies, excitation energies, spin-orbit parameters, and expectation values of r/sub m/ is comparable with that provided by fully relativistic Dirac-Hartree-Fock calculations

  17. 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

  18. 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

  19. Time-dependent Hartree approximation and time-dependent harmonic oscillator model

    International Nuclear Information System (INIS)

    Blaizot, J.P.

    1982-01-01

    We present an analytically soluble model for studying nuclear collective motion within the framework of the time-dependent Hartree (TDH) approximation. The model reduces the TDH equations to the Schroedinger equation of a time-dependent harmonic oscillator. Using canonical transformations and coherent states we derive a few properties of the time-dependent harmonic oscillator which are relevant for applications. We analyse the role of the normal modes in the time evolution of a system governed by TDH equations. We show how these modes couple together due to the anharmonic terms generated by the non-linearity of the theory. (orig.)

  20. 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.)

  1. 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.

  2. 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...

  3. 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

  4. β-decay rates of r-process nuclei in the relativistic quasiparticle random phase approximation

    International Nuclear Information System (INIS)

    Niksic, T.; Marketin, T.; Vretenar, D.; Paar, N.; Ring, P.

    2004-01-01

    The fully consistent relativistic proton-neutron quasiparticle random phase approximation (PN-RQRPA) is employed in the calculation of β-decay half-lives of neutron-rich nuclei in the N∼50 and N∼82 regions. A new density-dependent effective interaction, with an enhanced value of the nucleon effective mass, is used in relativistic Hartree-Bogolyubov calculation of nuclear ground states and in the particle-hole channel of the PN-RQRPA. The finite range Gogny D1S interaction is employed in the T=1 pairing channel, and the model also includes a proton-neutron particle-particle interaction. The theoretical half-lives reproduce the experimental data for the Fe, Zn, Cd, and Te isotopic chains, but overestimate the lifetimes of Ni isotopes and predict a stable 132 Sn. (orig.)

  5. β-decay rates of r-process nuclei in the relativistic quasiparticle random phase approximation

    International Nuclear Information System (INIS)

    Niksic, T.; Marketin, T.; Vretenar, D.; Paar, N.; Ring, P.

    2005-01-01

    The fully consistent relativistic proton-neutron quasiparticle random phase approximation (PN-RQRPA) is employed in the calculation of β-decay half-lives of neutron-rich nuclei in the N≅50 and N≅82 regions. A new density-dependent effective interaction, with an enhanced value of the nucleon effective mass, is used in relativistic Hartree-Bogoliubov calculation of nuclear ground states and in the particle-hole channel of the PN-RQRPA. The finite range Gogny D1S interaction is employed in the T=1 pairing channel, and the model also includes a proton-neutron particle-particle interaction. The theoretical half-lives reproduce the experimental data for the Fe, Zn, Cd, and Te isotopic chains but overestimate the lifetimes of Ni isotopes and predict a stable 132 Sn

  6. Relativistic quasiparticle random-phase approximation calculation of total muon capture rates

    International Nuclear Information System (INIS)

    Marketin, T.; Paar, N.; Niksic, T.; Vretenar, D.

    2009-01-01

    The relativistic proton-neutron quasiparticle random phase approximation (pn-RQRPA) is applied in the calculation of total muon capture rates on a large set of nuclei from 12 C to 244 Pu, for which experimental values are available. The microscopic theoretical framework is based on the relativistic Hartree-Bogoliubov (RHB) model for the nuclear ground state, and transitions to excited states are calculated using the pn-RQRPA. The calculation is fully consistent, i.e., the same interactions are used both in the RHB equations that determine the quasiparticle basis, and in the matrix equations of the pn-RQRPA. The calculated capture rates are sensitive to the in-medium quenching of the axial-vector coupling constant. By reducing this constant from its free-nucleon value g A =1.262 by 10% for all multipole transitions, the calculation reproduces the experimental muon capture rates to better than 10% accuracy.

  7. {beta}-decay rates of r-process nuclei in the relativistic quasiparticle random phase approximation

    Energy Technology Data Exchange (ETDEWEB)

    Niksic, T.; Marketin, T.; Vretenar, D. [Zagreb Univ. (Croatia). Faculty of Science, Physics Dept.; Paar, N. [Technische Univ. Darmstadt (Germany). Inst. fuer Kernphysik; Ring, P. [Technische Univ. Muenchen, Garching (Germany). Physik-Department

    2004-12-08

    The fully consistent relativistic proton-neutron quasiparticle random phase approximation (PN-RQRPA) is employed in the calculation of {beta}-decay half-lives of neutron-rich nuclei in the N{approx}50 and N{approx}82 regions. A new density-dependent effective interaction, with an enhanced value of the nucleon effective mass, is used in relativistic Hartree-Bogolyubov calculation of nuclear ground states and in the particle-hole channel of the PN-RQRPA. The finite range Gogny D1S interaction is employed in the T=1 pairing channel, and the model also includes a proton-neutron particle-particle interaction. The theoretical half-lives reproduce the experimental data for the Fe, Zn, Cd, and Te isotopic chains, but overestimate the lifetimes of Ni isotopes and predict a stable {sup 132}Sn. (orig.)

  8. Atomic structure calculations using the relativistic random phase approximation

    International Nuclear Information System (INIS)

    Cheng, K.T.; Johnson, W.R.

    1981-01-01

    A brief review is given for the relativistic random phase approximation (RRPA) applied to atomic transition problems. Selected examples of RRPA calculations on discrete excitations and photoionization are given to illustrate the need of relativistic many-body theories in dealing with atomic processes where both relativity and correlation are important

  9. 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

  10. Relativistic impulse approximation and deuteron spin structure

    International Nuclear Information System (INIS)

    Tokarev, M.V.

    1992-01-01

    The fragmentation processes were considered of tensor- and vector-polarized deuterons to protons in the framework of the covariant approach in the light cone variables on the basis of the relativistic deuteron wave function with one nucleon on-mass shell. The experimental verification of predicted dependences of T 20 and K is of interest for the research of the momentum and spin distributions of high momentum deuteron constituents. 21 refs.; 6 figs

  11. 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

  12. 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.

  13. 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

  14. 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.

  15. The trajectory-coherent approximation and the system of moments for the Hartree type equation

    Directory of Open Access Journals (Sweden)

    V. V. Belov

    2002-01-01

    Full Text Available The general construction of semiclassically concentrated solutions to the Hartree type equation, based on the complex WKB-Maslov method, is presented. The formal solutions of the Cauchy problem for this equation, asymptotic in small parameter ℏ (ℏ→0, are constructed with a power accuracy of O(ℏ N/2, where N is any natural number. In constructing the semiclassically concentrated solutions, a set of Hamilton-Ehrenfest equations (equations for centered moments is essentially used. The nonlinear superposition principle has been formulated for the class of semiclassically concentrated solutions of Hartree type equations. The results obtained are exemplified by a one-dimensional Hartree type equation with a Gaussian potential.

  16. 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

  17. The Post-Newtonian Approximation for Relativistic Compact Binaries

    Directory of Open Access Journals (Sweden)

    Futamase Toshifumi

    2007-03-01

    Full Text Available We discuss various aspects of the post-Newtonian approximation in general relativity. After presenting the foundation based on the Newtonian limit, we show a method to derive post-Newtonian equations of motion for relativistic compact binaries based on a surface integral approach and the strong field point particle limit. As an application we derive third post-Newtonian equations of motion for relativistic compact binaries which respect the Lorentz invariance in the post-Newtonian perturbative sense, admit a conserved energy, and are free from any ambiguity.

  18. Lowest lying 2+ and 3- vibrational states in Pb, Sn, and Ni isotopes in relativistic quasiparticle random-phase approximation

    International Nuclear Information System (INIS)

    Ansari, A.; Ring, P.

    2006-01-01

    The excitation energies and electric multipole decay rates of the lowest lying 2 + and 3 - vibrational states in Pb, Sn, and Ni nuclei are calculated following relativistic quasiparticle random-phase approximation formalism based on the relativistic Hartree-Bogoliubov mean field. Two sets of Lagrangian parameters, NL1 and NL3, are used to investigate the effect of the nuclear force. Overall there is good agreement with the available experimental data for a wide range of mass numbers considered here, and the NL3 set seems to be a better choice. However, strictly speaking, these studies point toward the need of a new set of force parameters that could produce more realistic single-particle levels, at least in vicinity of the Fermi surface, of a wide range of nuclear masses

  19. The O(N) model at nonzero temperature: renormalization of the gap equations in Hartree and large-N approximations

    International Nuclear Information System (INIS)

    Lenaghan, J.T.; Rischke, D.H.

    2000-01-01

    The temperature dependence of the sigma meson and pion masses is studied in the framework of the O(N ) model. The Cornwall-Jackiw-Tomboulis formalism is applied to derive gap equations for the masses in the Hartree and large-N approximations. Renormalization of the gap equations is carried out within the cut-off and counter-term renormalization schemes. A consistent renormalization of the gap equations within the cut-off scheme is found to be possible only in the large-N approximation and for a finite value of the cut-off. On the other hand, the counter-term scheme allows for a consistent renormalization of both the large-N and Hartree approximations. In these approximations, the meson masses at a given nonzero temperature depend in general on the choice of the cut-off or renormalization scale. As an application, we also discuss the in-medium on-shell decay widths for sigma mesons and pions at rest. (author)

  20. New approximation for Glauber theory on stripping of relativistic deuterons

    International Nuclear Information System (INIS)

    Nissen-Meyer, S.A.

    1978-03-01

    The momentum distribution of forward protons from relativistic collisions of deuterons with nuclei is computed from a Glauber theoretical Ansatz of Bertocchi and Tekou. The outgoing proton-neutron scattering state (disintegrated deuteron) with a plane wave minus the components of this plane wave along the deuteron bound state vector is approximated. With no fitted parameters good agreement is found with data from the reaction d + C 12 → p + X in the region corresponding to nonrelativistic Fermi momenta in the forward direction. At more relativistic Fermi momenta, the model deviates more from the data, which can be due to incorrect choice of the short distance part of the deuteron wave function as well as off-shell effects in the deuteron

  1. Isoscalar compression modes in relativistic random phase approximation

    International Nuclear Information System (INIS)

    Ma, Zhong-yu; Van Giai, Nguyen.; Wandelt, A.; Vretenar, D.; Ring, P.

    2001-01-01

    Monopole and dipole compression modes in nuclei are analyzed in the framework of a fully consistent relativistic random phase approximation (RRPA), based on effective mean-field Lagrangians with nonlinear meson self-interaction terms. The large effect of Dirac sea states on isoscalar strength distribution functions is illustrated for the monopole mode. The main contribution of Fermi and Dirac sea pair states arises through the exchange of the scalar meson. The effect of vector meson exchange is much smaller. For the monopole mode, RRPA results are compared with constrained relativistic mean-field calculations. A comparison between experimental and calculated energies of isoscalar giant monopole resonances points to a value of 250-270 MeV for the nuclear matter incompressibility. A large discrepancy remains between theoretical predictions and experimental data for the dipole compression mode

  2. MRS2016: Rigid Moon Rotation Series in the Relativistic Approximation

    Science.gov (United States)

    Pashkevich, V. V.

    2017-03-01

    The rigid Moon rotation problem is studied for the relativistic (kinematical) case, in which the geodetic perturbations in the Moon rotation are taken into account. As the result of this research the high-precision Moon Rotation Series MRS2016 in the relativistic approximation was constructed for the first time and the discrepancies between the high-precision numerical and the semi-analytical solutions of the rigid Moon rotation were investigated with respect to the fixed ecliptic of epoch J2000, by the numerical and analytical methods. The residuals between the numerical solution and MRS2016 in the perturbing terms of the physical librations do not exceed 80 mas and 10 arc seconds over 2000 and 6000 years, respectively.

  3. 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

  4. Hartree Fock-type equations in relativistic quantum electrodynamics with non-linear gauge fixing

    International Nuclear Information System (INIS)

    Dietz, K.; Hess, B.A.

    1990-08-01

    Relativistic mean-field equations are obtained by minimizing the effective energy obtained from the gauge-invariant energy density by eliminating electro-magnetic degrees of freedom in certain characteristic non-linear gauges. It is shown that by an appropriate choice of gauge many-body correlations, e.g. screening, three-body 'forces' etc. can be included already at the mean-field level. The many-body perturbation theory built on the latter is then expected to show improved 'convergence'. (orig.)

  5. Relativistic continuum random phase approximation in spherical nuclei

    International Nuclear Information System (INIS)

    Daoutidis, Ioannis

    2009-01-01

    Covariant density functional theory is used to analyze the nuclear response in the external multipole fields. The investigations are based on modern functionals with zero range and density dependent coupling constants. After a self-consistent solution of the Relativistic Mean Field (RMF) equations for the nuclear ground states multipole giant resonances are studied within the Relativistic Random Phase Approximation (RRPA), the small amplitude limit of the time-dependent RMF. The coupling to the continuum is treated precisely by calculating the single particle Greens-function of the corresponding Dirac equation. In conventional methods based on a discretization of the continuum this was not possible. The residual interaction is derived from the same RMF Lagrangian. This guarantees current conservation and a precise decoupling of the Goldstone modes. For nuclei with open shells pairing correlations are taken into account in the framework of BCS theory and relativistic quasiparticle RPA. Continuum RPA (CRPA) presents a robust method connected with an astonishing reduction of the numerical effort as compared to conventional methods. Modes of various multipolarities and isospin are investigated, in particular also the newly discovered Pygmy modes in the vicinity of the neutron evaporation threshold. The results are compared with conventional discrete RPA calculations as well as with experimental data. We find that the full treatment of the continuum is essential for light nuclei and the study of resonances in the neighborhood of the threshold. (orig.)

  6. Relativistic continuum random phase approximation in spherical nuclei

    Energy Technology Data Exchange (ETDEWEB)

    Daoutidis, Ioannis

    2009-10-01

    Covariant density functional theory is used to analyze the nuclear response in the external multipole fields. The investigations are based on modern functionals with zero range and density dependent coupling constants. After a self-consistent solution of the Relativistic Mean Field (RMF) equations for the nuclear ground states multipole giant resonances are studied within the Relativistic Random Phase Approximation (RRPA), the small amplitude limit of the time-dependent RMF. The coupling to the continuum is treated precisely by calculating the single particle Greens-function of the corresponding Dirac equation. In conventional methods based on a discretization of the continuum this was not possible. The residual interaction is derived from the same RMF Lagrangian. This guarantees current conservation and a precise decoupling of the Goldstone modes. For nuclei with open shells pairing correlations are taken into account in the framework of BCS theory and relativistic quasiparticle RPA. Continuum RPA (CRPA) presents a robust method connected with an astonishing reduction of the numerical effort as compared to conventional methods. Modes of various multipolarities and isospin are investigated, in particular also the newly discovered Pygmy modes in the vicinity of the neutron evaporation threshold. The results are compared with conventional discrete RPA calculations as well as with experimental data. We find that the full treatment of the continuum is essential for light nuclei and the study of resonances in the neighborhood of the threshold. (orig.)

  7. Extended quasiparticle approximation for relativistic electrons in plasmas

    Directory of Open Access Journals (Sweden)

    V.G.Morozov

    2006-01-01

    Full Text Available Starting with Dyson equations for the path-ordered Green's function, it is shown that the correlation functions for relativistic electrons (positrons in a weakly coupled non-equilibrium plasmas can be decomposed into sharply peaked quasiparticle parts and off-shell parts in a rather general form. To leading order in the electromagnetic coupling constant, this decomposition yields the extended quasiparticle approximation for the correlation functions, which can be used for the first principle calculation of the radiation scattering rates in QED plasmas.

  8. 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.)

  9. 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

  10. 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)

  11. A simple approximation for the current-voltage characteristics of high-power, relativistic diodes

    Energy Technology Data Exchange (ETDEWEB)

    Ekdahl, Carl, E-mail: cekdahl@lanl.gov [Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

    2016-06-15

    A simple approximation for the current-voltage characteristics of a relativistic electron diode is presented. The approximation is accurate from non-relativistic through relativistic electron energies. Although it is empirically developed, it has many of the fundamental properties of the exact diode solutions. The approximation is simple enough to be remembered and worked on almost any pocket calculator, so it has proven to be quite useful on the laboratory floor.

  12. Inclusive charged-current neutrino-nucleus reactions calculated with the relativistic quasiparticle random-phase approximation

    International Nuclear Information System (INIS)

    Paar, N.; Vretenar, D.; Marketin, T.; Ring, P.

    2008-01-01

    Inclusive neutrino-nucleus cross sections are calculated using a consistent relativistic mean-field theoretical framework. The weak lepton-hadron interaction is expressed in the standard current-current form, the nuclear ground state is described with the relativistic Hartree-Bogoliubov model, and the relevant transitions to excited nuclear states are calculated in the relativistic quasiparticle random-phase approximation. Illustrative test calculations are performed for charged-current neutrino reactions on 12 C, 16 O, 56 Fe, and 208 Pb, and results compared with previous studies and available data. Through the use of the experimental neutrino fluxes, the averaged cross sections are evaluated for nuclei of interest for neutrino detectors. We analyze the total neutrino-nucleus cross sections and the evolution of the contribution of the different multipole excitations as a function of neutrino energy. The cross sections for reactions of supernova neutrinos on 16 O and 208 Pb target nuclei are analyzed as functions of the temperature and chemical potential

  13. Relativistic quasiparticle time blocking approximation: Dipole response of open-shell nuclei

    International Nuclear Information System (INIS)

    Litvinova, E.; Ring, P.; Tselyaev, V.

    2008-01-01

    The self-consistent relativistic quasiparticle random-phase approximation (RQRPA) is extended by the quasiparticle-phonon coupling (QPC) model using the quasiparticle time blocking approximation (QTBA). The method is formulated in terms of the Bethe-Salpeter equation (BSE) in the two-quasiparticle space with an energy-dependent two-quasiparticle residual interaction. This equation is solved either in the basis of Dirac states forming the self-consistent solution of the ground state or in the momentum representation. Pairing correlations are treated within the Bardeen-Cooper-Schrieffer (BCS) model with a monopole-monopole interaction. The same NL3 set of the coupling constants generates the Dirac-Hartree-BCS single-quasiparticle spectrum, the static part of the residual two-quasiparticle interaction and the quasiparticle-phonon coupling amplitudes. A quantitative description of electric dipole excitations in the chain of tin isotopes (Z=50) with the mass numbers A=100,106,114,116,120, and 130 and in the chain of isotones with (N=50) 88 Sr, 90 Zr, 92 Mo is performed within this framework. The RQRPA extended by the coupling to collective vibrations generates spectra with a multitude of 2q x phonon (two quasiparticles plus phonon) states providing a noticeable fragmentation of the giant dipole resonance as well as of the soft dipole mode (pygmy resonance) in the nuclei under investigation. The results obtained for the photo absorption cross sections and for the integrated contributions of the low-lying strength to the calculated dipole spectra agree very well with the available experimental data

  14. Studies of Ionic Photoionization Using Relativistic Random Phase Approximation and Relativistic Multichannel Quantum Defect Theory

    Science.gov (United States)

    Haque, Ghousia Nasreen

    The absorption of electromagnetic radiation by positive ions is one of the fundamental processes of nature which occurs in every intensely hot environment. Due to the difficulties in producing sufficient densities of ions in a laboratory, there are very few measurements of ionic photoabsorption parameters. On the theoretical side, some calculations have been made of a few major photoionization parameters, but generally speaking, most of the work done so far has employed rather simple single particle models and any theoretical work which has adequately taken into account intricate atomic many-body and relativistic effects is only scanty. In the present work, several complex aspects of atomic/ionic photoabsorption parameters have been studied. Non -resonant photoionization in neon and argon isonuclear as well as isoelectronic sequences has been studied using a very sophisticated technique, namely the relativistic random phase approximation (RRPA). This technique takes into account relativistic effects as well as an important class of major many-body effects on the same footing. The present calculations confirmed that gross features of photoionization parameters calculated using simpler models were not an artifact of the simple model. Also, the present RRPA calculations on K^+ ion and neutral Ar brought out the relative importance of various many-body effects such the inter-channel coupling. Inter-channel coupling between discrete bound state photoexcitation channels from an inner atomic/ionic level and photoionization continuum channels from an outer atomic/ionic level leads to the phenomena of autoionization resonances in the photoionization process. These resonances lead to very complex effects in the atomic/ionic photoabsorption spectra. These resonances have been calculated and studied in the present work in the neon and magnesium isoelectronic sequences using the relativistic multi-channel quantum defect theory (RMQDT) within the framework of the RRPA. The

  15. Sensitivity of relativistic impulse approximation proton-nucleus elastic scattering calculations on relativistic mean-field parameterizations

    International Nuclear Information System (INIS)

    Hojsik, M.; Gmuca, S.

    1998-01-01

    Relativistic microscopic calculations are presented for proton elastic scattering from 40 Ca at 500 MeV. The underlying target densities are calculated within the framework of the relativistic mean-field theory with several parameter sets commonly in use. The self consistency of the scalar and vector densities (and thus to relativistic mean-field parameters) is investigated. Recently, the relativistic impulse approximation (RIA) has been widely and repeatedly used for the calculations of proton-nucleus scattering at intermediate energies. These calculations have exhibited significant improvements over the nonrelativistic approaches. The relativistic impulse approximation calculations. in particular, provide a dramatically better description of the spin observables, namely the analyzing power, A y , and the spin-rotation function, Q, at least for energies higher than 400 MeV. In the relativistic impulse approximation, the Dirac optical potential is obtained by folding of the local Lorentz-invariant amplitudes with the corresponding nuclear densities. For the spin zero targets the scalar and vector terms give the dominant contributions. Thus the scalar and vector nuclear densities (both, proton and neutron ones) play the dominant role in the relativistic impulse approximation. While the proton vector densities can be obtained by unfolding from the empirically known charge densities, all other densities used rely to a great extent on theoretical models. The various recipes are used to construct the neutron vector densities and the scalar densities for both, neutrons and protons. In this paper we will study the sensitivity of the relativistic impulse approximation results on the various sets of relativistic mean-field parameters currently in use

  16. Quasi-linear equation for magnetoplasma oscillations in the weakly relativistic approximation

    International Nuclear Information System (INIS)

    Rizzato, F.B.

    1985-01-01

    Some limitations which are present in the dynamical equations for collisionless plasmas are discussed. Some elementary corrections to the linear theories are obtained in a heuristic form, which directly lead to the so-called quasi-linear theories in its non-relativistic and relativistic forms. The effect of the relativistic variation of the gyrofrequency on the diffusion coefficient is examined in a typically perturbative approximation. (author)

  17. Electron correlation within the relativistic no-pair approximation

    DEFF Research Database (Denmark)

    Almoukhalalati, Adel; Knecht, Stefan; Jensen, Hans Jørgen Aa

    2016-01-01

    and that this is possible by full Multiconfigurational Self-Consistent Field (MCSCF) calculations, that is, MCSCF calculations using a no-pair full CI expansion, but including orbital relaxation from the negative-energy orbitals. We show by variational perturbation theory that the MCSCF correlation energy is a pure MP2....... The well-known 1/Z- expansion in nonrelativistic atomic theory follows from coordinate scaling. We point out that coordinate scaling for consistency should be accompanied by velocity scaling. In the nonrelativistic domain this comes about automatically, whereas in the relativistic domain an explicit...... scaling of the speed of light is required. This in turn explains why the relativistic correlation energy to the lowest order is not independent of nuclear charge, in contrast to nonrelativistic theory....

  18. Relativistic-particle quantum mechanics (applications and approximations) II

    International Nuclear Information System (INIS)

    Coester, F.

    1981-01-01

    In this lecture I hope to show that relativistic-particle quantum mechanics with direct interactions is a useful tool for building models applicable to hadron systems at intermediate energies. To do this I will first describe a class of models designed to incorporate nucleon-nucleon interactions, pion production, absorption and scattering into a single dynamical framework without dressing the nucleons with pion clouds. The second major topic concerns electromagnetic interactions. In the previous lecture I specifically excluded long-rang forces and zero-mass particles. Since many of the experimental data in hadron physics involve electromagnetic interactions this limitation is a major defect which must be addressed

  19. Relativistic effects on linear and nonlinear polarizabilities studied by effective-core potential, Douglas-Kroll, and Dirac-Hartree-Fock response theory

    DEFF Research Database (Denmark)

    Norman, Patrick; Schimmelpfennig, Bernd; Ruud, Kenneth

    2002-01-01

    A systematic investigation of a hierarchy of methods for including relativistic effects in the calculation of linear and nonlinear optical properties was carried out. The simple ECP method and the more involved spin-averaged Douglas-Kroll approximation were compared to benchmark results obtained...

  20. 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

  1. Importance of self-consistency in relativistic continuum random-phase approximation calculations

    International Nuclear Information System (INIS)

    Yang Ding; Cao Ligang; Tian Yuan; Ma Zhongyu

    2010-01-01

    A fully consistent relativistic continuum random phase approximation (RCRPA) is constructed, where the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single-particle Green's function technique. The full consistency of the calculations is achieved that the same effective Lagrangian is adopted for the ground state and the excited states. The negative energy states in the Dirac sea are also included in the single-particle Green's function in the no-sea approximation. The currents from the vector meson and photon exchanges and the Coulomb interaction in RCRPA are treated exactly. The spin-orbit interaction is included naturally in the relativistic frame. Numerical results of the RCRPA are checked with the constrained relativistic mean-field theory. We study the effects of the inconsistency, particularly the currents and Coulomb interaction in various collective multipole excitations.

  2. Collision strengths from ground levels of Ti XIII using relativistic-Breit-Pauli approximation

    International Nuclear Information System (INIS)

    Mohan, M.; Hibbert, H.; Burke, P.G.; Keenan, F.

    1998-09-01

    The R-matrix method is used to calculate collision strengths from ground state to the first twenty-six fine structure levels of neon-like titanium by including the relativistic term coupling coefficients in the semi-Breit-Pauli approximation. Configuration interaction wave-functions are used to represent the first fifteen lowest LS-coupled target states in the R-matrix expansion. Results obtained are compared with other calculations. This is the first detailed calculation on this ion in which relativistic, exchange, channel couplings and short-range correlation effects are taken into account. (author)

  3. Relativistic time-dependent local-density approximation theory and applications to atomic physics

    International Nuclear Information System (INIS)

    Parpia, F.Z.

    1984-01-01

    A time-dependent linear-response theory appropriate to the relativistic local-density approximation (RLDA) to quantum electrodynamics (QED) is developed. The resulting theory, the relativistic time-dependent local-density approximation (RTDLDA) is specialized to the treatment of electric excitations in closed-shell atoms. This formalism is applied to the calculation of atomic photoionization parameters in the dipole approximation. The static-field limit of the RTDLDA is applied to the calculation of dipole polarizabilities. Extensive numerical calculations of the photoionization parameters for the rare gases neon, argon, krypton, and xenon, and for mercury from the RTDLDA are presented and compared in detail with the results of other theories, in particular the relativistic random-phase approximation (RRPA), and with experimental measurements. The predictions of the RTDLDA are comparable with the RRPA calculations made to date. This is remarkable in that the RTDLDA entails appreciably less computational effort. Finally, the dipole polarizabilities predicted by the static-field RTDLDA are compared with other determinations of these quantities. In view of its simplicity, the static-field RTDLDA demonstrates itself to be one of the most powerful theories available for the calculation of dipole polarizabilities

  4. 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)

  5. PADÉ APPROXIMANTS FOR THE EQUATION OF STATE FOR RELATIVISTIC HYDRODYNAMICS BY KINETIC THEORY

    Energy Technology Data Exchange (ETDEWEB)

    Tsai, Shang-Hsi; Yang, Jaw-Yen, E-mail: shanghsi@gmail.com [Institute of Applied Mechanics, National Taiwan University, Taipei 10764, Taiwan (China)

    2015-07-20

    A two-point Padé approximant (TPPA) algorithm is developed for the equation of state (EOS) for relativistic hydrodynamic systems, which are described by the classical Maxwell–Boltzmann statistics and the semiclassical Fermi–Dirac statistics with complete degeneracy. The underlying rational function is determined by the ratios of the macroscopic state variables with various orders of accuracy taken at the extreme relativistic limits. The nonunique TPPAs are validated by Taub's inequality for the consistency of the kinetic theory and the special theory of relativity. The proposed TPPA is utilized in deriving the EOS of the dilute gas and in calculating the specific heat capacity, the adiabatic index function, and the isentropic sound speed of the ideal gas. Some general guidelines are provided for the application of an arbitrary accuracy requirement. The superiority of the proposed TPPA is manifested in manipulating the constituent polynomials of the approximants, which avoids the arithmetic complexity of struggling with the modified Bessel functions and the hyperbolic trigonometric functions arising from the relativistic kinetic theory.

  6. The time-dependent relativistic mean-field theory and the random phase approximation

    International Nuclear Information System (INIS)

    Ring, P.; Ma, Zhong-yu; Van Giai, Nguyen; Vretenar, D.; Wandelt, A.; Cao, Li-gang

    2001-01-01

    The Relativistic Random Phase Approximation (RRPA) is derived from the Time-Dependent Relativistic Mean-Field (TD RMF) theory in the limit of small amplitude oscillations. In the no-sea approximation of the RMF theory, the RRPA configuration space includes not only the usual particle-hole ph-states, but also αh-configurations, i.e. pairs formed from occupied states in the Fermi sea and empty negative-energy states in the Dirac sea. The contribution of the negative-energy states to the RRPA matrices is examined in a schematic model, and the large effect of Dirac-sea states on isoscalar strength distributions is illustrated for the giant monopole resonance in 116 Sn. It is shown that, because the matrix elements of the time-like component of the vector-meson fields which couple the αh-configurations with the ph-configurations are strongly reduced with respect to the corresponding matrix elements of the isoscalar scalar meson field, the inclusion of states with unperturbed energies more than 1.2 GeV below the Fermi energy has a pronounced effect on giant resonances with excitation energies in the MeV region. The influence of nuclear magnetism, i.e. the effect of the spatial components of the vector fields is examined, and the difference between the nonrelativistic and relativistic RPA predictions for the nuclear matter compression modulus is explained

  7. Relativistic Random-Phase Approximation with Density-dependent Meson-nucleon Couplings at Finite Temperature

    International Nuclear Information System (INIS)

    Niu, Y.; Paar, N.; Vretenar, D.; Meng, J.

    2009-01-01

    The fully self-consistent relativistic random-phase approximation (RRPA) framework based on effective interactions with a phenomenological density dependence is extended to finite temperatures. The RRPA configuration space is built from the spectrum of single-nucleon states at finite temperature obtained by the temperature dependent relativistic mean field (RMF-T) theory based on effective Lagrangian with density dependent meson-nucleon vertex functions. As an illustration, the dependence of binding energy, radius, entropy and single particle levels on temperature for spherical nucleus 2 08P b is investigated in RMF-T theory. The finite temperature RRPA has been employed in studies of giant monopole and dipole resonances, and the evolution of resonance properties has been studied as a function of temperature. In addition, exotic modes of excitation have been systematically explored at finite temperatures, with an emphasis on the case of pygmy dipole resonances.(author)

  8. Relativistic mean-field approximation with density-dependent screening meson masses in nuclear matter

    International Nuclear Information System (INIS)

    Sun, Baoxi; Lu, Xiaofu; Shen, Pengnian; Zhao, Enguang

    2003-01-01

    The Debye screening masses of the σ, ω and neutral ρ mesons and the photon are calculated in the relativistic mean-field approximation. As the density of the nucleon increases, all the screening masses of mesons increase. A different result with Brown–Rho scaling is shown, which implies a reduction in the mass of all the mesons in the nuclear matter, except the pion. Replacing the masses of the mesons with their corresponding screening masses in the Walecka-1 model, five saturation properties of the nuclear matter are fixed reasonably, and then a density-dependent relativistic mean-field model is proposed without introducing the nonlinear self-coupling terms of mesons. (author)

  9. Nucleon-nucleus inelastic scattering using a relativistic impulse approximation with exchange

    International Nuclear Information System (INIS)

    Rost, E.; Shepard, J.R.

    1987-01-01

    We formulate a microscopic relativistic treatment of nucleon-nucleus inelastic scattering in a distorted wave impulse approximation. The interaction is taken from a Lorentz invariant formulation with explicit direct and exchange terms constrained by fitting to experimental NN amplitudes. This procedure allows us to apply the theory in the lower range of intermediate energies (100--400 MeV) where exchange effects are likely to be important. Application to inelastic scattering uses this interaction for both the distorting potentials and the transition interaction. Effects of explicit exchange are studied and a preliminary analysis of /sup 12/C(p,p') data is presented

  10. Low-momentum-transfer nonrelativistic limit of the relativistic impulse approximation expression for Compton-scattering doubly differential cross sections and characterization of their relativistic contributions

    International Nuclear Information System (INIS)

    LaJohn, L. A.

    2010-01-01

    The nonrelativistic (nr) impulse approximation (NRIA) expression for Compton-scattering doubly differential cross sections (DDCS) for inelastic photon scattering is recovered from the corresponding relativistic expression (RIA) of Ribberfors [Phys. Rev. B 12, 2067 (1975)] in the limit of low momentum transfer (q→0), valid even at relativistic incident photon energies ω 1 >m provided that the average initial momentum of the ejected electron i > is not too high, that is, i > b 1 >m using nr expressions when θ is small. For example, a 1% accuracy can be obtained when ω 1 =1 MeV if θ 1 increases into the MeV range, the maximum θ at which an accurate Compton peak can be obtained from nr expressions approaches closer to zero, because the θ at which the relativistic shift of CP to higher energy is greatest, which starts at 180 deg. when ω 1 min ,ρ rel ) (where p min is the relativistic version of the z component of the momentum of the initial electron and ρ rel is the relativistic charge density) and K(p min ) on p min . This characterization approach was used as a guide for making the nr QED S-matrix expression for the Compton peak kinematically relativistic. Such modified nr expressions can be more readily applied to large systems than the fully relativistic version.

  11. 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)

  12. Roles of antinucleon degrees of freedom in the relativistic random phase approximation

    Science.gov (United States)

    Kurasawa, Haruki; Suzuki, Toshio

    2015-11-01

    The roles of antinucleon degrees of freedom in the relativistic random phase approximation (RPA) are investigated. The energy-weighted sum of the RPA transition strengths is expressed in terms of the double commutator between the excitation operator and the Hamiltonian, as in nonrelativistic models. The commutator, however, should not be calculated in the usual way in the local field theory, because, otherwise, the sum vanishes. The sum value obtained correctly from the commutator is infinite, owing to the Dirac sea. Most of the previous calculations take into account only some of the nucleon-antinucleon states, in order to avoid divergence problems. As a result, RPA states with negative excitation energy appear, which make the sum value vanish. Moreover, disregarding the divergence changes the sign of nuclear interactions in the RPA equation that describes the coupling of the nucleon particle-hole states with the nucleon-antinucleon states. Indeed, the excitation energies of the spurious state and giant monopole states in the no-sea approximation are dominated by these unphysical changes. The baryon current conservation can be described without touching the divergence problems. A schematic model with separable interactions is presented, which makes the structure of the relativistic RPA transparent.

  13. 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

  14. Magnetohydrodynamic Kelvin-Helmholtz instabilities in astrophysics. 1. Relativistic flows-plane boundary layer in vortex sheet approximation

    Energy Technology Data Exchange (ETDEWEB)

    Ferrari, A; Trussoni, E; Zaninetti, L [Consiglio Nazionale delle Ricerche, Turin (Italy). Lab. di Cosmo-Geofisica; Turin Univ. (Italy). Ist. di Fisica)

    1980-11-01

    In this paper some unsolved problems of the linear MHD Kelvin-Helmholtz instability are re-examined, starting from the analysis of relativistic (and non-relativistic) flows in the approximation of a plane vortex sheet, for the contact layer between the fluids in relative motion. Results are discussed for a range of physical parameters in specific connection with application to models of jets in extragalactic radio sources. Other physical aspects of the instability will be considered in forthcoming papers.

  15. General Relativistic Radiant Shock Waves in the Post-Quasistatic Approximation

    Energy Technology Data Exchange (ETDEWEB)

    H, Jorge A Rueda [Centro de Fisica Fundamental, Universidad de Los Andes, Merida 5101, Venezuela Escuela de Fisica, Universidad Industrial de Santander, A.A. 678, Bucaramanga (Colombia); Nunez, L A [Centro de Fisica Fundamental, Universidad de Los Andes, Merida 5101, Venezuela Centro Nacional de Calculo Cientifico, Universidad de Los Andes, CeCalCULA, Corporacion Parque Tecnologico de Merida, Merida 5101, Venezuela (Venezuela)

    2007-05-15

    An evolution of radiant shock wave front is considered in the framework of a recently presented method to study self-gravitating relativistic spheres, whose rationale becomes intelligible and finds full justification within the context of a suitable definition of the post-quasistatic approximation. The spherical matter configuration is divided into two regions by the shock and each side of the interface having a different equation of state and anisotropic phase. In order to simulate dissipation effects due to the transfer of photons and/or neutrinos within the matter configuration, we introduce the flux factor, the variable Eddington factor and a closure relation between them. As we expected the strong of the shock increases the speed of the fluid to relativistic ones and for some critical values is larger than light speed. In addition, we find that energy conditions are very sensible to the anisotropy, specially the strong energy condition. As a special feature of the model, we find that the contribution of the matter and radiation to the radial pressure are the same order of magnitude as in the mant as in the core, moreover, in the core radiation pressure is larger than matter pressure.

  16. General Relativistic Radiant Shock Waves in the Post-Quasistatic Approximation

    International Nuclear Information System (INIS)

    H, Jorge A Rueda; Nunez, L A

    2007-01-01

    An evolution of radiant shock wave front is considered in the framework of a recently presented method to study self-gravitating relativistic spheres, whose rationale becomes intelligible and finds full justification within the context of a suitable definition of the post-quasistatic approximation. The spherical matter configuration is divided into two regions by the shock and each side of the interface having a different equation of state and anisotropic phase. In order to simulate dissipation effects due to the transfer of photons and/or neutrinos within the matter configuration, we introduce the flux factor, the variable Eddington factor and a closure relation between them. As we expected the strong of the shock increases the speed of the fluid to relativistic ones and for some critical values is larger than light speed. In addition, we find that energy conditions are very sensible to the anisotropy, specially the strong energy condition. As a special feature of the model, we find that the contribution of the matter and radiation to the radial pressure are the same order of magnitude as in the mant as in the core, moreover, in the core radiation pressure is larger than matter pressure

  17. Isospin-dependent term in the relativistic microscopic optical potential

    International Nuclear Information System (INIS)

    Rong Jian; Ma Zhongyu; National Laboratory of Heavy Ion Accelerator of Lanzhou, Lanzhou; Chinese Academy of Sciences, Beijing

    2005-01-01

    The isospin-dependence of the relativistic microscopic optical potential is investigated in the Dirac Brueckner-Hartree-Fock approach. The isospin part of the microscopic optical potential is emphasized. A local density approximation is adopted for finite nuclei. Taking 208 Pb as example, the difference between proton and neutron optical potentials is studied and compared with the phenomenological Lane Model potential. (authors)

  18. 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

  19. On the radiation emitted by a particle falling into a black hole in the semi-relativistic approximation

    International Nuclear Information System (INIS)

    Coretti, C.; Ferrari, V.

    1986-01-01

    In this paper the limits of applicability of the semi-relativistic approximation for estimating the radiation emitted in processes of capture of particles by black holes are discussed. It is shown that it gives reliable estimates in the case of spherically symmetric black holes, but it fails in the case of rotating black holes

  20. The experimental test of the adequateness of relativistic impulse approximation when describing the lightest nuclei break-up

    International Nuclear Information System (INIS)

    Sitnik, I.M.

    1995-01-01

    The behaviour of the lightest nuclei break-up cross sections at zero angle has been analyzed in vicinity of the maximum. It is shown that asymmetry of cross sections relatively maximum is in conflict with nonrelativistic impulse approximation, but agrees well with one of relativistic approaches to describe this process. 10 refs., 9 figs

  1. 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

  2. Solid neutron matter the energy density in the relativistic harmonic approximation

    International Nuclear Information System (INIS)

    Cattani, M.; Fernandes, N.C.

    A relativistic expression for the energy density as a function of particle density for solid neutron matter is obtained using Dirac's equation with a truncated harmonic potential. Ultrabaric and superluminous effects are not found in our approach [pt

  3. FULLY GENERAL RELATIVISTIC SIMULATIONS OF CORE-COLLAPSE SUPERNOVAE WITH AN APPROXIMATE NEUTRINO TRANSPORT

    Energy Technology Data Exchange (ETDEWEB)

    Kuroda, Takami; Kotake, Kei [Division of Theoretical Astronomy, National Astronomical Observatory of Japan, 2-21-1, Osawa, Mitaka, Tokyo 181-8588 (Japan); Takiwaki, Tomoya [Center for Computational Astrophysics, National Astronomical Observatory of Japan, 2-21-1, Osawa, Mitaka, Tokyo 181-8588 (Japan)

    2012-08-10

    We present results from the first generation of multi-dimensional hydrodynamic core-collapse simulations in full general relativity (GR) that include an approximate treatment of neutrino transport. Using an M1 closure scheme with an analytic variable Eddington factor, we solve the energy-independent set of radiation energy and momentum based on the Thorne's momentum formalism. Our newly developed code is designed to evolve the Einstein field equation together with the GR radiation hydrodynamic equations. We follow the dynamics starting from the onset of gravitational core collapse of a 15 M{sub Sun} star, through bounce, up to about 100 ms postbounce in this study. By computing four models that differ according to 1D to 3D and by switching from special relativistic (SR) to GR hydrodynamics, we study how the spacial multi-dimensionality and GR would affect the dynamics in the early postbounce phase. Our 3D results support the anticipation in previous 1D results that the neutrino luminosity and average neutrino energy of any neutrino flavor in the postbounce phase increase when switching from SR to GR hydrodynamics. This is because the deeper gravitational well of GR produces more compact core structures, and thus hotter neutrino spheres at smaller radii. By analyzing the residency timescale to the neutrino-heating timescale in the gain region, we show that the criterion to initiate neutrino-driven explosions can be most easily satisfied in 3D models, irrespective of SR or GR hydrodynamics. Our results suggest that the combination of GR and 3D hydrodynamics provides the most favorable condition to drive a robust neutrino-driven explosion.

  4. Higher-order approximate solutions to the relativistic and Duffing-harmonic oscillators by modified He's homotopy methods

    International Nuclear Information System (INIS)

    Belendez, A; Pascual, C; Fernandez, E; Neipp, C; Belendez, T

    2008-01-01

    A modified He's homotopy perturbation method is used to calculate higher-order analytical approximate solutions to the relativistic and Duffing-harmonic oscillators. The He's homotopy perturbation method is modified by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution in the second-order linear differential equation, and so on. We find this modified homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. The approximate formulae obtained show excellent agreement with the exact solutions, and are valid for small as well as large amplitudes of oscillation, including the limiting cases of amplitude approaching zero and infinity. For the relativistic oscillator, only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate frequency of less than 1.6% for small and large values of oscillation amplitude, while this relative error is 0.65% for two iterations with two harmonics and as low as 0.18% when three harmonics are considered in the second approximation. For the Duffing-harmonic oscillator the relative error is as low as 0.078% when the second approximation is considered. Comparison of the result obtained using this method with those obtained by the harmonic balance methods reveals that the former is very effective and convenient

  5. Report of seminar on relativistic approach to nuclear reaction and nuclear structure

    International Nuclear Information System (INIS)

    1986-05-01

    A seminar on 'Relativistic Approach to Nuclear Reaction and Nuclear Structure' was held in 1985 at Osaka University. This booklet includes twenty-four reports given at the seminar, which deal with: Conventional Nonrelativistic Description of Nuclear Matter and Nuclear Spin-Orbit Interactions; Relativistic Approach to Nuclear Structure; Atomic and Molecular Structure Calculations; Electromagnetic Interaction in Nucleus and Relativistic Effect; Nuclear Magnetic Moment in the Relativistic Mean Field Theory, Effective Mass and Particle-Vibration Coupling in the Relativistic σ-ω Model; Gauge Invariance in Relativistic Many-Body Theory; Relativistic Description of Nucleon-Nucleon Interaction in Review; σ-Particle in NN Interaction; Nuclear Optical Potentials Based on the Brueckner-Hartree-Fock Approach; Elastic Backscattering and Optical Potential; Description of Intermediate-Energy Nuclear Reactions; Dirac Phenomenology at E(p) = 65 MeV; Relativistic Impulse Approximation; Reaction Studies with Intermediate Energy Deuterons at SATURNE; Folding Model for Intermediate-Energy Deutron Scattering; Folding Model for Polarized Deutron Scattering at 700 MeV; Dirac Approach Problems and a Different Viewpoint; Relativistic Approach and EMC Effect; Quasielastic Electron Scattering; Response Function of Quasielastic Electron Scattering; Relativistic Hartree Response Function for Quasielastic Electron Scattering on 12 C and 40 Ca; Backflow-, Retardation- and Relativistic Effects on the Longitudinal Response Function of Nuclear Matter; Pion-Photoproduction in the σ-ω Model. (Nogami, K.)

  6. Magnetic moments in present relativistic nuclear theories: a mean-field problem

    International Nuclear Information System (INIS)

    Desplanques, B.

    1986-07-01

    We show that the magnetic moments of LS closed shell nuclei plus or minus one nucleon derived from non-relativistic Hartree-Fock mean-fields are as bad as those obtained in relativistic approaches of nuclear structure. Deviations with respect to more complete results in both cases are ascribed to the mean-field approximation which neglects some degrees of freedom in the nucleus description. 18 refs

  7. Effective potentials of the relativistic three-body problem with electromagnetic interaction in adiabatic approximation

    International Nuclear Information System (INIS)

    Bakalov, D.D.; Melezhik, V.S.

    1987-01-01

    The relativistic Hamiltonian for 3-spin particles with electromagnetic interaction has been represented in the form of a sum of terms with factorized dependence on spin, angular and spheroidal variable, and its matrix elements have been expressed in terms of the matrix elements of a small number of ''basic'' operators. The numerical values of the latter have been tabulated, thus allowing for the evaluation of the leading relativistic effects in any 3-body system (with unit particle charge) with and accuracy of ∼ 0(1/2M), where 1/2M=(M 1 -1 +M 2 -1 )/2(M 1 -1 +M 3 -1 ) is the small parameter of the adiabatic expansion (M i , i=1,2,3 being particle masses)

  8. Relativistic atomic matrix elements of rq for arbitrary states in the quantum-defect approximation

    International Nuclear Information System (INIS)

    Owono Owono, L.C.; Owona Angue, M.L.C.; Kwato Njock, M.G.; Oumarou, B.

    2004-01-01

    Recurrence relations used in the calculation of matrix elements of r q for arbitrary q and states of the relativistic one-electron atom with a point-like ionic core are obtained with Dirac and quasirelativistic effective radial Hamiltonians. The phenomenological and supersymmetry-inspired quantum-defect approaches introduced in previous works to model the electron-core interactions are employed. The formulas worked out on the basis of a hypervirial inspired method may be viewed as a generalization to off-diagonal cases of our recently reported results on the evaluation of expectation values of r q

  9. Relativistic nuclear magnetic resonance J-coupling with ultrasoft pseudopotentials and the zeroth-order regular approximation

    International Nuclear Information System (INIS)

    Green, Timothy F. G.; Yates, Jonathan R.

    2014-01-01

    We present a method for the first-principles calculation of nuclear magnetic resonance (NMR) J-coupling in extended systems using state-of-the-art ultrasoft pseudopotentials and including scalar-relativistic effects. The use of ultrasoft pseudopotentials is allowed by extending the projector augmented wave (PAW) method of Joyce et al. [J. Chem. Phys. 127, 204107 (2007)]. We benchmark it against existing local-orbital quantum chemical calculations and experiments for small molecules containing light elements, with good agreement. Scalar-relativistic effects are included at the zeroth-order regular approximation level of theory and benchmarked against existing local-orbital quantum chemical calculations and experiments for a number of small molecules containing the heavy row six elements W, Pt, Hg, Tl, and Pb, with good agreement. Finally, 1 J(P-Ag) and 2 J(P-Ag-P) couplings are calculated in some larger molecular crystals and compared against solid-state NMR experiments. Some remarks are also made as to improving the numerical stability of dipole perturbations using PAW

  10. Self-consistent embedded-cluster calculations of the electronic structure of alkaline earth fluorides in the Hartree-Fock-Slater approximation

    International Nuclear Information System (INIS)

    Amaral, N.C.; Maffeo, B.; Guenzburger, D.J.R.

    1982-01-01

    Molecular orbitals calculations were performed for clusters representing the CaF 2 , SrF 2 and BaF 2 ionic crystals. The discrete variational method was employed, with the Xα approximation for the exchange interaction; a detailed investigation of different models for embedding the clusters in the solids led to a realistic description of the effect of neighbour ions in the infinite crystal. The results obtained were used to interpret optical and photoelectron data reported in the literature. In the case of CaF 2 , comparisons were made with existing band structure calculations. (Author) [pt

  11. 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

  12. 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.

  13. Rotating relativistic neutron stars

    Energy Technology Data Exchange (ETDEWEB)

    Weber, F.; Glendenning, N.K.

    1991-07-21

    Models of rotating neutron stars are constructed in the framework of Einstein's theory of general relativity. For this purpose a refined version of Hartle's method is applied. The properties of these objects, e.g. gravitational mass, equatorial and polar radius, eccentricity, red- and blueshift, quadrupole moment, are investigated for Kepler frequencies of 4000 s{sup {minus}1} {le} {Omega}{sub K} {le} 9000 s{sup {minus}1}. Therefore a self-consistency problem inherent in the determination of {Omega}{sub K} must be solved. The investigation is based on neutron star matter equations of state derived from the relativistic Martin-Schwinger hierarch of coupled Green's functions. By means of introducing the Hartree, Hartree-Fock, and ladder ({Lambda}) approximations, models of the equation of state derived. A special feature of the latter approximation scheme is the inclusion of dynamical two-particle correlations. These have been calculated from the relativistic T-matrix applying both the HEA and Bonn meson-exchange potentials of the nucleon-nucleon force. The nuclear forces of the former two treatments are those of the standard scalar-vector-isovector model of quantum hadron dynamics, with parameters adjusted to the nuclear matter data. An important aspect of this work consists in testing the compatibility of different competing models of the nuclear equation of state with data on pulsar periods. By this the fundamental problem of nuclear physics concerning the behavior of the equation of state at supernuclear densities can be treated.

  14. Reply to ''Comments on 'Time-symmetric, approximately relativistic particle interactions and radiation' ''

    International Nuclear Information System (INIS)

    Krizan, J.E.

    1982-01-01

    The inclusion of screening effects, as argued by Jones, effectively brings in terms of higher order than c -2 . The Darwin Hamiltonian, like the Darwin Lagrangian, usually is written in perturbative expansion, to order c -2 . The physical effects of the Cerenkov radiation (order c -2 ) and the Bohr polarization effect result from a weak-damping analysis with the Darwin Hamiltonian; contact has been made also in previous agreement with quantum field-theoretic calculations for degenerate systems, with the same Hamiltonian. The significance of adding screening should be examined within an approximation which includes c -3 terms and higher: so neither the Darwin Hamiltonian nor the Darwin Lagrangian is sufficient to analyze these situations. The medium modifications of Jones involve macroscopic considerations and higher orders and so the criticism of the microscopic Darwin Hamiltonian is misplaced

  15. Semi-classical approximation and the problem of boundary conditions in the theory of relativistic particle radiation

    International Nuclear Information System (INIS)

    Akhiezer, A.I.; Shul'ga, N.F.

    1991-01-01

    The process of relativistic particle radiation in an external field has been studied in the semi-classical approximation rather extensively. The main problem arising in the studies is in expressing the formula of the quantum theory of radiation in terms of classical quantities, for example of the classical trajectories. However, it still remains unclear how the particle trajectory is assigned, that is which particular initial or boundary conditions determine the trajectory in semi-classical approximation quantum theory of radiation. We shall try to solve this problem. Its importance comes from the fact that in some cases one and the same boundary conditions may give rise to two or more trajectories. We demonstrate that this fact must necessarily be taken into account on deriving the classical limit for the formulae of the quantum theory of radiation, since it leads to a specific interference effect in radiation. The method we used to deal with the problem is similar to the method employed by Fock to analyze the problem of a canonical transformation in classical and quantum mechanics. (author)

  16. 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

  17. Mean free paths and in-medium scattering cross sections of energetic nucleons in neutron-rich nucleonic matter within the relativistic impulse approximation

    International Nuclear Information System (INIS)

    Jiang Weizhou; Li Baoan; Chen Liewen

    2007-01-01

    The mean free paths and in-medium scattering cross sections of energetic nucleons in neutron-rich nucleonic matter are investigated using the nucleon optical potential obtained within the relativistic impulse approximation with the empirical nucleon-nucleon scattering amplitudes and the nuclear densities obtained in the relativistic mean-field model. It is found that the isospin-splitting of nucleon mean free paths, sensitive to the imaginary part of the symmetry potential, changes its sign at certain high kinetic energy. The in-medium nucleon-nucleon cross sections are analytically and numerically demonstrated to be essentially independent of the isospin asymmetry of the medium and increase linearly with density in the high-energy region where the relativistic impulse approximation is applicable

  18. Thermal effects in gravitational Hartree systems

    Energy Technology Data Exchange (ETDEWEB)

    Aki, Gonca L. [Weierstrass-Institut fuer Angewandte Analysis und Stochastik (WIAS) im Forschungsverbund Berlin e.V. (Germany); Dolbeault, Jean [Paris-Dauphine Univ. (FR). Ceremade (UMR CNRS 7534); Sparber, Christof [Illinois Univ., Chicago, IL (United States). Dept. of Mathematics, Statistics, and Computer Science

    2010-07-01

    We consider the non-relativistic Hartree model in the gravitational case, i.e. with attractive Coulomb-Newton interaction. For a given mass M>0, we construct stationary states with non-zero temperature T by minimizing the corresponding free energy functional. It is proved that minimizers exist if and only if the temperature of the system is below a certain threshold T*>0 (possibly infinite), which itself depends on the specific choice of the entropy functional. We also investigate whether the corresponding minimizers are mixed or pure quantum states and characterize a critical temperature T{sub c} element of (0,T*) above which mixed states appear. (orig.)

  19. Thermal Effects in Gravitational Hartree Systems

    KAUST Repository

    Aki, Gonca L.

    2011-04-06

    We consider the non-relativistic Hartree model in the gravitational case, i. e. with attractive Coulomb-Newton interaction. For a given mass M > 0, we construct stationary states with non-zero temperature T by minimizing the corresponding free energy functional. It is proved that minimizers exist if and only if the temperature of the system is below a certain threshold T* > 0 (possibly infinite), which itself depends on the specific choice of the entropy functional. We also investigate whether the corresponding minimizers are mixed or pure quantum states and characterize a critical temperature Tc ∈ (0,T*) above which mixed states appear. © 2011 Springer Basel AG.

  20. Classical limit for semirelativistic Hartree systems

    KAUST Repository

    Aki, Gonca L.

    2008-01-01

    We consider the three-dimensional semirelativistic Hartree model for fast quantum mechanical particles moving in a self-consistent field. Under appropriate assumptions on the initial density matrix as a (fully) mixed quantum state we prove by using Wigner transformation techniques that its classical limit yields the well known relativistic Vlasov-Poisson system. The result holds for the case of attractive and repulsive mean-field interactions, with an additional size constraint in the attractive case. © 2008 American Institute of Physics.

  1. Thermal Effects in Gravitational Hartree Systems

    KAUST Repository

    Aki, Gonca L.; Dolbeault, Jean; Sparber, Christof

    2011-01-01

    We consider the non-relativistic Hartree model in the gravitational case, i. e. with attractive Coulomb-Newton interaction. For a given mass M > 0, we construct stationary states with non-zero temperature T by minimizing the corresponding free energy functional. It is proved that minimizers exist if and only if the temperature of the system is below a certain threshold T* > 0 (possibly infinite), which itself depends on the specific choice of the entropy functional. We also investigate whether the corresponding minimizers are mixed or pure quantum states and characterize a critical temperature Tc ∈ (0,T*) above which mixed states appear. © 2011 Springer Basel AG.

  2. Isoscalar giant resonances in a relativistic model

    International Nuclear Information System (INIS)

    L'Huillier, M.; Nguyen Van Giai.

    1988-07-01

    Isoscalar giant resonances in finite nuclei are studied in a relativistic Random Phase Approximation (RRPA) approach. The model is self-consistent in the sense that one set of coupling constants generates the Dirac-Hartree single-particle spectrum and the residual particle-hole interaction. The RRPA is used to calculate response functions of multipolarity L = 0,2,3, and 4 in light and medium nuclei. It is found that monopole and quadrupole modes exhibit a collective character. The peak energies are overestimated, but not as much as one might think if the bulk properties (compression modulus, effective mass) were the only relevant quantities

  3. Symmetric and asymmetric nuclear matter in the relativistic approach

    International Nuclear Information System (INIS)

    Huber, H.; Weber, F.; Weigel, M.K.

    1995-01-01

    Symmetric and asymmetric nuclear matter is studied in the framework of the relativistic Brueckner-Hartree-Fock and in the relativistic version of the so-called Λ 00 approximation. The equations are solved self-consistently in the full Dirac space, so avoiding the ambiguities in the choice of the effective scattering amplitude in matter. The calculations were performed for some modern meson-exchange potentials constructed by Brockmann and Machleidt. In some cases we used also the Groningen potentials. First, we examine the outcome for symmetric matter with respect to other calculations, which restrict themselves to positive-energy states only. The main part is devoted to the properties of asymmetric matter. In this case we obtain additionally to the good agreement with the parameters of symmetric matter, also a quite satisfactory agreement with the semiempirical macroscopic coefficients of asymmetric matter. Furthermore, we tested the assumption of a quadratic dependence of the asymmetry energy for a large range of asymmetries. Included is also the dependence of nucleon self-energies on density and neutron excess. For the purpose of comparison we discuss further the similarities and differences with relativistic Hartree and Hartree-Fock calculations and nonrelativistic Skyrme calculations

  4. The neutron's Dirac-equation: Its rigorous solution at slab-like magnetic fields, non-relativistic approximation, energy spectra and statistical characteristics

    International Nuclear Information System (INIS)

    Zhang Yongde.

    1987-03-01

    In this paper, the neutron Dirac-equation is presented. After decoupling it into two equations of the simple spinors, the rigorous solution of this equation is obtained in the case of slab-like uniform magnetic fields at perpendicular incidence. At non-relativistic approximation and first order approximation of weak field (NRWFA), our results have included all results that have been obtained in references for this case up to now. The corresponding transformations of the neutron's spin vectors are given. The single particle spectrum and its approximate expression are obtained. The characteristics of quantum statistics with the approximate expression of energy spectrum are studied. (author). 15 refs

  5. Inner-shell ionization of heavy atoms by slow ions. A study of electronic relativistic effects and projectile Coulomb deflection in the Semiclassical Approximation

    International Nuclear Information System (INIS)

    Amundsen, P.A.

    1978-08-01

    Several investigations have been made on K and L shell ionization of the heavy collision partner in slow asymmetric collisions based on the SCA. The use of the SCA can only be defended for slow collisions if the projectile has a charge much less than the target. Thus this approximation should first be tested for proton impact on very heavy target elements. For these elements the inner shell electrons move sufficiently fast for a relativistic description to be mandatory. These relativistic effects are in themselves of some interest, as they can be quite large. After discussion of the formulation of the SCA used throughout this work, a further introduction is given on relativistic effects in Coulomb ionisation. Two papers on electronic relativistic effects in K and L shell ionization follow. The next two papers discuss calculations with an exact Coulomb projectile path. The latter of these also touches upon the inclusion of corrections to the SCA from terms beyond first order perturbation theory. In the last paper of this thesis it is shown how the theoretical apparatus developed for the SCA- calculations can immediately be used also for making calculations of more symmetric systems with the Briggs model. Thus, at least for direct ionization in very slow collisions a unification of the SA and MO approaches has apparently been reached. (JIW)

  6. A relativistic point coupling model for nuclear structure calculations

    International Nuclear Information System (INIS)

    Buervenich, T.; Maruhn, J.A.; Madland, D.G.; Reinhard, P.G.

    2002-01-01

    A relativistic point coupling model is discussed focusing on a variety of aspects. In addition to the coupling using various bilinear Dirac invariants, derivative terms are also included to simulate finite-range effects. The formalism is presented for nuclear structure calculations of ground state properties of nuclei in the Hartree and Hartree-Fock approximations. Different fitting strategies for the determination of the parameters have been applied and the quality of the fit obtainable in this model is discussed. The model is then compared more generally to other mean-field approaches both formally and in the context of applications to ground-state properties of known and superheavy nuclei. Perspectives for further extensions such as an exact treatment of the exchange terms using a higher-order Fierz transformation are discussed briefly. (author)

  7. Circumstances under which various approximate relativistic and nonrelativistic theories yield accurate Compton scattering doubly differential cross sections at high photon energy

    International Nuclear Information System (INIS)

    LaJohn, L A; Pratt, R H

    2009-01-01

    We discuss the increase in error with increasing nuclear charge Z in the use of the relativistic impulse approximation (RIA) for the calculation of Compton K-shell scattering doubly differential cross sections (DDCS). We also show that nonrelativistic (nr) expressions can be used to obtain accurate peak region DDCS at scattering angles less than about 35 0 even at incident photon energies ω i exceeding 1 MeV, if Z<30. This is possible because in the Compton peak region, as θ→0, a low momentum transfer limit is being approached.

  8. Pseudospin symmetry in the relativistic Manning-Rosen potential including a Pekeris-type approximation to the pseudo-centrifugal term

    International Nuclear Information System (INIS)

    Wei Gaofeng; Dong Shihai

    2010-01-01

    Based on the Sturm-Liouville theorem and shape invariance formalism, we study by applying a Pekeris-type approximation to the pseudo-centrifugal term the pseudospin symmetry of a Dirac nucleon subjected to scalar and vector Manning-Rosen potentials including the spin-orbit coupling term. A quartic energy equation and spinor wave functions with arbitrary spin-orbit coupling quantum number k are presented. The bound states are calculated numerically. The relativistic Manning-Rosen potential could not trap a Dirac nucleon in the limit case β→∞.

  9. Approximative analytic study of fermions in magnetar's crust; ultra-relativistic plane waves, Heun and Mathieu solutions and beyond

    Science.gov (United States)

    Dariescu, Marina-Aura; Dariescu, Ciprian

    2012-10-01

    Working with a magnetic field periodic along Oz and decaying in time, we deal with the Dirac-type equation characterizing the fermions evolving in magnetar's crust. For ultra-relativistic particles, one can employ the perturbative approach, to compute the conserved current density components. If the magnetic field is frozen and the magnetar is treated as a stationary object, the fermion's wave function is expressed in terms of the Heun's Confluent functions. Finally, we are extending some previous investigations on the linearly independent fermionic modes solutions to the Mathieu's equation and we discuss the energy spectrum and the Mathieu Characteristic Exponent.

  10. 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

  11. 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.

  12. Spin symmetry in the relativistic symmetrical well potential including a proper approximation to the spin-orbit coupling term

    International Nuclear Information System (INIS)

    Wei Gaofeng; Dong Shihai

    2010-01-01

    In the case of exact spin symmetry, we approximately solve the Dirac equation with scalar and vector symmetrical well potentials by using a proper approximation to the spin-orbit coupling term, and obtain the corresponding energy equation and spinor wave functions for the bound states. We find that there exist only positive-energy bound states in the case of spin symmetry. Also, the energy eigenvalue approaches a constant when the potential parameter α goes to zero. The special case for equally scalar and vector symmetrical well potentials is studied briefly.

  13. An exactly soluble Hartree problem in an external potential

    International Nuclear Information System (INIS)

    Gunn, J.C.; Gunn, J.M.F.

    1987-09-01

    The problem of N bosons interacting with each other via repulsive delta function interactions and with an external, attractive, delta function potential is solved within the Hartree approximation, exactly. It is found that if the interparticle interactions are above a certain value, there is no bound state. Thus the bound state does not just expand to compensate for the increase in the repulsive Hartree potential. Moreover as the interaction strength is increased to that value, the ground state wave function develops a pole at the position of the attractive potential. (author)

  14. 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

  15. Relativistic effects in the intermolecular interaction-induced nuclear magnetic resonance parameters of xenon dimer

    DEFF Research Database (Denmark)

    Hanni, Matti; Lantto, Perttu; Ilias, Miroslav

    2007-01-01

    Relativistic effects on the 129Xe nuclear magnetic resonance shielding and 131Xe nuclear quadrupole coupling (NQC) tensors are examined in the weakly bound Xe2 system at different levels of theory including the relativistic four-component Dirac-Hartree-Fock (DHF) method. The intermolecular...... interaction-induced binary chemical shift d, the anisotropy of the shielding tensor ?s, and the NQC constant along the internuclear axis ?ll are calculated as a function of the internuclear distance. DHF shielding calculations are carried out using gauge-including atomic orbitals. For comparison, the full...... is obtained for d and ?s in Xe2. For these properties, the currently most complete theoretical description is obtained by a piecewise approximation where the uncorrelated relativistic DHF results obtained close to the basis-set limit are corrected, on the one hand, for NR correlation effects and, on the other...

  16. Zeroth order regular approximation approach to electric dipole moment interactions of the electron

    Science.gov (United States)

    Gaul, Konstantin; Berger, Robert

    2017-07-01

    A quasi-relativistic two-component approach for an efficient calculation of P ,T -odd interactions caused by a permanent electric dipole moment of the electron (eEDM) is presented. The approach uses a (two-component) complex generalized Hartree-Fock and a complex generalized Kohn-Sham scheme within the zeroth order regular approximation. In applications to select heavy-elemental polar diatomic molecular radicals, which are promising candidates for an eEDM experiment, the method is compared to relativistic four-component electron-correlation calculations and confirms values for the effective electric field acting on the unpaired electron for RaF, BaF, YbF, and HgF. The calculations show that purely relativistic effects, involving only the lower component of the Dirac bi-spinor, are well described by treating only the upper component explicitly.

  17. 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.

  18. Temperature dependent relativistic microscopic optical potential and mean free paths of nucleons

    International Nuclear Information System (INIS)

    Han Yinlu; Shen Qingbiao; Zhuo Yizhong

    1993-01-01

    The relativistic microscopic optical potential, mean free paths and Schroedinger equivalent potential of nucleons at finite temperature in nuclear matter are studied based on Walecka's model and thermo field dynamics. We let only the Hartree-Fock self-energy of nucleon represent to be the real part of the microscopic optical potential and the fourth order of meson exchange diagrams, i.e. the core polarization represent the imaginary part of microscopic optical potential in nuclear matter. The microscopic optical potential of finite nuclei is obtained with the local density approximation

  19. An approximate factorization procedure for solving nine-point elliptic difference equations. Application for a fast 2-D relativistic Fokker-Planck solver

    International Nuclear Information System (INIS)

    Peysson, Y.

    1997-09-01

    A full implicit numerical procedure based on the use of a nine-point difference operator is presented to solve the two dimensional (2 D ) relativistic Fokker-Planck equation for the current drive problem and synergetic effects between the lower hybrid and the electron cyclotron waves in tokamaks. As compared to the standard approach based on the use of a five-point difference operator [M. Shoucri, I. Shkarofsky, Comput. Phys. Comm. 82 (1994) 287], the convergence rate towards the steady state solution may be significantly enhanced with no loss of accuracy on the distribution function. Moreover, it is shown that the numerical stability may be strongly improved without a large degradation of the CPU time consumption as in the five-point scheme, making this approach very attractive for a fast solution of the 2-D Fokker-Planck equation on a fine grid in conjunction with other numerical codes for realistic plasma simulations. This new algorithm, based on an approximate matrix factorization technique, may be applied to all numerical problems with large sets of equations which involve nine-point difference operators. (author)

  20. An approximate factorization procedure for solving nine-point elliptic difference equations. Application for a fast 2-D relativistic Fokker-Planck solver

    Energy Technology Data Exchange (ETDEWEB)

    Peysson, Y. [Association Euratom-CEA, CEA Grenoble, 38 (France). Dept. de Recherches sur la Fusion Controlee; Choucri, M. [Centre Canadien de Fusion Magnetique, Varennes, PQ (Canada)

    1997-09-01

    A full implicit numerical procedure based on the use of a nine-point difference operator is presented to solve the two dimensional (2{sub D}) relativistic Fokker-Planck equation for the current drive problem and synergetic effects between the lower hybrid and the electron cyclotron waves in tokamaks. As compared to the standard approach based on the use of a five-point difference operator [M. Shoucri, I. Shkarofsky, Comput. Phys. Comm. 82 (1994) 287], the convergence rate towards the steady state solution may be significantly enhanced with no loss of accuracy on the distribution function. Moreover, it is shown that the numerical stability may be strongly improved without a large degradation of the CPU time consumption as in the five-point scheme, making this approach very attractive for a fast solution of the 2-D Fokker-Planck equation on a fine grid in conjunction with other numerical codes for realistic plasma simulations. This new algorithm, based on an approximate matrix factorization technique, may be applied to all numerical problems with large sets of equations which involve nine-point difference operators. (author) 21 refs.

  1. Relativistic quantum kinetic analysis of a pion--nucleon system

    International Nuclear Information System (INIS)

    Alonso, J.D.

    1985-01-01

    A relativistic plasma of nucleons interacting through pions via the usual isospin-invariant Yukawa coupling is analyzed in the framework of the covariant Wigner function technique. The method is manifestly covariant and the temperature effects are considered. The relativistic quantum BBGKY hierarchy for the pion--nucleon system is derived. By generalizing the Bogolioubov analysis of the classical BBGKY hierarchy a non-perturbative renormalizable method is elaborated which allows the solution of the kinetic problem in form of power series of two cluster parameters which measure the importance of correlations. In the lowest order of the cluster expansion (Hartree approximation of zero-order approximation) the quasi-nucleon Fock space is introduced, the fermion Wigner function in the thermodynamic equilibrium is obtained and the vacuum effects are renormalized. In this approximation the plasma behaves as a perfect Fermi gas of nucleons and antinucleons, but there exists an abnormal configuration with a uniform pion condensate which is unstable. In the next approximation (quadratic in the small parameters) the quasi-pion dispersion relation is obtained and the vacuum polarization tensor is renormalized. The quasi-pion rest-mass spectra (''plasma frequency'') and the effective-coupling behaviour as functions of the thermodynamic state are given. By estimating the size of the cluster parameters the self-consistency of the approximation scheme is proved. The quasi-pion Fock space is introduced and the quasi-pion equilibrium Wigner function is obtained. From these results the problem of the higher-order corrections to the Hartree thermodynamics is outlined

  2. Self-consistent relativistic QRPA studies of soft modes and spin-isospin resonances in unstable nuclei

    International Nuclear Information System (INIS)

    Paar, N.; Niksic, T.; Marketin, T.; Vretenar, D.; Ring, P.

    2005-01-01

    The excitation phenomena in unstable nuclei are investigated in the framework of the relativistic quasiparticle random-phase approximation (RQRPA) in the relativistic Hartree-Bogolyubov model (RHB) which is extended to include effective interactions with explicit density-dependent meson-nucleon couplings. The properties of the pygmy dipole resonance (PDR) are examined in 132 Sn and within isotopic chains, showing that already at moderate proton-neutron asymmetry the PDR peak energy is located above the neutron emission threshold. A method is suggested for determining the size of the neutron skin within an isotopic chain, based on the measurement of the excitation energies of the Gamow-Teller resonance relative to the isobaric analog state. In addition, for the first time the relativistic RHB+RQRPA model, with tensor ω meson-nucleon couplings, is employed in calculations of β-decay half-lives of nuclei of the relevance for the r-process. (orig.)

  3. Self-consistent relativistic QRPA studies of soft modes and spin-isospin resonances in unstable nuclei

    Energy Technology Data Exchange (ETDEWEB)

    Paar, N. [Technische Universitaet Darmstadt, Institut fuer Kernphysik, Darmstadt (Germany); University of Zagreb, Physics Department, Faculty of Science (Croatia); University of Washington, Institute for Nuclear Theory, Seattle (United States); Niksic, T. [University of Zagreb, Physics Department, Faculty of Science (Croatia); University of Washington, Institute for Nuclear Theory, Seattle (United States); Marketin, T.; Vretenar, D. [University of Zagreb, Physics Department, Faculty of Science (Croatia); Ring, P. [Physik-Department der Technischen Universitaet Muenchen, Garching (Germany)

    2005-09-01

    The excitation phenomena in unstable nuclei are investigated in the framework of the relativistic quasiparticle random-phase approximation (RQRPA) in the relativistic Hartree-Bogolyubov model (RHB) which is extended to include effective interactions with explicit density-dependent meson-nucleon couplings. The properties of the pygmy dipole resonance (PDR) are examined in {sup 132}Sn and within isotopic chains, showing that already at moderate proton-neutron asymmetry the PDR peak energy is located above the neutron emission threshold. A method is suggested for determining the size of the neutron skin within an isotopic chain, based on the measurement of the excitation energies of the Gamow-Teller resonance relative to the isobaric analog state. In addition, for the first time the relativistic RHB+RQRPA model, with tensor {omega} meson-nucleon couplings, is employed in calculations of {beta}-decay half-lives of nuclei of the relevance for the r-process. (orig.)

  4. Pion propagator in relativistic quantum field theories of the nuclear many-body problem

    International Nuclear Information System (INIS)

    Matsui, T.; Serot, B.D.

    1982-01-01

    Pion interactions in the nuclear medium are studied using renormalizable relativistic quantum field theories. Previous studies using pseudoscalar πN coupling encountered difficulties due to the large strength of the πNN vertex. We therefore formulate renormalizable field theories with pseudovector πN coupling using techniques introduced by Weinberg and Schwinger. Calculations are performed for two specific models; the scalar-vector theory of Walecka, extended to include π and rho mesons in a non-chiral fashion, and the linear sigma-model with an additional neutral vector meson. Both models qualitatively reproduce low-energy πN phenomenology and lead to nuclear matter saturation in the relativistic Hartree formalism, which includes baryon vacuum fluctuations. The pions propagator is evaluated in the one-nucleon-loop approximation, which corresponds to a relativistic random-phase approximation built on the Hartree ground state. Virtual NN-bar loops are included, and suitable renormalization techniques are illustrated. The local-density approximation is used to compare the threshold pion self-energy to the s-wave pion-nucleus optical potential. In the non-chiral model, s-wave pion-nucleus scattering is too large in both pseudoscalar and pseudovector calculations, indicating that additional constraints must be imposed on the Lagrangian. In the chiral model, the threshold self-energy vanishes automatically in the pseudovector case, but does so for pseudoscalar coupling only if the baryon effective mass is chosen self-consistently Since extrapolation from free space to nuclear density can lead to large effects, pion propagation in the medium can determine which πN coupling is more suitable for the relativistic nuclear many-body problem. Conversely, pion interactions constrain the model Lagrangian and the nuclear matter equation of state. An approximately chiral model with pseudovector coupling is favored

  5. 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...

  6. Treating Coulomb exchange contributions in relativistic mean field calculations: why and how

    International Nuclear Information System (INIS)

    Giai, Nguyen Van; Liang, Haozhao; Gu, Huai-Qiang; Long, Wenhui; Meng, Jie

    2014-01-01

    The energy density functional (EDF) method is very widely used in nuclear physics, and among the various existing functionals those based on the relativistic Hartree (RH) approximation are very popular because the exchange contributions (Fock terms) are numerically rather onerous to calculate. Although it is possible to somehow ‘mock up’ the effects of meson-induced exchange terms by adjusting the meson–nucleon couplings, the lack of Coulomb exchange contributions hampers the accuracy of predictions. In this work, we show that the Coulomb exchange effects can be easily included with good accuracy in a perturbative approach. Therefore, it would be desirable for future relativistic EDF models to incorporate Coulomb exchange effects, at least to some order of perturbation

  7. Beta decay and muon capture rates in a self-consistent relativistic framework

    Energy Technology Data Exchange (ETDEWEB)

    Marketin, Tomislav; Paar, Nils; Niksic, Tamara; Vretenar, Dario [Physics Department, Faculty of Science, University of Zagreb (Croatia); Ring, Peter [Physik-Department, Technische Universitaet Muenchen, D-85748 Muenchen (Germany)

    2009-07-01

    A fully consistent calculation of muon capture and beta decay rates is presented, based on a microscopic theoretical framework describing the semileptonic weak interaction processes. Nuclear ground state is determined using the Relativistic Hartree-Bogolyubov (RHB) model with density dependent meson-nucleon coupling constants, and transition rates are calculated via proton-neutron relativistic quasiparticle RPA using the same interaction as in the RHB equations. Muon capture rates are calculated for a wide range of nuclei along the valley of stability, from {sup 12}C to {sup 244}Pu, with accuracy of approximately 30%, using the interaction DD-ME2. Previous studies of beta decay rates have only taken into account Gamow-Teller transitions. We extend this approach by including forbidden transitions and systematically study their contribution to decay rates of exotic nuclei along the r-process path, which are important for constraining the conditions in which nucleosynthesis takes place.

  8. Temperature-dependent relativistic microscopic optical potential and the mean free path of a nucleon based on Walecka's model

    International Nuclear Information System (INIS)

    Han Yinlu; Shen Qingbiao; Zhuo Yizhong

    1994-01-01

    The relativistic microscopic optical potential, the Schroedinger equivalent potential, and mean free paths of a nucleon at finite temperature in nuclear matter and finite nuclei are studied based on Walecka's model and thermo-field dynamics. We let only the Hartree-Fock self-energy of a nucleon represent the real part of the microscopic optical potential and the fourth order of meson exchange diagrams, i.e. the polarization diagrams represent the imaginary part of the microscopic optical potential in nuclear matter. The microscopic optical potential of finite nuclei is obtained by means of the local density approximation. (orig.)

  9. Beyond the relativistic mean-field approximation. II. Configuration mixing of mean-field wave functions projected on angular momentum and particle number

    International Nuclear Information System (INIS)

    Niksic, T.; Vretenar, D.; Ring, P.

    2006-01-01

    The framework of relativistic self-consistent mean-field models is extended to include correlations related to the restoration of broken symmetries and to fluctuations of collective variables. The generator coordinate method is used to perform configuration mixing of angular-momentum and particle-number projected relativistic wave functions. The geometry is restricted to axially symmetric shapes, and the intrinsic wave functions are generated from the solutions of the relativistic mean-field+Lipkin-Nogami BCS equations, with a constraint on the mass quadrupole moment. The model employs a relativistic point-coupling (contact) nucleon-nucleon effective interaction in the particle-hole channel, and a density-independent δ-interaction in the pairing channel. Illustrative calculations are performed for 24 Mg, 32 S, and 36 Ar, and compared with results obtained employing the model developed in the first part of this work, i.e., without particle-number projection, as well as with the corresponding nonrelativistic models based on Skyrme and Gogny effective interactions

  10. 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.

  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. 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

  13. Four-Component Relativistic Density-Functional Theory Calculations of Nuclear Spin-Rotation Constants: Relativistic Effects in p-Block Hydrides.

    Science.gov (United States)

    Komorovsky, Stanislav; Repisky, Michal; Malkin, Elena; Demissie, Taye B; Ruud, Kenneth

    2015-08-11

    We present an implementation of the nuclear spin-rotation (SR) constants based on the relativistic four-component Dirac-Coulomb Hamiltonian. This formalism has been implemented in the framework of the Hartree-Fock and Kohn-Sham theory, allowing assessment of both pure and hybrid exchange-correlation functionals. In the density-functional theory (DFT) implementation of the response equations, a noncollinear generalized gradient approximation (GGA) has been used. The present approach enforces a restricted kinetic balance condition for the small-component basis at the integral level, leading to very efficient calculations of the property. We apply the methodology to study relativistic effects on the spin-rotation constants by performing calculations on XHn (n = 1-4) for all elements X in the p-block of the periodic table and comparing the effects of relativity on the nuclear SR tensors to that observed for the nuclear magnetic shielding tensors. Correlation effects as described by the density-functional theory are shown to be significant for the spin-rotation constants, whereas the differences between the use of GGA and hybrid density functionals are much smaller. Our calculated relativistic spin-rotation constants at the DFT level of theory are only in fair agreement with available experimental data. It is shown that the scaling of the relativistic effects for the spin-rotation constants (varying between Z(3.8) and Z(4.5)) is as strong as for the chemical shieldings but with a much smaller prefactor.

  14. Calculations of electronic structure of UF6 molecule and crystal UO2 with relativistic pseudopotential

    International Nuclear Information System (INIS)

    Ehvarestov, R.A.; Panin, A.I.; Bandura, A.V.

    2008-01-01

    Account of relativistic effects on the properties of uranium hexafluoride is testified. Detailed comparison of single electron energies spectrum revealed in nonrelativistic (by Hartree-Fock method), relativistic (by Dirac-Fock method), and scalar-relativistic (using relativistic potential of atomic uranium frame) has been conducted. Optimization procedures of atomic basis in LCAO calculations of molecules and crystals permissive taking into account distortion of atomic orbitals when chemical bonding are discussed, and optimization effect of atomic basis on the results of scalar-relativistic calculations of UF 6 molecule properties is analyzed. Calculations of electronic structure and properties of UO 2 crystal having relativistic and nonrelativistic pseudopotentials have been realized [ru

  15. Evolution of the low-lying dipole strength in deformed nuclei with extreme neutron excess with the Relativistic QRPA

    International Nuclear Information System (INIS)

    Pena Arteaga, D.; Khan, E.; Ring, P.

    2009-01-01

    Covariant density functional theory, in the framework of self-consistent Relativistic Hartree Bogoliubov (HFB) and Relativistic Quasiparticle Random Phase approximation (RQRPA), is for the first time applied to axially deformed nuclei [1]. The fully self-consistent RHB+RQRPA equations are posed for the case of axial symmetry and different energy functionals, and solved with the help of a new parallel code. As a sample application, the El strength is systematically analyzed in very neutron-rich Sn nuclei, beyond 1 32S n until 1 66S n [2]. The great neutron excess favors the appearance of a deformed ground state for 1 42-162S n. The evolution of the low-lying strength in deformed nuclei is discussed, and in particular its dependence on the interplay of two major and competing factors, isospin asymmetry and deformation.(author)

  16. 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...

  17. 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

  18. 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...

  19. Relativistic equations

    International Nuclear Information System (INIS)

    Gross, F.

    1986-01-01

    Relativistic equations for two and three body scattering are discussed. Particular attention is paid to relativistic three body kinetics because of recent form factor measurements of the Helium 3 - Hydrogen 3 system recently completed at Saclay and Bates and the accompanying speculation that relativistic effects are important for understanding the three nucleon system. 16 refs., 4 figs

  20. 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

  1. Berry phases for 3D Hartree-type equations with a quadratic potential and a uniform magnetic field

    International Nuclear Information System (INIS)

    Litvinets, F N; Shapovalov, A V; Trifonov, A Yu

    2007-01-01

    A countable set of asymptotic space-localized solutions is constructed for a 3D Hartree-type equation with a quadratic potential by the complex germ method in the adiabatic approximation. The asymptotic parameter is 1/T, where T >> 1 is the adiabatic evolution time. A generalization of the Berry phase of the linear Schroedinger equation is formulated for the Hartree-type equation. For the solutions constructed, the Berry phases are found in an explicit form

  2. 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

  3. Relativistic multiple scattering X-alpha calculations

    International Nuclear Information System (INIS)

    Chermette, H.; Goursot, A.

    1986-01-01

    The necessity to include self-consistent relativistic corrections in molecular calculations has been pointed out for all compounds involving heavy atoms. Most of the changes in the electronic properties are due to the mass-velocity and the so-called Darwin terms so that the use of Wood and Boring's Hamiltonian is very convenient for this purpose as it can be easily included in MSXalpha programs. Although the spin orbit operator effects are only obtained by perturbation theory, the results compare fairly well with experiment and with other relativistic calculations, namely Hartree-Fock-Slater calculations

  4. 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...

  5. Halo nuclei studied by relativistic mean-field approach

    International Nuclear Information System (INIS)

    Gmuca, S.

    1997-01-01

    Density distributions of light neutron-rich nuclei are studied by using the relativistic mean-field approach. The effective interaction which parameterizes the recent Dirac-Brueckner-Hartree-Fock calculations of nuclear matter is used. The results are discussed and compared with the experimental observations with special reference to the neutron halo in the drip-line nuclei. (author)

  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. 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)

  8. 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.

  9. Neutron star properties and the relativistic nuclear equation of state of many-baryon matter

    International Nuclear Information System (INIS)

    Weber, F.; Weigel, M.K.

    1989-01-01

    A relativistic model of baryons interacting via the exchange of σ-, ω-, π- and ρ-mesons (scalar-vector-isovector (SVI) theory) is used to describe the properties of both dense and superdense matter. For the theoretical frame, we used the temperature-dependent Green's function formalism. The equation of state (EOS) is calculated for nuclear as well as neutron matter in the Hartree (H) and Hartree-Fock (HF) approximation. The existence of phase transitions has been investigated. The isotherms of pressure as a function of density show for nuclear matter a critical temperature of about T c HF =16.6 MeV. (As in the usual scalar-vector (SV) theory, the phase transition is absent for neutron matter. A phase transition of both many-baryon systems in the high-pressure and high-density region, which has been found within the SV many-baryon theory, appears in the SVI theory too. The calculated maximum stable masses of neutron stars depend on 1. the underlying parameter set and/or 2. on the chosen approximation (i.e., H, HF; SV-, SVI theory, respectively). Hartree calculations lead to a mass stability limit of M max H ≤2.87 M sun (M max H ≤2.44 M sun when hyperons are taken into account). For the HF calculations we obtained M max HF ≤3.00 M sun (M max HF ≤2.85 M sun ). The corresponding maximum radii are (same notation as above) R H ≤13.2 km (R H ≤11.8 km), R HF ≤14.0 km (R HF ≤13.94 km).) The influence of the approximations, parameter sets and hyperons on the neutron star's moment of inertia is exhibited. (orig.)

  10. 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

  11. Relativistic many-body theory of high density matter

    International Nuclear Information System (INIS)

    Chin, S.A.

    1977-01-01

    A fully relativistic quantum many-body theory is applied to the study of high-density matter. The latter is identified with the zero-temperature ground state of a system of interacting baryons. In accordance with the observed short-range repulsive and long-range attractive character of the nucleon--nucleon force, baryons are described as interacting with each other via a massive scalar and a massive vector meson exchange. In the Hartree approximation, the theory yields the same result as the mean-field theory, but with additional vacuum fluctuation corrections. The resultant equation of state for neutron matter is used to determine properties of neutron stars. The relativistic exchange energy, its corresponding single-particle excitation spectrum, and its effect on the neutron matter equation of state, are calculated. The correlation energy from summing the set of ring diagrams is derived directly from the energy-momentum tensor, with renormalization carried out by adding counterterms to the original Lagrangian and subtracting purely vacuum expectation values. Terms of order g 4 lng 2 are explicitly given. Effects of scalar-vector mixing are discussed. Collective modes corresponding to macroscopic density fluctuation are investigated. Two basic modes are found, a plasma-like mode and zero sound, with the latter dominant at high density. The stability and damping of these modes are studied. Last, the effect of vacuum polarization in high-density matter is examined

  12. 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.

  13. Relativistic astrophysics

    CERN Document Server

    Demianski, Marek

    2013-01-01

    Relativistic Astrophysics brings together important astronomical discoveries and the significant achievements, as well as the difficulties in the field of relativistic astrophysics. This book is divided into 10 chapters that tackle some aspects of the field, including the gravitational field, stellar equilibrium, black holes, and cosmology. The opening chapters introduce the theories to delineate gravitational field and the elements of relativistic thermodynamics and hydrodynamics. The succeeding chapters deal with the gravitational fields in matter; stellar equilibrium and general relativity

  14. Electronic structure of molecules using relativistic effective core potentials

    International Nuclear Information System (INIS)

    Hay, P.J.

    1981-01-01

    Starting with one-component Cowan-Griffin relativistic Hartree-Fock orbitals, which successfully incorporate the mass-velocity and Darwin terms present in more complicated wavefunctions such as Dirac-Hartree-Fock, one can derive relativistic effective core potentials (RECP's) to carry out molecular calculations. These potentials implicitly include the dominant relativistic terms for molecules while allowing one to use the traditional quantum chemical techniques for studying the electronic structure of molecules. The effects of spin-orbit coupling can then be included using orbitals from such calculations using an effective 1-electron, 1-center spin-orbit operator. Applications to molecular systems involving heavy atoms, show good agreement with available spectroscopic data on molecular geometries and excitation energies

  15. 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

  16. Relativistic correlations in atoms

    International Nuclear Information System (INIS)

    Dietz, K.

    1987-01-01

    Atoms are particularly well-suited objects when it comes to testing certain concepts of many-body theories. They play a unique role in this respect because of two constructively interfering reasons: first of all, the laws describing the interactions of their constituents are the ones best known in all of Physics; secondly, their structure is comparatively simple and amenable to concise theoretical treatment. Because of these two reasons, physically motivated many-body approximation schemes, ordered in a systematic hierarchy of precision, can be carefully tested; discrepancies between theory and experiment are due to many-body effects and are never masked by uncertainties in the constituent-interaction (needless to say, the very small hadronic contributions to atomic structure is left out. Many-body effects in atoms are solely produced by the electron-electron interaction which derives from the laws of Quantum Electrodynamics or, in a very good approximation from the repulsive Coulomb potential; in the general nomenclature they are named correlations. The material is organized in two chapters: chapter 1 deals with a general introduction and discussion of g-Hartree mean-field theories, chapter 2 deals with applications. The role of vacuum fluctuations and deformations of the Dirac sea in a consistent construction of mean-fields is emphasized and their explicit form in the g-Hartree theory is given. 21 references, 5 figures, 3 tables

  17. Relativistic mean field theory with density dependent coupling constants for nuclear matter and finite nuclei with large charge asymmetry

    Energy Technology Data Exchange (ETDEWEB)

    Typel, S; Wolter, H H [Sektion Physik, Univ. Muenchen, Garching (Germany)

    1998-06-01

    Nuclear matter and ground state properties for (proton and neutron) semi-closed shell nuclei are described in relativistic mean field theory with coupling constants which depend on the vector density. The parametrization of the density dependence for {sigma}-, {omega}- and {rho}-mesons is obtained by fitting to properties of nuclear matter and some finite nuclei. The equation of state for symmetric and asymmetric nuclear matter is discussed. Finite nuclei are described in Hartree approximation, including a charge and an improved center-of-mass correction. Pairing is considered in the BCS approximation. Special attention is directed to the predictions for properties at the neutron and proton driplines, e.g. for separation energies, spin-orbit splittings and density distributions. (orig.)

  18. Classical limit for semirelativistic Hartree systems

    KAUST Repository

    Aki, Gonca L.; Markowich, Peter A.; Sparber, Christof

    2008-01-01

    Wigner transformation techniques that its classical limit yields the well known relativistic Vlasov-Poisson system. The result holds for the case of attractive and repulsive mean-field interactions, with an additional size constraint in the attractive

  19. 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)

  20. Relativistic corrections to molecular dynamic dipole polarizabilities

    DEFF Research Database (Denmark)

    Kirpekar, Sheela; Oddershede, Jens; Jensen, Hans Jørgen Aagaard

    1995-01-01

    obtained from the use of the Darwin and mass-velocity operators to first order are included at both levels of approximation. We find that correlation and relativistic contributions are not even approximately additive for the two molecules. The importance of the relativistic corrections is smallest...

  1. 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)

  2. Spin-orbit ZORA and four-component Dirac-Coulomb estimation of relativistic corrections to isotropic nuclear shieldings and chemical shifts of noble gas dimers.

    Science.gov (United States)

    Jankowska, Marzena; Kupka, Teobald; Stobiński, Leszek; Faber, Rasmus; Lacerda, Evanildo G; Sauer, Stephan P A

    2016-02-05

    Hartree-Fock and density functional theory with the hybrid B3LYP and general gradient KT2 exchange-correlation functionals were used for nonrelativistic and relativistic nuclear magnetic shielding calculations of helium, neon, argon, krypton, and xenon dimers and free atoms. Relativistic corrections were calculated with the scalar and spin-orbit zeroth-order regular approximation Hamiltonian in combination with the large Slater-type basis set QZ4P as well as with the four-component Dirac-Coulomb Hamiltonian using Dyall's acv4z basis sets. The relativistic corrections to the nuclear magnetic shieldings and chemical shifts are combined with nonrelativistic coupled cluster singles and doubles with noniterative triple excitations [CCSD(T)] calculations using the very large polarization-consistent basis sets aug-pcSseg-4 for He, Ne and Ar, aug-pcSseg-3 for Kr, and the AQZP basis set for Xe. For the dimers also, zero-point vibrational (ZPV) corrections are obtained at the CCSD(T) level with the same basis sets were added. Best estimates of the dimer chemical shifts are generated from these nuclear magnetic shieldings and the relative importance of electron correlation, ZPV, and relativistic corrections for the shieldings and chemical shifts is analyzed. © 2015 Wiley Periodicals, Inc.

  3. Relativistic hydrodynamics

    CERN Document Server

    Luciano, Rezzolla

    2013-01-01

    Relativistic hydrodynamics is a very successful theoretical framework to describe the dynamics of matter from scales as small as those of colliding elementary particles, up to the largest scales in the universe. This book provides an up-to-date, lively, and approachable introduction to the mathematical formalism, numerical techniques, and applications of relativistic hydrodynamics. The topic is typically covered either by very formal or by very phenomenological books, but is instead presented here in a form that will be appreciated both by students and researchers in the field. The topics covered in the book are the results of work carried out over the last 40 years, which can be found in rather technical research articles with dissimilar notations and styles. The book is not just a collection of scattered information, but a well-organized description of relativistic hydrodynamics, from the basic principles of statistical kinetic theory, down to the technical aspects of numerical methods devised for the solut...

  4. Dielectric response of a relativistic degenerate electron plasma in a strong magnetic field

    International Nuclear Information System (INIS)

    Delsante, A.E.; Frankel, N.E.

    1979-01-01

    The longitudinal dielectric response of a relativistic ultradegenerate electron plasma in a strong magnetic field is obtained via a relativistic generalization of the Hartree self-consistent field method. Dispersion relations and damping conditions for plasma oscillations both parallel and perpendicular to the magnetic field are obtained. Detailed results for the zero-field case, and applications to white dwarf stars and pulsars are given

  5. Calculation of β-decay rates in a relativistic model with momentum-dependent self-energies

    International Nuclear Information System (INIS)

    Marketin, T.; Vretenar, D.; Ring, P.

    2007-01-01

    The relativistic proton-neutron quasiparticle random phase approximation (PN-RQRPA) is applied in the calculation of β-decay half-lives of neutron-rich nuclei in the Z≅28 and Z≅50 regions. The study is based on the relativistic Hartree-Bogoliubov calculation of nuclear ground states, using effective Lagrangians with density-dependent meson-nucleon couplings, and also extended by the inclusion of couplings between the isoscalar meson fields and the derivatives of the nucleon fields. This leads to a linear momentum dependence of the scalar and vector nucleon self-energies. The residual QRPA interaction in the particle-hole channel includes the π+ρ exchange plus a Landau-Migdal term. The finite-range Gogny interaction is employed in the T=1 pairing channel, and the model also includes a proton-neutron particle-particle interaction. The results are compared with available data, and it is shown that an extension of the standard relativistic mean-field framework to include momentum-dependent nucleon self-energies naturally leads to an enhancement of the effective (Landau) nucleon mass, and thus to an improved PN-QRPA description of β - -decay rates

  6. 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

  7. 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.

  8. Relativistic Calculations and Measurements of Energies, Auger Rates, and Lifetimes.

    Science.gov (United States)

    1982-12-01

    Research and Industry, Denton, Texas, 8-10 November 1982. 7. B. Crasemann: "Efectos Relativ’sticos y de QED Sobre las Transiciones Rayos - X y Auger Entre...INNER-SHELL IONIZATION BY PROTONS X -RAY EMISSION BREIT INTERACTION AUGER TRANSITIONS DIRAC-HARTREE-SLATER COMPUTATIONS SYNCHROTRON RADIATION RESONANT...computations, including relativistic and quantum- electrodynamic effects, of atomic energy levels and of x -ray and Auger transitions in atoms with one or

  9. 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

  10. Relativistic astrophysics

    CERN Document Server

    Price, R H

    1993-01-01

    Work reported in the workshop on relativistic astrophysics spanned a wide varicy of topics. Two specific areas seemed of particular interest. Much attention was focussed on gravitational wave sources, especially on the waveforms they produce, and progress was reported in theoretical and observational aspects of accretion disks.

  11. Relativistic Kinematics

    OpenAIRE

    Sahoo, Raghunath

    2016-01-01

    This lecture note covers Relativistic Kinematics, which is very useful for the beginners in the field of high-energy physics. A very practical approach has been taken, which answers "why and how" of the kinematics useful for students working in the related areas.

  12. Relativistic Astrophysics

    International Nuclear Information System (INIS)

    Font, J. A.

    2015-01-01

    The relativistic astrophysics is the field of astrophysics employing the theory of relativity Einstein as physical-mathematical model is to study the universe. This discipline analyzes astronomical contexts in which the laws of classical mechanics of Newton's law of gravitation are not valid. (Author)

  13. Relativistic many-body theory of atomic transitions: the relativistic equation-of-motion approach

    International Nuclear Information System (INIS)

    Huang, K.N.

    1981-01-01

    An equation-of-motion approach is used to develop the relativistic many-body theory of atomic transitions. The relativistic equations of motion for transition matrices are formulated using techniques of quantum field theory. To reduce the equation of motion to a tractable form which is appropriate for numerical calculations, a graphical method is employed to resolve the complication arising from the antisymmetrization and angular momentum coupling. The relativistic equation-of-motion method allows an ab initio treatment of correlation and relativistic effects in both closed- and open-shell many-body systems. A special case of the present formulation reduces to the relativistic random-phase approximation

  14. 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)

  15. Relativistic Quantum Mechanics

    International Nuclear Information System (INIS)

    Antoine, J-P

    2004-01-01

    The aim of relativistic quantum mechanics is to describe the finer details of the structure of atoms and molecules, where relativistic effects become nonnegligible. It is a sort of intermediate realm, between the familiar nonrelativistic quantum mechanics and fully relativistic quantum field theory, and thus it lacks the simplicity and elegance of both. Yet it is a necessary tool, mostly for quantum chemists. Pilkuhn's book offers to this audience an up-to-date survey of these methods, which is quite welcome since most previous textbooks are at least ten years old. The point of view of the author is to start immediately in the relativistic domain, following the lead of Maxwell's equations rather than classical mechanics, and thus to treat the nonrelativistic version as an approximation. Thus Chapter 1 takes off from Maxwell's equations (in the noncovariant Coulomb gauge) and gradually derives the basic aspects of Quantum Mechanics in a rather pedestrian way (states and observables, Hilbert space, operators, quantum measurement, scattering,. Chapter 2 starts with the Lorentz transformations, then continues with the Pauli spin equation and the Dirac equation and some of their applications (notably the hydrogen atom). Chapter 3 is entitled 'Quantum fields and particles', but falls short of treating quantum field theory properly: only creation/annihilation operators are considered, for a particle in a box. The emphasis is on two-electron states (the Pauli principle, the Foldy--Wouthuysen elimination of small components of Dirac spinors, Breit projection operators. Chapter 4 is devoted to scattering theory and the description of relativistic bound states. Chapter 5, finally, covers hyperfine interactions and radiative corrections. As we said above, relativistic quantum mechanics is by nature limited in scope and rather inelegant and Pilkuhn's book is no exception. The notation is often heavy (mostly noncovariant) and the mathematical level rather low. The central topic

  16. The relativistic gravity train

    Science.gov (United States)

    Seel, Max

    2018-05-01

    The gravity train that takes 42.2 min from any point A to any other point B that is connected by a straight-line tunnel through Earth has captured the imagination more than most other applications in calculus or introductory physics courses. Brachystochron and, most recently, nonlinear density solutions have been discussed. Here relativistic corrections are presented. It is discussed how the corrections affect the time to fall through Earth, the Sun, a white dwarf, a neutron star, and—the ultimate limit—the difference in time measured by a moving, a stationary and the fiducial observer at infinity if the density of the sphere approaches the density of a black hole. The relativistic gravity train can serve as a problem with approximate and exact analytic solutions and as numerical exercise in any introductory course on relativity.

  17. Relativistic klystrons

    International Nuclear Information System (INIS)

    Allen, M.A.; Azuma, O.; Callin, R.S.

    1989-03-01

    Experimental work is underway by a SLAC-LLNL-LBL collaboration to investigate the feasibility of using relativistic klystrons as a power source for future high gradient accelerators. Two different relativistic klystron configurations have been built and tested to date: a high grain multicavity klystron at 11.4 GHz and a low gain two cavity subharmonic buncher driven at 5.7 GHz. In both configurations power is extracted at 11.4 GHz. In order to understand the basic physics issues involved in extracting RF from a high power beam, we have used both a single resonant cavity and a multi-cell traveling wave structure for energy extraction. We have learned how to overcome our previously reported problem of high power RF pulse shortening, and have achieved peak RF power levels of 170 MW with the RF pulse of the same duration as the beam current pulse. 6 refs., 3 figs., 3 tabs

  18. Gravitation relativiste

    CERN Document Server

    Hakim, Rémi

    1994-01-01

    Il existe à l'heure actuelle un certain nombre de théories relativistes de la gravitation compatibles avec l'expérience et l'observation. Toutefois, la relativité générale d'Einstein fut historiquement la première à fournir des résultats théoriques corrects en accord précis avec les faits.

  19. Relativistic klystron

    International Nuclear Information System (INIS)

    Marks, R.

    1985-09-01

    Theoretical analysis is presented of a relativisic klystron; i.e. a high-relativistic bunched electron beam which is sent through a succession of tuned cavities and has its energy replenished by periodic induction accelerator units. Parameters are given for a full-size device and for an experimental device using the FEL at the ETA; namely the ELF Facility. 6 refs., 2 figs

  20. Relativistic calculations of coalescing binary neutron stars

    Indian Academy of Sciences (India)

    We have designed and tested a new relativistic Lagrangian hydrodynamics code, which treats gravity in the conformally flat approximation to general relativity. We have tested the resulting code extensively, finding that it performs well for calculations of equilibrium single-star models, collapsing relativistic dust clouds, and ...

  1. 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)

  2. 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.

  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. An introduction to relativistic hydrodynamics

    Energy Technology Data Exchange (ETDEWEB)

    Font, Jose A [Departamento de AstronomIa y AstrofIsica, Universidad de Valencia, Dr. Moliner 50, 46100 Burjassot (Valencia) (Spain)

    2007-11-15

    We review formulations of the equations of (inviscid) general relativistic hydrodynamics and (ideal) magnetohydrodynamics, along with methods for their numerical solution. Both systems can be cast as first-order, hyperbolic systems of conservation laws, following the explicit choice of an Eulerian observer and suitable fluid and magnetic field variables. During the last fifteen years, the so-called (upwind) high-resolution shock-capturing schemes based on Riemann solvers have been successfully extended from classical to relativistic fluid dynamics, both special and general. Nowadays, general relativistic hydrodynamical simulations in relativistic astrophysics are routinely performed, particularly within the test-fluid approximation but also for dynamical spacetimes. While such advances also hold true in the case of the MHD equations, the astrophysical applications investigated so far are still limited, yet the field is bound to witness major developments in the near future. The article also presents a brief overview of numerical techniques, providing state-of-the-art examples of their applicability to general relativistic fluids and magneto-fluids in characteristic scenarios of relativistic astrophysics.

  5. Relativistic effects in the intermolecular interaction-induced nuclear magnetic resonance parameters of xenon dimer.

    Science.gov (United States)

    Hanni, Matti; Lantto, Perttu; Ilias, Miroslav; Jensen, Hans Jorgen Aagaard; Vaara, Juha

    2007-10-28

    Relativistic effects on the (129)Xe nuclear magnetic resonance shielding and (131)Xe nuclear quadrupole coupling (NQC) tensors are examined in the weakly bound Xe(2) system at different levels of theory including the relativistic four-component Dirac-Hartree-Fock (DHF) method. The intermolecular interaction-induced binary chemical shift delta, the anisotropy of the shielding tensor Deltasigma, and the NQC constant along the internuclear axis chi( parallel) are calculated as a function of the internuclear distance. DHF shielding calculations are carried out using gauge-including atomic orbitals. For comparison, the full leading-order one-electron Breit-Pauli perturbation theory (BPPT) is applied using a common gauge origin. Electron correlation effects are studied at the nonrelativistic (NR) coupled-cluster singles and doubles with perturbational triples [CCSD(T)] level of theory. The fully relativistic second-order Moller-Plesset many-body perturbation (DMP2) theory is used to examine the cross coupling between correlation and relativity on NQC. The same is investigated for delta and Deltasigma by BPPT with a density functional theory model. A semiquantitative agreement between the BPPT and DHF binary property curves is obtained for delta and Deltasigma in Xe(2). For these properties, the currently most complete theoretical description is obtained by a piecewise approximation where the uncorrelated relativistic DHF results obtained close to the basis-set limit are corrected, on the one hand, for NR correlation effects and, on the other hand, for the BPPT-based cross coupling of relativity and correlation. For chi( parallel), the fully relativistic DMP2 results obtain a correction for NR correlation effects beyond MP2. The computed temperature dependence of the second virial coefficient of the (129)Xe nuclear shielding is compared to experiment in Xe gas. Our best results, obtained with the piecewise approximation for the binary chemical shift combined with the

  6. Relativistic models of nuclear structure

    International Nuclear Information System (INIS)

    Gillet, V.; Kim, E.J.; Cauvin, M.; Kohmura, T.; Ohnaka, S.

    1991-01-01

    The introduction of the relativistic field formalism for the description of nuclear structure has improved our understanding of fundamental nuclear mechanisms such as saturation or many body forces. We discuss some of these progresses, both in the semi-classical mean field approximation and in a quantized meson field approach. (author)

  7. Relativistic pn-QRPA to the double beta decay

    International Nuclear Information System (INIS)

    Conti, Claudio de; Krmpotic, F.; Carlson, Brett Vern

    2010-01-01

    Full text: In nature there are about 50 nuclear systems where the single beta-decay is energetically forbidden, and double- beta decay turns out to be only possible mode of disintegration. It is the nuclear pairing force which causes such an 'anomaly', by making the mass of the odd-odd isobar, (N - 1;Z + 1), to be greater than the masses of its even-even neighbors, (N;Z) and (N - 2;Z +2). The modes by which the double-beta decay can take place are connected with the neutrino and antineutrino distinction. In case the lepton number is strictly conserved the neutrino is a Dirac fermion and the two-neutrino mode is the only possible mode of disintegration. On the other hand, if this conservation is violated, the neutrino is a Majorana particle and neutrinoless double-beta decay also can occur. Both two-neutrino and neutrinoless double-beta decay processes have attracted much attention, because a comparison between experiment and theory for the first, provides a measure of confidence one may have in the nuclear wave function employed for extracting the unknown parameters from neutrinoless lifetime measurements. The proton-neutron (pn) quasiparticle random phase approximation (QRPA) has turned out be the most simple model for calculating the nuclear wave function involved in the double-beta decay transitions. In this work the transition matrix elements for 0 + -> 0 + double-beta decay are calculated for 48 Ca, 76 Ge, 82 Se, 100 Mo, 128 Te and 130 Te nuclei, using a relativistic pn-QRPA based on Hartree-Bogoliubov approximation to the single-particle motion. (author)

  8. Relativistic pn-QRPA to the double beta decay

    International Nuclear Information System (INIS)

    Conti, Claudio de; Krmpotic, Francisco; Carlson, Brett Vern

    2011-01-01

    Full text: In nature there are about 50 nuclear systems where the single beta-decay is energetically forbidden, and double-beta decay turns out to be only possible mode of disintegration. It is the nuclear pairing force which causes such an 'anomaly', by making the mass of the odd-odd isobar, (N - 1;Z + 1), to be greater than the masses of its even-even neighbors, (N;Z) and (N - 2;Z +2). The modes by which the double-beta decay can take place are connected with the neutrino and antineutrino distinction. In case the lepton number is strictly conserved the neutrino is a Dirac fermion and the two-neutrino mode is the only possible mode of disintegration. On the other hand, if this conservation is violated, the neutrino is a Majorana particle and neutrinoless double-beta decay also can occur. Both two-neutrino and neutrinoless double-beta decay processes have attracted much attention, because a comparison between experiment and theory for the first, provides a measure of confidence one may have in the nuclear wave function employed for extracting the unknown parameters from neutrinoless lifetime measurements. The proton-neutron (pn) quasiparticle random phase approximation (QRPA) has turned out be the most simple model for calculating the nuclear wave function involved in the double-beta decay transitions. In this work the transition matrix elements for 0 + → 0 + double-beta decay are calculated for 48 Ca, 76 Ge, 82 Se, 100 Mo, 128 Te and 130 Te nuclei, using a relativistic pn-QRPA based on Hartree-Bogoliubov approximation to the single-particle motion. (author)

  9. SPECIAL RELATIVISTIC HYDRODYNAMICS WITH GRAVITATION

    Energy Technology Data Exchange (ETDEWEB)

    Hwang, Jai-chan [Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu (Korea, Republic of); Noh, Hyerim [Korea Astronomy and Space Science Institute, Daejon (Korea, Republic of)

    2016-12-20

    Special relativistic hydrodynamics with weak gravity has hitherto been unknown in the literature. Whether such an asymmetric combination is possible has been unclear. Here, the hydrodynamic equations with Poisson-type gravity, considering fully relativistic velocity and pressure under the weak gravity and the action-at-a-distance limit, are consistently derived from Einstein’s theory of general relativity. An analysis is made in the maximal slicing, where the Poisson’s equation becomes much simpler than our previous study in the zero-shear gauge. Also presented is the hydrodynamic equations in the first post-Newtonian approximation, now under the general hypersurface condition. Our formulation includes the anisotropic stress.

  10. 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.

  11. Relativistic Astronomy

    Science.gov (United States)

    Zhang, Bing; Li, Kunyang

    2018-02-01

    The “Breakthrough Starshot” aims at sending near-speed-of-light cameras to nearby stellar systems in the future. Due to the relativistic effects, a transrelativistic camera naturally serves as a spectrograph, a lens, and a wide-field camera. We demonstrate this through a simulation of the optical-band image of the nearby galaxy M51 in the rest frame of the transrelativistic camera. We suggest that observing celestial objects using a transrelativistic camera may allow one to study the astronomical objects in a special way, and to perform unique tests on the principles of special relativity. We outline several examples that suggest transrelativistic cameras may make important contributions to astrophysics and suggest that the Breakthrough Starshot cameras may be launched in any direction to serve as a unique astronomical observatory.

  12. Relativistic magnetohydrodynamics

    Energy Technology Data Exchange (ETDEWEB)

    Hernandez, Juan; Kovtun, Pavel [Department of Physics and Astronomy, University of Victoria,Victoria, BC, V8P 5C2 (Canada)

    2017-05-02

    We present the equations of relativistic hydrodynamics coupled to dynamical electromagnetic fields, including the effects of polarization, electric fields, and the derivative expansion. We enumerate the transport coefficients at leading order in derivatives, including electrical conductivities, viscosities, and thermodynamic coefficients. We find the constraints on transport coefficients due to the positivity of entropy production, and derive the corresponding Kubo formulas. For the neutral state in a magnetic field, small fluctuations include Alfvén waves, magnetosonic waves, and the dissipative modes. For the state with a non-zero dynamical charge density in a magnetic field, plasma oscillations gap out all propagating modes, except for Alfvén-like waves with a quadratic dispersion relation. We relate the transport coefficients in the “conventional” magnetohydrodynamics (formulated using Maxwell’s equations in matter) to those in the “dual” version of magnetohydrodynamics (formulated using the conserved magnetic flux).

  13. 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

  14. 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

  15. 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

  16. 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

  17. Inertial parameters in the interacting boson fermion approximation

    International Nuclear Information System (INIS)

    Dukelsky, J.; Lima, C.

    1986-06-01

    The Hartree-Bose-Fermi and the adiabatic approximations are used to derive analytic formulas for the moment of inertia and the decoupling parameter of the interacting boson fermion approximation for deformed systems. These formulas are applied to the SU(3) dynamical symmetry, obtaining perfect agreement with the exact results. (Authors) [pt

  18. A new approach to the semi-classical relativistic two-body problem for charged fermions

    International Nuclear Information System (INIS)

    Leiter, D.

    1978-01-01

    Generalizing from a recently developed hybrid formulation of classical electrodynamics with ''direct (charge-field) action'' structure an analogous semi-classical Dirac formulation of the theory is constructed, which is capable of describing the semi-classical quantum mechanics of two identical spin-1/2 particles. This semi-classical formulation is to be used as a heuristic aid in searching for the theoretical structure of a fully ''second quantized'' theory. The Pauli exclusion principle is incorporated by making the interaction fields (in the action principle) antisymmetric with respect to ''charge-field'' labeling. In this manner, ''position correlation'' effects associated with ''configuration interaction'' can also be accounted for. By studying the nature of the stationary-state solutions, the formalism is compared with the conventional quantum-mechanical one (to understand the similarities and the differences between this approach and the usual correlated Hartree-Fock approximation of ordinary relativistic quantum theory). The stationary-state solutions to the semi-classical formalism are shown to closely approximate the usual quantum-mechanical solutions when the wave functions are represented as a superposition of Slater determinants of Dirac-Coulombic-type wave functions with radial parts having a form which extremizes the total Breit energy. The manner in which this semi-classical theory might be extended to a fully ''second quantized'' formalism is sketched. (author)

  19. shape change in Hf, W and Os-isotopes: A non-relativistic Hartree ...

    Indian Academy of Sciences (India)

    tories, it is now possible to study the structural properties of light nuclei near the ... Application of angular momentum projection (AMp) project the good angular ..... function of the quadrupole deformation parameter. ¬. 2 . W e find tw o distinct.

  20. QCD-based relativistic Hartree-Fock calculations for identical quarks

    International Nuclear Information System (INIS)

    Dey, J.; Dey, M.; Le Tourneux, J.

    1985-12-01

    As was first pointed out by Witten, large number of colours (Nsub(c)) leads to a simplification in the theory of baryon masses in that the quarks may be assumed to move in a mean field which can be found self-consistently. The interquark potential in such a description can be borrowed from the meson sector phenomenology in the absence of an accurate evaluation of it from large Nsub(c) quantum chromodynamics (QCD). We have carried out this program with such a potential due to Richardson, used often by workers in the meson sector. This potential has the advantage of incorporating the two main features of QCD, namely confinement and asymptotic freedom. In view of the small number of parameters involved, the results agree surprisingly well with experiment for the case of three identical quarks. (author)

  1. Relativistic Outflows from ADAFs

    Science.gov (United States)

    Becker, Peter; Subramanian, Prasad; Kazanas, Demosthenes

    2001-04-01

    Advection-dominated accretion flows (ADAFs) have a positive Bernoulli parameter, and are therefore gravitationally bound. The Newtonian ADAF model has been generalized recently to obtain the ADIOS model that includes outflows of energy and angular momentum, thereby allowing accretion to proceed self-consistently. However, the utilization of a Newtonian gravitational potential limits the ability of this model to describe the inner region of the disk, where any relativistic outflows are likely to originate. In this paper we modify the ADIOS scenario to incorporate a seudo - Newtonian potential, which approximates the effects of general relativity. The analysis yields a unique, self - similar solution for the structure of the coupled disk/wind system. Interesting features of the new solution include the relativistic character of the outflow in the vicinity of the radius of marginal stability, which represents the inner edge of the quasi-Keplerian disk in our model. Our self - similar model may therefore help to explain the origin of relativistic jets in active galaxies. At large distances the radial dependence of the accretion rate approachs the unique form dot M ∝ r^1/2, with an associated density variation given by ρ ∝ r-1. This density variation agrees with that implied by the dependence of the X-ray hard time lags on the Fourier frequency for a number of accreting galactic black hole candidates. While intriguing, the results of our self-similar model need to be confirmed in the future by incorporating a detailed physical description of the energization mechanism that drives the outflow, which is likely to be powered by the shear of the underlying accretion disk.

  2. 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.

  3. From the Hartree dynamics to the Vlasov equation

    DEFF Research Database (Denmark)

    Benedikter, Niels Patriz; Porta, Marcello; Saffirio, Chiara

    2016-01-01

    We consider the evolution of quasi-free states describing N fermions in the mean field limit, as governed by the nonlinear Hartree equation. In the limit of large N, we study the convergence towards the classical Vlasov equation. For a class of regular interaction potentials, we establish precise...

  4. Analytical relativistic self-consistent-field calculations for atoms

    International Nuclear Information System (INIS)

    Barthelat, J.C.; Pelissier, M.; Durand, P.

    1980-01-01

    A new second-order representation of the Dirac equation is presented. This representation which is exact for a hydrogen atom is applied to approximate analytical self-consistent-field calculations for atoms. Results are given for the rare-gas atoms from helium to radon and for lead. The results compare favorably with numerical Dirac-Hartree-Fock solutions

  5. Modified Fourth-Order Kinetic Energy Gradient Expansion with Hartree Potential-Dependent Coefficients.

    Science.gov (United States)

    Constantin, Lucian A; Fabiano, Eduardo; Della Sala, Fabio

    2017-09-12

    Using the semiclassical neutral atom theory, we developed a modified fourth-order kinetic energy (KE) gradient expansion (GE4m) that keeps unchanged all the linear-response terms of the uniform electron gas and gives a significant improvement with respect to the known semilocal functionals for both large atoms and jellium surfaces. On the other hand, GE4m is not accurate for light atoms; thus, we modified the GE4m coefficients making them dependent on a novel ingredient, the reduced Hartree potential, recently introduced in the Journal of Chemical Physics 2016, 145, 084110, in the context of exchange functionals. The resulting KE gradient expansion functional, named uGE4m, belongs to the novel class of u-meta-generalized-gradient-approximations (uMGGA) whose members depend on the conventional ingredients (i.e., the reduced gradient and Laplacian of the density) as well as on the reduced Hartree potential. To test uGE4m, we defined an appropriate benchmark (including total KE and KE differences for atoms, molecules and jellium clusters) for gradient expansion functionals, that is, including only those systems which are mainly described by a slowly varying density regime. While most of the GGA and meta-GGA KE functionals (we tested 18 of them) are accurate for some properties and inaccurate for others, uGE4m shows a consistently good performance for all the properties considered. This represents a qualitative boost in the KE functional development and highlights the importance of the reduced Hartree potential for the construction of next-generation KE functionals.

  6. Penetration of relativistic heavy ions through matter

    International Nuclear Information System (INIS)

    Scheidenberger, C.; Geissel, H.

    1997-07-01

    New heavy-ion accelerators covering the relativistic and ultra-relativistic energy regime allow to study atomic collisions with bare and few-electron projectiles. High-resolution magnetic spectrometers are used for precise stopping-power and energy-loss straggling measurements. Refined theories beyond the Born approximation have been developed and are confirmed by experiments. This paper summarizes the large progress in the understanding of relativistic heavy-ion penetration through matter, which has been achieved in the last few years. (orig.)

  7. The ionisation equation in a relativistic gas

    International Nuclear Information System (INIS)

    Kichenassamy, S.; Krikorian, R.A.

    1983-01-01

    By deriving the relativistic form of the ionisation equation for a perfect gas it is shown that the usual Saha equation is valid to 3% for temperatures below one hundred million Kelvin. Beyond 10 9 K, the regular Saha equation is seriously incorrect and a relativistic distribution function for electrons must be taken into account. Approximate forms are derived when only the electrons are relativistic (appropriate up to 10 12 K) and also for the ultrarelativistic case (temperatures greater than 10 15 K). (author)

  8. Dechanneling function for relativistic axially channeled electrons

    International Nuclear Information System (INIS)

    Muralev, V.A.; Telegin, V.I.

    1981-01-01

    Behaviour of the x(t) dechanneling function depending on the depth is theoretically studied. Theoretical consideration of x(t) for axial channeled relativistic electrons in anisotropic medium results in two-dimensional kinetic equation with mixed derivatives of the parabolic type. The kinetic equation in the approximation of the continuous Lindchard model for relativistic axial channeled electrons is numerically solved. The depth dependence of the x(t) dechanneling function is obtained [ru

  9. 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.

  10. 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.

  11. 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.

  12. The relativistic virial theorem

    International Nuclear Information System (INIS)

    Lucha, W.; Schoeberl, F.F.

    1989-11-01

    The relativistic generalization of the quantum-mechanical virial theorem is derived and used to clarify the connection between the nonrelativistic and (semi-)relativistic treatment of bound states. 12 refs. (Authors)

  13. Relativistic plasma dispersion functions

    International Nuclear Information System (INIS)

    Robinson, P.A.

    1986-01-01

    The known properties of plasma dispersion functions (PDF's) for waves in weakly relativistic, magnetized, thermal plasmas are reviewed and a large number of new results are presented. The PDF's required for the description of waves with small wave number perpendicular to the magnetic field (Dnestrovskii and Shkarofsky functions) are considered in detail; these functions also arise in certain quantum electrodynamical calculations involving strongly magnetized plasmas. Series, asymptotic series, recursion relations, integral forms, derivatives, differential equations, and approximations for these functions are discussed as are their analytic properties and connections with standard transcendental functions. In addition a more general class of PDF's relevant to waves of arbitrary perpendicular wave number is introduced and a range of properties of these functions are derived

  14. Relativistic quantum similarities in atoms in position and momentum spaces

    International Nuclear Information System (INIS)

    Maldonado, P.; Sarsa, A.; Buendia, E.; Galvez, F.J.

    2011-01-01

    A study of different quantum similarity measures and their corresponding quantum similarity indices is carried out for the atoms from H to Lr (Z=1-103). Relativistic effects in both position and momentum spaces have been studied by comparing the relativistic values to the non-relativistic ones. We have used the atomic electron density in both position and momentum spaces obtained within relativistic and non-relativistic numerical-parameterized optimized effective potential approximations. -- Highlights: → Quantum similarity measures and indices in electronic structure of atoms. → Position and momentum electronic densities. → Similarity of relativistic and non-relativistic densities. → Similarity of core and valence regions of different atoms. → Dependence with Z along the Periodic Table.

  15. 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

  16. 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

  17. Elastic and inelastic form factors of the Ne20 in the Hartree-Fock approximation

    International Nuclear Information System (INIS)

    Oliveira, S.A.C. de.

    1977-01-01

    Properties of Ne 20 fundamental band are studied such as particle densities and elastic and inelastic form factors. A two body interaction is used and its matrix elements involve only the independent particle states of the 1s-0d shell [pt

  18. Spontaneous spin-polarization and phase transition in the relativistic approach

    International Nuclear Information System (INIS)

    Maruyama, Tomoyuki; Tatsumi, Toshitaka

    2001-01-01

    We study the spin-polarization mechanism in the highly dense nuclear matter with the relativistic mean-field approach. In the relativistic Hartree-Fock framework we find that there are two kinds of spin-spin interaction channels, which are the axial-vector and tensor exchange ones. If each interaction is strong and different sign, the system loses the spherical symmetry and holds the spin-polarization in the high-density region. When the axial-vector interaction is negative enough, the system holds ferromagnetism. (author)

  19. Relativistic QRPA Calculation of β-Decay Rates of r-process Nuclei

    International Nuclear Information System (INIS)

    Marketin, T.; Paar, N.; Niksic, T.; Vretenar, D.; Ring, P.

    2009-01-01

    A systematic, fully self-consistent calculation of β-decay rates is presented, based on a microscopic theoretical framework. Analysis is performed on a large number of nuclei from the valley of β stability towards the neutron drip-line. Nuclear ground state is determined using the Relativistic Hartree-Bogoliubov (RHB) model with density-dependent meson-nucleon coupling constants. Transition rates are calculated within the proton-neutron relativistic quasiparticle RPA (pn-RQRPA) using the same interaction that was used in the RHB equations.

  20. The relativistic mean-field description of nuclei and nuclear dynamics

    International Nuclear Information System (INIS)

    Reinhard, P.G.

    1989-01-01

    The relativistic mean-field model of the nucleus is reviewed. It describes the nucleus as a system of Dirac-Nucleons which interact in a relativistic covariant manner via meson fields. The meson fields are treated as mean fields, i.e. as non quantal c-number fields. The effects of the Dirac sea of the nucleons is neglected. The model is interpreted as a phenomenological ansatz providing a selfconsistent relativistic description of nuclei and nuclear dynamics. It is viewed, so to say, as the relativistic generalisation of the Skyrme-Hartree-Fock ansatz. The capability and the limitations of the model to describe nuclear properties are discussed. Recent applications to spherical and deformed nuclei and to nuclear dynamics are presented. (orig.)

  1. Theoretical study of relativistic effects in the electronic structure and chemical bonding of UF6

    International Nuclear Information System (INIS)

    Onoe, Jun; Takeuchi, Kazuo; Sekine, Rika; Nakamatsu, Hirohide; Mukoyama, Takeshi; Adachi, Hirohiko.

    1992-01-01

    We have performed the relativistic molecular orbital calculation for the ground state of UF 6 , using the discrete-variational Dirac-Slater method (DV-DS), in order to elucidate the relativistic effects in the electronic structure and chemical bonding. Compared with the electronic structure calculated by the non-relativistic Hartree-Fock-Slater (DV-X α )MO method, not only the direct relativistic effects (spin-orbit splitting etc), but also the indirect effect due to the change in screening core potential charge are shown to be important in the MO level structure. From the U-F bond overlap population analysis, we found that the U-F bond formation can be explained only by the DV-DS, not by the DV-X α . The calculated electronic structure in valence energy region (-20-OeV) and excitation energies in UV region are in agreement with experiments. (author)

  2. Relativistic effects on magnetic circular dichroism studied by GUHF/SECI method

    Science.gov (United States)

    Honda, Y.; Hada, M.; Ehara, M.; Nakatsuji, H.; Downing, J.; Michl, J.

    2002-04-01

    Quasi-relativistic formulation of the Magnetic circular dichroism (MCD) Faraday terms are presented using the generalized unrestricted Hartree-Fock (GUHF)/single excitation configuration interaction (SECI) method combined with the finite perturbation method and applied to the MCD of the three n-σ ∗ states ( 3Q1, 3Q0, 1Q1) of CH 3I. The Faraday B term for the 1Q1 state was 0.1976( Debye) 2( Bohr magneton )/(10 3 cm-1) in the non-relativistic theory, but was dramatically improved by the relativistic effect and became 0.0184 in agreement with the experimental values, 0.014 and 0.0257. This change was mainly due to the one-electron spin-orbit (SO1) term rather than the spin-free relativistic (SFR) and the two-electron spin-orbit (SO2) terms.

  3. Relativistic many-body theory of atomic transitions. The relativistic equation-of-motion approach

    International Nuclear Information System (INIS)

    Huang, K.

    1982-01-01

    An equation-of-motion approach is used to develop the relativistic many-body theory of atomic transitions. The relativistic equations of motion for transition matrices are formulated with the use of techniques of quantum-field theory. To reduce the equations of motion to a tractable form which is appropriate for numerical calculations, a graphical method to resolve the complication arising from the antisymmetrization and angular-momentum coupling is employed. The relativistic equation-of-motion method allows an ab initio treatment of correlation and relativistic effects in both closed- and open-shell many-body systems. A special case of the present formulation reduces to the relativistic random-phase approximation

  4. 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

  5. Hydrogen: Beyond the Classic Approximation

    International Nuclear Information System (INIS)

    Scivetti, Ivan

    2003-01-01

    The classical nucleus approximation is the most frequently used approach for the resolution of problems in condensed matter physics.However, there are systems in nature where it is necessary to introduce the nuclear degrees of freedom to obtain a correct description of the properties.Examples of this, are the systems with containing hydrogen.In this work, we have studied the resolution of the quantum nuclear problem for the particular case of the water molecule.The Hartree approximation has been used, i.e. we have considered that the nuclei are distinguishable particles.In addition, we have proposed a model to solve the tunneling process, which involves the resolution of the nuclear problem for configurations of the system away from its equilibrium position

  6. 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

  7. 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)

  8. 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

  9. Relativistic coupled-cluster-theory analysis of energies, hyperfine-structure constants, and dipole polarizabilities of Cd+

    Science.gov (United States)

    Li, Cheng-Bin; Yu, Yan-Mei; Sahoo, B. K.

    2018-02-01

    Roles of electron correlation effects in the determination of attachment energies, magnetic-dipole hyperfine-structure constants, and electric-dipole (E 1 ) matrix elements of the low-lying states in the singly charged cadmium ion (Cd+) have been analyzed. We employ the singles and doubles approximated relativistic coupled-cluster (RCC) method to calculate these properties. Intermediate results from the Dirac-Hartree-Fock approximation,the second-order many-body perturbation theory, and considering only the linear terms of the RCC method are given to demonstrate propagation of electron correlation effects in this ion. Contributions from important RCC terms are also given to highlight the importance of various correlation effects in the evaluation of these properties. At the end, we also determine E 1 polarizabilities (αE 1) of the ground and 5 p 2P1 /2 ;3 /2 states of Cd+ in the ab initio approach. We estimate them again by replacing some of the E 1 matrix elements and energies from the measurements to reduce their uncertainties so that they can be used in the high-precision experiments of this ion.

  10. 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.

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. Perturbation expansions generated by an approximate propagator

    International Nuclear Information System (INIS)

    Znojil, M.

    1987-01-01

    Starting from a knowledge of an approximate propagator R at some trial energy guess E 0 , a new perturbative prescription for p-plet of bound states and of their energies is proposed. It generalizes the Rayleigh-Schroedinger (RS) degenerate perturbation theory to the nondiagonal operators R (eliminates a RS need of their diagnolisation) and defines an approximate Hamiltonian T by mere inversion. The deviation V of T from the exact Hamiltonian H is assumed small only after a substraction of a further auxiliary Hartree-Fock-like separable ''selfconsistent'' potential U of rank p. The convergence is illustrated numerically on the anharmonic oscillator example

  17. 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

  18. Relativistic Linear Restoring Force

    Science.gov (United States)

    Clark, D.; Franklin, J.; Mann, N.

    2012-01-01

    We consider two different forms for a relativistic version of a linear restoring force. The pair comes from taking Hooke's law to be the force appearing on the right-hand side of the relativistic expressions: d"p"/d"t" or d"p"/d["tau"]. Either formulation recovers Hooke's law in the non-relativistic limit. In addition to these two forces, we…

  19. Relativistic quantum logic

    International Nuclear Information System (INIS)

    Mittelstaedt, P.

    1983-01-01

    on the basis of the well-known quantum logic and quantum probability a formal language of relativistic quantum physics is developed. This language incorporates quantum logical as well as relativistic restrictions. It is shown that relativity imposes serious restrictions on the validity regions of propositions in space-time. By an additional postulate this relativistic quantum logic can be made consistent. The results of this paper are derived exclusively within the formal quantum language; they are, however, in accordance with well-known facts of relativistic quantum physics in Hilbert space. (author)

  20. Hartree--Slater calculation of the cross section for L-shell ionization of argon by simple heavy charged particles

    International Nuclear Information System (INIS)

    Choi, B.

    1975-01-01

    The cross sections for L-shell and subshell ionization by direct Coulomb excitation of argon by incident heavy charged particles are evaluated. Incident particles are described in the plane-wave Born approximation, and nonrelativistic Hartree-Slater (HS) wave functions are used for the atomic electrons. Form factors, energy distributions, and ionization cross sections are compared with those obtained from screened hydrogenic wave functions. At most incident energies, the HS results for the total ionization cross section are only slightly smaller than those obtained with screened hydrogenic wave functions, but considerable discrepancies are found for form factors and energy distributions near the ionization threshold

  1. A Comprehensive Comparison of Relativistic Particle Integrators

    Science.gov (United States)

    Ripperda, B.; Bacchini, F.; Teunissen, J.; Xia, C.; Porth, O.; Sironi, L.; Lapenta, G.; Keppens, R.

    2018-03-01

    We compare relativistic particle integrators commonly used in plasma physics, showing several test cases relevant for astrophysics. Three explicit particle pushers are considered, namely, the Boris, Vay, and Higuera–Cary schemes. We also present a new relativistic fully implicit particle integrator that is energy conserving. Furthermore, a method based on the relativistic guiding center approximation is included. The algorithms are described such that they can be readily implemented in magnetohydrodynamics codes or Particle-in-Cell codes. Our comparison focuses on the strengths and key features of the particle integrators. We test the conservation of invariants of motion and the accuracy of particle drift dynamics in highly relativistic, mildly relativistic, and non-relativistic settings. The methods are compared in idealized test cases, i.e., without considering feedback onto the electrodynamic fields, collisions, pair creation, or radiation. The test cases include uniform electric and magnetic fields, {\\boldsymbol{E}}× {\\boldsymbol{B}} fields, force-free fields, and setups relevant for high-energy astrophysics, e.g., a magnetic mirror, a magnetic dipole, and a magnetic null. These tests have direct relevance for particle acceleration in shocks and in magnetic reconnection.

  2. 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.

  3. 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.)

  4. 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.)

  5. 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

  6. Kinetic analysis of thermally relativistic flow with dissipation

    International Nuclear Information System (INIS)

    Yano, Ryosuke; Suzuki, Kojiro

    2011-01-01

    Nonequilibrium flow of thermally relativistic matter with dissipation is considered in the framework of the relativistic kinetic theory. As an object of the analysis, the supersonic rarefied flow of thermally relativistic matter around the triangle prism is analyzed using the Anderson-Witting model. Obtained numerical results indicate that the flow field changes in accordance with the flow velocity and temperature of the uniform flow owing to both effects derived from the Lorentz contraction and thermally relativistic effects, even when the Mach number of the uniform flow is fixed. The profiles of the heat flux along the stagnation streamline can be approximated on the basis of the relativistic Navier-Stokes-Fourier (NSF) law except for a strong nonequilibrium regime such as the middle of the shock wave and the vicinity of the wall, whereas the profile of the heat flux behind the triangle prism cannot be approximated on the basis of the relativistic NSF law owing to rarefied effects via the expansion behind the triangle prism. Additionally, the heat flux via the gradient of the static pressure is non-negligible owing to thermally relativistic effects. The profile of the dynamic pressure is different from that approximated on the basis of the NSF law, which is obtained by the Eckart decomposition. Finally, variations of convections of the mass and momentum owing to the effects derived from the Lorentz contraction and thermally relativistic effects are numerically confirmed.

  7. Relativistic beaming and quasar statistics

    International Nuclear Information System (INIS)

    Orr, M.J.L.; Browne, I.W.A.

    1982-01-01

    The statistical predictions of a unified scheme for the radio emission from quasars are explored. This scheme attributes the observed differences between flat- and steep-spectrum quasars to projection and the effects of relativistic beaming of the emission from the nuclear components. We use a simple quasar model consisting of a compact relativistically beamed core with spectral index zero and unbeamed lobes, spectral index - 1, to predict the proportion of flat-spectrum sources in flux-limited samples selected at different frequencies. In our model this fraction depends on the core Lorentz factor, γ and we find that a value of approximately 5 gives satisfactory agreement with observation. In a similar way the model is used to construct the expected number/flux density counts for flat-spectrum quasars from the observed steep-spectrum counts. Again, good agreement with the observations is obtained if the average core Lorentz factor is about 5. Independent estimates of γ from observations of superluminal motion in quasars are of the same order of magnitude. We conclude that the statistical properties of quasars are entirely consistent with the predictions of simple relativistic-beam models. (author)

  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. 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.)

  10. Radiative transitions in mesons within a non relativistic quark model

    International Nuclear Information System (INIS)

    Bonnaz, R.; Silvestre-Brac, B.; Gignoux, C.

    2002-01-01

    An exhaustive study of radiative transitions in mesons is performed in a non relativistic quark model. Three different types of mesons wave functions are tested. The effect of some usual approximations is commented. Overall agreement with experimental data is obtained

  11. Relativistic quantum mechanics; Mecanique quantique relativiste

    Energy Technology Data Exchange (ETDEWEB)

    Ollitrault, J.Y. [CEA Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique]|[Universite Pierre et Marie Curie, 75 - Paris (France)

    1998-12-01

    These notes form an introduction to relativistic quantum mechanics. The mathematical formalism has been reduced to the minimum in order to enable the reader to calculate elementary physical processes. The second quantification and the field theory are the logical followings of this course. The reader is expected to know analytical mechanics (Lagrangian and Hamiltonian), non-relativistic quantum mechanics and some basis of restricted relativity. The purpose of the first 3 chapters is to define the quantum mechanics framework for already known notions about rotation transformations, wave propagation and restricted theory of relativity. The next 3 chapters are devoted to the application of relativistic quantum mechanics to a particle with 0,1/5 and 1 spin value. The last chapter deals with the processes involving several particles, these processes require field theory framework to be thoroughly described. (A.C.) 2 refs.

  12. Towards relativistic quantum geometry

    Energy Technology Data Exchange (ETDEWEB)

    Ridao, Luis Santiago [Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina); Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina)

    2015-12-17

    We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.

  13. Relativistic Coulomb Fission

    Science.gov (United States)

    Norbury, John W.

    1992-01-01

    Nuclear fission reactions induced by the electromagnetic field of relativistic nuclei are studied for energies relevant to present and future relativistic heavy ion accelerators. Cross sections are calculated for U-238 and Pu-239 fission induced by C-12, Si-28, Au-197, and U-238 projectiles. It is found that some of the cross sections can exceed 10 b.

  14. Relativistic Shock Acceleration

    International Nuclear Information System (INIS)

    Duffy, P.; Downes, T.P.; Gallant, Y.A.; Kirk, J.G.

    1999-01-01

    In this paper we briefly review the basic theory of shock waves in relativistic hydrodynamics and magneto-hydrodynamics, emphasising some astrophysically interesting cases. We then present an overview of the theory of particle acceleration at such shocks describing the methods used to calculate the spectral indices of energetic particles. Recent results on acceleration at ultra-relativistic shocks are discussed. (author)

  15. 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

  16. 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)

  17. Quantum dynamics through conical intersections in macrosystems: Combining effective modes and time-dependent Hartree

    International Nuclear Information System (INIS)

    Basler, Mathias; Gindensperger, Etienne; Meyer, Hans-Dieter; Cederbaum, Lorenz S.

    2008-01-01

    We address the nonadiabatic quantum dynamics of (macro)systems involving a vast number of nuclear degrees of freedom (modes) in the presence of conical intersections. The macrosystem is first decomposed into a system part carrying a few, strongly coupled modes, and an environment, comprising the remaining modes. By successively transforming the modes of the environment, a hierarchy of effective Hamiltonians for the environment can be constructed. Each effective Hamiltonian depends on a reduced number of effective modes, which carry cumulative effects. The environment is described by a few effective modes augmented by a residual environment. In practice, the effective modes can be added to the system's modes and the quantum dynamics of the entire macrosystem can be accurately calculated on a limited time-interval. For longer times, however, the residual environment plays a role. We investigate the possibility to treat fully quantum mechanically the system plus a few effective environmental modes, augmented by the dynamics of the residual environment treated by the time-dependent Hartree (TDH) approximation. While the TDH approximation is known to fail to correctly reproduce the dynamics in the presence of conical intersections, it is shown that its use on top of the effective-mode formalism leads to much better results. Two numerical examples are presented and discussed; one of them is known to be a critical case for the TDH approximation

  18. Is the relativistic approach really useful to nuclear reactions?

    CERN Document Server

    Miyazaki, K

    2003-01-01

    We have reconsidered the non-relativistic distorted-wave t-matrix approximation (NR-DWTA) for proton knockout (p,2p) reaction using modern high-quality phenomenological optical potentials and NN t-matrix. We have calculated 40Ca(p,2p) reactions at T_LAB=200MeV and compared the results with the relativistic distorted-wave impulse approximation (RDWIA) calculations. It is found that the NR-DWTA is superior to the RDWIA in consistent description of the cross section and the analyzing power. An immediate relativistic extension of the DWIA to the nuclear reaction has a problem.

  19. Using MUSIC to study relativistic nuclear collisions

    International Nuclear Information System (INIS)

    1983-01-01

    A large Multiple Sampling Ionization Chamber (MUSIC) has been developed as a part of the Heavy Ion Spectrometer System (HISS). This facility is being used for the study of relativistic nuclear collisions at the Bevalac of Lawrence Berkeley Laboratory. Preliminary data from MUSIC indicate that a charge resolution of one unit should be achieved from Z approximately equal to 7 to Z approximately equal to 100. (author)

  20. 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

  1. Relativistic deuteron wave function on light front

    International Nuclear Information System (INIS)

    Karmanov, V.A.

    1980-01-01

    In the framework of the one boson exchange model the approximate analytical expression for the deuteron wave function (WF) at relativistic relative momenta is obtained. WF depends on extra variable having the form of a unit vector and is determined by six functions instead of two ones (S-and D-waves) in the nonrelativistic case. At moderate momenta the WF is matched with WF in the Reid model. It is emphasized the importance of indication of the qualitative observed phenomena associated with change of parametrization and spin structure of relativistic deuteron WF

  2. Theoretical study of the relativistic molecular rotational g-tensor

    Energy Technology Data Exchange (ETDEWEB)

    Aucar, I. Agustín, E-mail: agustin.aucar@conicet.gov.ar; Gomez, Sergio S., E-mail: ssgomez@exa.unne.edu.ar [Institute for Modeling and Technological Innovation, IMIT (CONICET-UNNE) and Faculty of Exact and Natural Sciences, Northeastern University of Argentina, Avenida Libertad 5400, W3404AAS Corrientes (Argentina); Giribet, Claudia G.; Ruiz de Azúa, Martín C. [Physics Department, Faculty of Exact and Natural Sciences, University of Buenos Aires and IFIBA CONICET, Ciudad Universitaria, Pab. I, 1428 Buenos Aires (Argentina)

    2014-11-21

    An original formulation of the relativistic molecular rotational g-tensor valid for heavy atom containing compounds is presented. In such formulation, the relevant terms of a molecular Hamiltonian for non-relativistic nuclei and relativistic electrons in the laboratory system are considered. Terms linear and bilinear in the nuclear rotation angular momentum and an external uniform magnetic field are considered within first and second order (relativistic) perturbation theory to obtain the rotational g-tensor. Relativistic effects are further analyzed by carrying out the linear response within the elimination of the small component expansion. Quantitative results for model systems HX (X=F, Cl, Br, I), XF (X=Cl, Br, I), and YH{sup +} (Y=Ne, Ar, Kr, Xe, Rn) are obtained both at the RPA and density functional theory levels of approximation. Relativistic effects are shown to be small for this molecular property. The relation between the rotational g-tensor and susceptibility tensor which is valid in the non-relativistic theory does not hold within the relativistic framework, and differences between both molecular parameters are analyzed for the model systems under study. It is found that the non-relativistic relation remains valid within 2% even for the heavy HI, IF, and XeH{sup +} systems. Only for the sixth-row Rn atom a significant deviation of this relation is found.

  3. Theoretical study of the relativistic molecular rotational g-tensor

    International Nuclear Information System (INIS)

    Aucar, I. Agustín; Gomez, Sergio S.; Giribet, Claudia G.; Ruiz de Azúa, Martín C.

    2014-01-01

    An original formulation of the relativistic molecular rotational g-tensor valid for heavy atom containing compounds is presented. In such formulation, the relevant terms of a molecular Hamiltonian for non-relativistic nuclei and relativistic electrons in the laboratory system are considered. Terms linear and bilinear in the nuclear rotation angular momentum and an external uniform magnetic field are considered within first and second order (relativistic) perturbation theory to obtain the rotational g-tensor. Relativistic effects are further analyzed by carrying out the linear response within the elimination of the small component expansion. Quantitative results for model systems HX (X=F, Cl, Br, I), XF (X=Cl, Br, I), and YH + (Y=Ne, Ar, Kr, Xe, Rn) are obtained both at the RPA and density functional theory levels of approximation. Relativistic effects are shown to be small for this molecular property. The relation between the rotational g-tensor and susceptibility tensor which is valid in the non-relativistic theory does not hold within the relativistic framework, and differences between both molecular parameters are analyzed for the model systems under study. It is found that the non-relativistic relation remains valid within 2% even for the heavy HI, IF, and XeH + systems. Only for the sixth-row Rn atom a significant deviation of this relation is found

  4. Relativistic Kinetic Theory

    Science.gov (United States)

    Vereshchagin, Gregory V.; Aksenov, Alexey G.

    2017-02-01

    Preface; Acknowledgements; Acronyms and definitions; Introduction; Part I. Theoretical Foundations: 1. Basic concepts; 2. Kinetic equation; 3. Averaging; 4. Conservation laws and equilibrium; 5. Relativistic BBGKY hierarchy; 6. Basic parameters in gases and plasmas; Part II. Numerical Methods: 7. The basics of computational physics; 8. Direct integration of Boltzmann equations; 9. Multidimensional hydrodynamics; Part III. Applications: 10. Wave dispersion in relativistic plasma; 11. Thermalization in relativistic plasma; 12. Kinetics of particles in strong fields; 13. Compton scattering in astrophysics and cosmology; 14. Self-gravitating systems; 15. Neutrinos, gravitational collapse and supernovae; Appendices; Bibliography; Index.

  5. Static correlation beyond the random phase approximation

    DEFF Research Database (Denmark)

    Olsen, Thomas; Thygesen, Kristian Sommer

    2014-01-01

    derived from Hedin's equations (Random Phase Approximation (RPA), Time-dependent Hartree-Fock (TDHF), Bethe-Salpeter equation (BSE), and Time-Dependent GW) all reproduce the correct dissociation limit. We also show that the BSE improves the correlation energies obtained within RPA and TDHF significantly...... and confirms that BSE greatly improves the RPA and TDHF results despite the fact that the BSE excitation spectrum breaks down in the dissociation limit. In contrast, second order screened exchange gives a poor description of the dissociation limit, which can be attributed to the fact that it cannot be derived...

  6. 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

  7. 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.)

  8. 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

  9. 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.

  10. Plasma relativistic microwave electronics

    International Nuclear Information System (INIS)

    Kuzelev, M.V.; Loza, O.T.; Rukhadze, A.A.; Strelkov, P.S.; Shkvarunets, A.G.

    2001-01-01

    One formulated the principles of plasma relativistic microwave electronics based on the induced Cherenkov radiation of electromagnetic waves at interaction of a relativistic electron beam with plasma. One developed the theory of plasma relativistic generators and accelerators of microwave radiation, designed and studied the prototypes of such devices. One studied theoretically the mechanisms of radiation, calculated the efficiencies and the frequency spectra of plasma relativistic microwave generators and accelerators. The theory findings are proved by the experiment: intensity of the designed sources of microwave radiation is equal to 500 μW, the frequency of microwave radiation is increased by 7 times (from 4 up to 28 GHz), the width of radiation frequency band may vary from several up to 100%. The designed sources of microwave radiation are no else compared in the electronics [ru

  11. 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)

  12. 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.

  13. 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

  14. The relativistic rocket

    Energy Technology Data Exchange (ETDEWEB)

    Antippa, Adel F [Departement de Physique, Universite du Quebec a Trois-Rivieres, Trois-Rivieres, Quebec G9A 5H7 (Canada)

    2009-05-15

    We solve the problem of the relativistic rocket by making use of the relation between Lorentzian and Galilean velocities, as well as the laws of superposition of successive collinear Lorentz boosts in the limit of infinitesimal boosts. The solution is conceptually simple, and technically straightforward, and provides an example of a powerful method that can be applied to a wide range of special relativistic problems of linear acceleration.

  15. Exact Relativistic `Antigravity' Propulsion

    Science.gov (United States)

    Felber, Franklin S.

    2006-01-01

    The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.

  16. Relativistic Quantum Revivals

    International Nuclear Information System (INIS)

    Strange, P.

    2010-01-01

    Quantum revivals are now a well-known phenomena within nonrelativistic quantum theory. In this Letter we display the effects of relativity on revivals and quantum carpets. It is generally believed that revivals do not occur within a relativistic regime. Here we show that while this is generally true, it is possible, in principle, to set up wave packets with specific mathematical properties that do exhibit exact revivals within a fully relativistic theory.

  17. Relativistic interpretation of the nature of the nuclear tensor force

    Science.gov (United States)

    Zong, Yao-Yao; Sun, Bao-Yuan

    2018-02-01

    The spin-dependent nature of the nuclear tensor force is studied in detail within the relativistic Hartree-Fock approach. The relativistic formalism for the tensor force is supplemented with an additional Lorentz-invariant tensor formalism in the σ-scalar channel, so as to take into account almost fully the nature of the tensor force brought about by the Fock diagrams in realistic nuclei. Specifically, the tensor sum rules are tested for the spin and pseudo-spin partners with and without nodes, to further understand the nature of the tensor force within the relativistic model. It is shown that the interference between the two components of nucleon spinors causes distinct violations of the tensor sum rules in realistic nuclei, mainly due to the opposite signs on the κ quantities of the upper and lower components, as well as the nodal difference. However, the sum rules can be precisely reproduced if the same radial wave functions are taken for the spin/pseudo-spin partners in addition to neglecting the lower/upper components, revealing clearly the nature of the tensor force. Supported by National Natural Science Foundation of China (11375076, 11675065) and the Fundamental Research Funds for the Central Universities (lzujbky-2016-30)

  18. Relativistic viscoelastic fluid mechanics

    International Nuclear Information System (INIS)

    Fukuma, Masafumi; Sakatani, Yuho

    2011-01-01

    A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.

  19. Relativistic viscoelastic fluid mechanics.

    Science.gov (United States)

    Fukuma, Masafumi; Sakatani, Yuho

    2011-08-01

    A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.

  20. Dissipative relativistic hydrodynamics

    International Nuclear Information System (INIS)

    Imshennik, V.S.; Morozov, Yu.I.

    1989-01-01

    Using the comoving reference frame in the general non-inertial case, the relativistic hydrodynamics equations are derived with an account for dissipative effects in the matter. From the entropy production equation, the exact from for the dissipative tensor components is obtained. As a result, the closed system of equations of dissipative relativistic hydrodynamics is obtained in the comoving reference frame as a relativistic generalization of the known Navier-Stokes equations for Lagrange coordinates. Equations of relativistic hydrodynamics with account for dissipative effects in the matter are derived using the assocoated reference system in general non-inertial case. True form of the dissipative tensor components is obtained from entropy production equation. Closed system of equations for dissipative relativistic hydrodynamics is obtained as a result in the assocoated reference system (ARS) - relativistic generalization of well-known Navier-Stokes equations for Lagrange coordinates. Equation system, obtained in this paper for ARS, may be effectively used in numerical models of explosive processes with 10 51 erg energy releases which are characteristic for flashes of supernovae, if white dwarf type compact target suggested as presupernova

  1. Relativistic BCS-BEC Crossover at Quark Level

    Directory of Open Access Journals (Sweden)

    Zhuang P.

    2010-10-01

    Full Text Available The non-relativistic G0G formalism of BCS-BEC crossover at finite temperature is extended to relativistic fermion systems. The theory recovers the BCS mean field approximation at zero temperature and the non-relativistic results in a proper limit. For massive fermions, when the coupling strength increases, there exist two crossovers from the weak coupling BCS superfluid to the non-relativistic BEC state and then to the relativistic BEC state. For color superconductivity at moderate baryon density, the matter is in the BCS-BEC crossover region, and the behavior of the pseudogap is quite similar to that found in high temperature superconductors.

  2. Relativistic simulation of the Vlasov equation for plasma expansion into vacuum

    Directory of Open Access Journals (Sweden)

    H Abbasi

    2012-12-01

    Full Text Available   In this study, relativistic Vlasov simulation of plasma for expansion of collisionless plasma for into vacuum is presented. The model is based on 1+1 dimensional phase space and electrostatic approximation. For this purpose, the electron dynamics is studied by the relativistic Vlasov equation. Regardless of the ions temperature, fluid equations are used for their dynamics. The initial electrons distribution function is the relativistic Maxwellian. The results show that due to the electrons relativistic temperature, the process of the plasma expansion takes place faster, the resulting electric field is stronger and the ions are accelerated to higher velocities, in comparison to the non-relativistic case.

  3. Approximate Likelihood

    CERN Multimedia

    CERN. Geneva

    2015-01-01

    Most physics results at the LHC end in a likelihood ratio test. This includes discovery and exclusion for searches as well as mass, cross-section, and coupling measurements. The use of Machine Learning (multivariate) algorithms in HEP is mainly restricted to searches, which can be reduced to classification between two fixed distributions: signal vs. background. I will show how we can extend the use of ML classifiers to distributions parameterized by physical quantities like masses and couplings as well as nuisance parameters associated to systematic uncertainties. This allows for one to approximate the likelihood ratio while still using a high dimensional feature vector for the data. Both the MEM and ABC approaches mentioned above aim to provide inference on model parameters (like cross-sections, masses, couplings, etc.). ABC is fundamentally tied Bayesian inference and focuses on the “likelihood free” setting where only a simulator is available and one cannot directly compute the likelihood for the dat...

  4. Diophantine approximation

    CERN Document Server

    Schmidt, Wolfgang M

    1980-01-01

    "In 1970, at the U. of Colorado, the author delivered a course of lectures on his famous generalization, then just established, relating to Roth's theorem on rational approxi- mations to algebraic numbers. The present volume is an ex- panded and up-dated version of the original mimeographed notes on the course. As an introduction to the author's own remarkable achievements relating to the Thue-Siegel-Roth theory, the text can hardly be bettered and the tract can already be regarded as a classic in its field."(Bull.LMS) "Schmidt's work on approximations by algebraic numbers belongs to the deepest and most satisfactory parts of number theory. These notes give the best accessible way to learn the subject. ... this book is highly recommended." (Mededelingen van het Wiskundig Genootschap)

  5. 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

  6. Internal structure of relativistic astrophysical objects in the wave approximation

    International Nuclear Information System (INIS)

    Bogdanov, I.V.; Demkov, Yu.N.

    1987-01-01

    Spherically symmetric inverse problems for the scattering of quantum particles by a static gravitational field are considered within the framework of general relativity theory. Methods are developed for determining the metric tensor on the basis of scattering data for a fixed energy or zero angular momentum for the Klein-Fock-Gordon equation in the Schwarzschild metric. The relation between the S-matrix and squared 4-momentum operator in curved space is investigated. The main elements of the algorithms developed are two definite nonlinear ordinary differential equations of the third and fourth order based on the scattering data. On the one hand, the inverse problems studied extend the classical inverse problems for the gravitational field, solved previously, to the quantum case. On the other hand, they extend the Marchenko and Regge-Newton methods familiar in quantum theory to the case of a gravitational field. An analogy is established between the motion of a scalar particle in a strong gravitational field and the motion in a field with a potential depending on the angular momentum or energy in nonrelativistic quantum mechanics

  7. Magnetic structure of a nanoparticle in mean-field approximation

    International Nuclear Information System (INIS)

    Usov, N.A.; Gudoshnikov, S.A.

    2005-01-01

    Quantum mechanical Hartree-Fock approximation is used to calculate a magnetic state of a nanoparticle. The cases of ferromagnetic (FM), antiferromagnetic (AFM) and composite particles having an FM core surrounded by an AFM shell are considered in a unified manner. It is shown that effective interaction at the boundary between FM and AFM areas rotates FM and AFM spins perpendicular to each other. The coercive force of a composite particle increases as a function of the AFM shell thickness

  8. Relativistic theory of spontaneous emission

    International Nuclear Information System (INIS)

    Barut, A.O.; Salamin, Y.I.

    1987-06-01

    We derive a formula for the relativistic decay rates in atoms in a formulation of Quantum Electrodynamics based upon the electron's self energy. Relativistic Coulomb wavefunctions are used, the full spin calculation is carried out and the dipole approximation is not employed. The formula has the correct nonrelativistic limit and is used here for calculating the decay rates in Hydrogen and Muonium for the transitions 2P → 1S 1/2 and 2S 1/2 → 1S 1/2 . The results for Hydrogen are: Γ(2P → 1S 1/2 )=6.2649x10 8 s -1 and Γ(2S 1/2 → 1S 1/2 )=2.4946x10 -6 s -1 . Our result for the 2P → 1S 1/2 transition rate is in perfect agreement with the best nonrelativistic calculations as well as with the results obtained from the best known radiative decay lifetime measurements. As for the Hydrogen 2S 1/2 → 1S 1/2 decay rate, the result obtained here is also in good agreement with the best known magnetic dipole calculations. For Muonium we get: Γ(2P → 1S 1/2 )=6.2382x10 8 s -1 and Γ(2S 1/2 → 1S 1/2 )=2.3997x10 -6 s -1 . (author). 23 refs, 4 tabs

  9. Relativistic treatment of fermion-antifermion bound states

    International Nuclear Information System (INIS)

    Lucha, W.; Rupprecht, H.; Schoeberl, F.F.

    1990-01-01

    We discuss the relativistic treatment of fermion-antifermion bound states by an effective-Hamiltonian method which imitates their description in terms of nonrelativistic potential models: the effective interaction potential, to be used in a Schroedinger equation which incorporates relativistic kinematics, is derived from the underlying quantum field theory. This approach is equivalent to the instantaneous approximation to the Bethe-Salpeter equation called Salpeter equation but comes closer to physical intuition than the latter one. (Author) 14 refs

  10. Relativistic and non-relativistic studies of nuclear matter

    NARCIS (Netherlands)

    Banerjee, MK; Tjon, JA

    2002-01-01

    We point out that the differences between the results of the non-relativistic lowest order Brueckner theory (LOBT) and the relativistic Dirac-Brueckner analysis predominantly arise from two sources. Besides effects from a nucleon mass modification M* in nuclear medium we have in a relativistic

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. Cosmic gamma-ray burst from intergalactic relativistic dust grains

    International Nuclear Information System (INIS)

    Dasgupta, A.K.

    1979-01-01

    Charged dust grains of radii a approximately 3 x 10 -6 approximately 3 x 10 -5 cm may acquire relativistic energy (>10 18 eV) in the intergalactic medium. In order to attain relativistic energy, dust grains have to move in and out ('scattering') of the magnetic field of the medium. A relativistic grain of radius a -5 cm with Lorentz factor γ approximately 10 3 approaching the Earth will break up either due to electrostatic charge or due to sputtering about 150 approximately 100 km, and may scatter solar photons via a fluorescence process. Dust grains may also melt into droplets in the solar vicinity and may contribute towards observed gamma-ray bursts. (Auth.)

  16. Relativistic calculations of one-photon bound-free transition amplitudes in hydrogenic atoms

    International Nuclear Information System (INIS)

    Simo, E.; Kwato Njock, M.G.

    2005-04-01

    Photoionization transition matrix of hydrogenic systems are investigated theoretically within the framework of the tensorial formalism with relativistic arguments. Calculations are carried out exactly, without approximation. We derive continuum second-order Dirac-Coulomb Sturmian functions. The numerical simulation of our results is performed in the dipole approximation. We test our theory on selected nucleus from the Periodic Table. The results of the fully relativistic calculations are compared with those of the quasi-relativistic calculations. A conclusion is drawn about the level of reliability of the quite simplified quasi-relativistic approach. (author)

  17. 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

  18. Relativistic quantum mechanics

    International Nuclear Information System (INIS)

    Ollitrault, J.Y.

    1998-12-01

    These notes form an introduction to relativistic quantum mechanics. The mathematical formalism has been reduced to the minimum in order to enable the reader to calculate elementary physical processes. The second quantification and the field theory are the logical followings of this course. The reader is expected to know analytical mechanics (Lagrangian and Hamiltonian), non-relativistic quantum mechanics and some basis of restricted relativity. The purpose of the first 3 chapters is to define the quantum mechanics framework for already known notions about rotation transformations, wave propagation and restricted theory of relativity. The next 3 chapters are devoted to the application of relativistic quantum mechanics to a particle with 0,1/5 and 1 spin value. The last chapter deals with the processes involving several particles, these processes require field theory framework to be thoroughly described. (A.C.)

  19. Relativistic solitons and pulsars

    Energy Technology Data Exchange (ETDEWEB)

    Karpman, V I [Inst. of Terrestrial Magnetism, Ionosphere, and Radio-Wave Propagation, Moscow; Norman, C A; ter Haar, D; Tsytovich, V N

    1975-05-01

    A production mechanism for stable electron bunches or sheets of localized electric fields is investigated which may account for pulsar radio emission. Possible soliton phenomena in a one-dimensional relativistic plasma are analyzed, and it is suggested that the motion of a relativistic soliton, or ''relaton'', along a curved magnetic-field line may produce radio emission with the correct polarization properties. A general MHD solution is obtained for relatons, the radiation produced by a relativistic particle colliding with a soliton is evaluated, and the emission by a soliton moving along a curved field line is estimated. It is noted that due to a number of severe physical restrictions, curvature radiation is not a very likely solution to the problem of pulsar radio emission. (IAA)

  20. Relativistic quantum mechanics

    CERN Document Server

    Horwitz, Lawrence P

    2015-01-01

    This book describes a relativistic quantum theory developed by the author starting from the E.C.G. Stueckelberg approach proposed in the early 40s. In this framework a universal invariant evolution parameter (corresponding to the time originally postulated by Newton) is introduced to describe dynamical evolution. This theory is able to provide solutions for some of the fundamental problems encountered in early attempts to construct a relativistic quantum theory. A relativistically covariant construction is given for which particle spins and angular momenta can be combined through the usual rotation group Clebsch-Gordan coefficients. Solutions are defined for both the classical and quantum two body bound state and scattering problems. The recently developed quantum Lax-Phillips theory of semigroup evolution of resonant states is described. The experiment of Lindner and coworkers on interference in time is discussed showing how the property of coherence in time provides a simple understanding of the results. Th...

  1. Relativistic theories of materials

    CERN Document Server

    Bressan, Aldo

    1978-01-01

    The theory of relativity was created in 1905 to solve a problem concerning electromagnetic fields. That solution was reached by means of profound changes in fundamental concepts and ideas that considerably affected the whole of physics. Moreover, when Einstein took gravitation into account, he was forced to develop radical changes also in our space-time concepts (1916). Relativistic works on heat, thermodynamics, and elasticity appeared as early as 1911. However, general theories having a thermodynamic basis, including heat conduction and constitutive equations, did not appear in general relativity until about 1955 for fluids and appeared only after 1960 for elastic or more general finitely deformed materials. These theories dealt with materials with memory, and in this connection some relativistic versions of the principle of material indifference were considered. Even more recently, relativistic theories incorporating finite deformations for polarizable and magnetizable materials and those in which couple s...

  2. Handbook of relativistic quantum chemistry

    International Nuclear Information System (INIS)

    Liu, Wenjian

    2017-01-01

    This handbook focuses on the foundations of relativistic quantum mechanics and addresses a number of fundamental issues never covered before in a book. For instance: How can many-body theory be combined with quantum electrodynamics? How can quantum electrodynamics be interfaced with relativistic quantum chemistry? What is the most appropriate relativistic many-electron Hamiltonian? How can we achieve relativistic explicit correlation? How can we formulate relativistic properties? - just to name a few. Since relativistic quantum chemistry is an integral component of computational chemistry, this handbook also supplements the ''Handbook of Computational Chemistry''. Generally speaking, it aims to establish the 'big picture' of relativistic molecular quantum mechanics as the union of quantum electrodynamics and relativistic quantum chemistry. Accordingly, it provides an accessible introduction for readers new to the field, presents advanced methodologies for experts, and discusses possible future perspectives, helping readers understand when/how to apply/develop the methodologies.

  3. Handbook of relativistic quantum chemistry

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Wenjian (ed.) [Peking Univ., Beijing (China). Center for Computational Science and Engineering

    2017-03-01

    This handbook focuses on the foundations of relativistic quantum mechanics and addresses a number of fundamental issues never covered before in a book. For instance: How can many-body theory be combined with quantum electrodynamics? How can quantum electrodynamics be interfaced with relativistic quantum chemistry? What is the most appropriate relativistic many-electron Hamiltonian? How can we achieve relativistic explicit correlation? How can we formulate relativistic properties? - just to name a few. Since relativistic quantum chemistry is an integral component of computational chemistry, this handbook also supplements the ''Handbook of Computational Chemistry''. Generally speaking, it aims to establish the 'big picture' of relativistic molecular quantum mechanics as the union of quantum electrodynamics and relativistic quantum chemistry. Accordingly, it provides an accessible introduction for readers new to the field, presents advanced methodologies for experts, and discusses possible future perspectives, helping readers understand when/how to apply/develop the methodologies.

  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 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

  7. 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

  8. 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

  9. Biquaternions and relativistic kinematics

    International Nuclear Information System (INIS)

    Bogush, A.A.; Kurochkin, Yu.A.; Fedorov, F.I.

    1979-01-01

    The problems concerning the use of quaternion interpretation of the Lorentz group vector parametrization are considered for solving relativistic kinematics problems. A vector theory convenient for describing the characteristic features of the Lobachevsky space is suggested. The kinematics of elementary particle scattering is investigated on the basis of this theory. A synthesis of vector parametrization and of quaternion calculation has been shown to lead to natural formulation of the theory of vectors in the three-dimensional Lobachevsky space, realized on mass hyperboloids of relativistic particles

  10. Relativistic heavy ion collisions

    International Nuclear Information System (INIS)

    Barz, H.W.; Kaempfer, B.; Schulz, H.

    1984-12-01

    An elementary introduction is given into the scenario of relativistic heavy ion collisions. It deals with relativistic kinematics and estimates of energy densities, extrapolations of the present knowledge of hadron-hadron and hadron-nuleus to nucleus-nucleus collisions, the properties of the quark-gluon plasma and the formation of the plasma and possible experimental signatures. Comments are made on a cosmic ray experiment which could be interpreted as a first indication of the quark-gluon phase of the matter. (author)

  11. Relativistic effects in resonance absorption

    International Nuclear Information System (INIS)

    Drake, J.F.; Lee, Y.C.

    1976-01-01

    The role of the relativistic-electron-mass variation in the generation of plasma waves by the linear mode conversion of intense electromagnetic waves is investigated. The increase in the electron mass in high intensity regions of the mode-converted wave reduces the local plasma frequency and thereby strongly modifies the plasma-driver resonance. A spatial discontinuity in the structure of the mode-converted wave results and causes the wave to break. Under rather modest restrictions, the wave breaking resulting from these effects occurs before the wave amplitude is limited either by thermal convection or by breaking caused by previously investigated nonrelativistic effects. Consequently, the amplitude of the mode-converted plasma wave should saturate at a much lower level than previously predicted. For simplicity, the analysis is limited to the initial stages of mode conversion where the ion dynamics can be neglected. The validity of this approximation is discussed

  12. Parton distribution in relativistic hadrons

    International Nuclear Information System (INIS)

    Kopeliovich, B.Z.; Lapidus, L.I.; Zamolodchikov, Al.B.

    1979-01-01

    The distribution in the slow-parton number in the relativistic hadron is considered as a function of its rapidity (y). Neglecting corrections due to the tarton chain recombination the equation is derived and its explicit solution is found. It describes this distribution depending on the initial distribution at y approximately 1. Comparison with the reggeon diagrams results in relations between the parton model and the regaeon field theory parameters. The interpretation of the cutting rules in the framework of the parton model is presented. The numerical estimation of the parton model parameters is performed. It is shown that the slow-parton density corresponding to accessible energies seems to be close to the saturated density. Therefore, the enhanced graphs contributions turn out to be of considerable importance

  13. Relativistic particle in a box

    OpenAIRE

    Alberto, P.; Fiolhais, Carlos; Gil, Victor

    1996-01-01

    The problem of a relativistic spin 1/2 particle confined to a one-dimensional box is solved in a way that resembles closely the solution of the well known quantum-mechanical textbook problem of a non-relativistic particle in a box. The energy levels and probability density are computed and compared with the non-relativistic case

  14. Liouville equation of relativistic charged fermion

    International Nuclear Information System (INIS)

    Wang Renchuan; Zhu Dongpei; Huang Zhuoran; Ko Che-ming

    1991-01-01

    As a form of density martrix, the Wigner function is the distribution in quantum phase space. It is a 2 X 2 matrix function when one uses it to describe the non-relativistic fermion. While describing the relativistic fermion, it is usually represented by 4 x 4 matrix function. In this paper authors obtain a Wigner function for the relativistic fermion in the form of 2 x 2 matrix, and the Liouville equation satisfied by the Wigner function. this equivalent to the Dirac equation of changed fermion in QED. The equation is also equivalent to the Dirac equation in the Walecka model applied to the intermediate energy nuclear collision while the nucleon is coupled to the vector meson only (or taking mean field approximation for the scalar meson). Authors prove that the 2 x 2 Wigner function completely describes the quantum system just the same as the relativistic fermion wave function. All the information about the observables can be obtained with above Wigner function

  15. Relativistic impulse dynamics.

    Science.gov (United States)

    Swanson, Stanley M

    2011-08-01

    Classical electrodynamics has some annoying rough edges. The self-energy of charges is infinite without a cutoff. The calculation of relativistic trajectories is difficult because of retardation and an average radiation reaction term. By reconceptuallizing electrodynamics in terms of exchanges of impulses rather than describing it by forces and potentials, we eliminate these problems. A fully relativistic theory using photonlike null impulses is developed. Numerical calculations for a two-body, one-impulse-in-transit model are discussed. A simple relationship between center-of-mass scattering angle and angular momentum was found. It reproduces the Rutherford cross section at low velocities and agrees with the leading term of relativistic distinguishable-particle quantum cross sections (Møller, Mott) when the distance of closest approach is larger than the Compton wavelength of the particle. Magnetism emerges as a consequence of viewing retarded and advanced interactions from the vantage point of an instantaneous radius vector. Radiation reaction becomes the local conservation of energy-momentum between the radiating particle and the emitted impulse. A net action is defined that could be used in developing quantum dynamics without potentials. A reinterpretation of Newton's laws extends them to relativistic motion.

  16. Non-relativistic supersymmetry

    International Nuclear Information System (INIS)

    Clark, T.E.; Love, S.T.

    1984-01-01

    The most general one- and two-body hamiltonian invariant under galilean supersymmetry is constructed in superspace. The corresponding Feynman rules are given for the superfield Green functions. As demonstrated by a simple example, it is straightforward to construct models in which the supersymmetry is spontaneously broken by the non-relativistic vacuum. (orig.)

  17. Relativistic stellar dynamics

    International Nuclear Information System (INIS)

    Contopoulos, G.

    1983-01-01

    In this paper, three main areas of relativistic stellar dynamics are reviewed: (a) The dynamics of clusters, or nuclei of galaxies, of very high density; (b) The dynamics of systems containing a massive black hole; and (c) The dynamics of particles (and photons) in an expanding Universe. The emphasis is on the use of orbit perturbations. (Auth.)

  18. Relativistic Wigner functions

    Directory of Open Access Journals (Sweden)

    Bialynicki-Birula Iwo

    2014-01-01

    Full Text Available Original definition of the Wigner function can be extended in a natural manner to relativistic domain in the framework of quantum field theory. Three such generalizations are described. They cover the cases of the Dirac particles, the photon, and the full electromagnetic field.

  19. The Relativistic Rocket

    Science.gov (United States)

    Antippa, Adel F.

    2009-01-01

    We solve the problem of the relativistic rocket by making use of the relation between Lorentzian and Galilean velocities, as well as the laws of superposition of successive collinear Lorentz boosts in the limit of infinitesimal boosts. The solution is conceptually simple, and technically straightforward, and provides an example of a powerful…

  20. Relativistic few body calculations

    International Nuclear Information System (INIS)

    Gross, F.

    1988-01-01

    A modern treatment of the nuclear few-body problem must take into account both the quark structure of baryons and mesons, which should be important at short range, and the relativistic exchange of mesons, which describes the long range, peripheral interactions. A way to model both of these aspects is described. The long range, peripheral interactions are calculated using the spectator model, a general approach in which the spectators to nucleon interactions are put on their mass-shell. Recent numerical results for a relativistic OBE model of the NN interaction, obtained by solving a relativistic equation with one-particle on mass-shell, will be presented and discussed. Two meson exchange models, one with only four mesons (π,σ,/rho/,ω) but with a 25% admixture of γ 5 coupling for the pion, and a second with six mesons (π,σ,/rho/,ω,δ,/eta/) but pure γ 5 γ/sup μ/ pion coupling, are shown to give very good quantitative fits to the NN scattering phase shifts below 400 MeV, and also a good description of the /rvec p/ 40 Ca elastic scattering observables. Applications of this model to electromagnetic interactions of the two body system, with emphasis on the determination of relativistic current operators consistent with the dynamics and the exact treatment of current conservation in the presence of phenomenological form factors, will be described. 18 refs., 8 figs

  1. Relativistic Polarizable Embedding

    DEFF Research Database (Denmark)

    Hedegård, Erik Donovan; Bast, Radovan; Kongsted, Jacob

    2017-01-01

    Most chemistry, including chemistry where relativistic effects are important, occurs in an environment, and in many cases, this environment has a significant effect on the chemistry. In nonrelativistic quantum chemistry, a lot of progress has been achieved with respect to including environments s...

  2. Relativistic length agony continued

    Directory of Open Access Journals (Sweden)

    Redžić D.V.

    2014-01-01

    Full Text Available We made an attempt to remedy recent confusing treatments of some basic relativistic concepts and results. Following the argument presented in an earlier paper (Redžić 2008b, we discussed the misconceptions that are recurrent points in the literature devoted to teaching relativity such as: there is no change in the object in Special Relativity, illusory character of relativistic length contraction, stresses and strains induced by Lorentz contraction, and related issues. We gave several examples of the traps of everyday language that lurk in Special Relativity. To remove a possible conceptual and terminological muddle, we made a distinction between the relativistic length reduction and relativistic FitzGerald-Lorentz contraction, corresponding to a passive and an active aspect of length contraction, respectively; we pointed out that both aspects have fundamental dynamical contents. As an illustration of our considerations, we discussed briefly the Dewan-Beran-Bell spaceship paradox and the ‘pole in a barn’ paradox. [Projekat Ministarstva nauke Republike Srbije, br. 171028

  3. Relativistic Coulomb excitation

    International Nuclear Information System (INIS)

    Winther, A.; Alder, K.

    1979-01-01

    Coulomb excitation of both target and projectile in relativistic heavy ion collisions is evaluated including the lowest order correction for the deviation from a straight line trajectory. Explicit results for differential and total cross sections are given in the form of tables and figures. (Auth.)

  4. Fundamental Relativistic Rotator

    International Nuclear Information System (INIS)

    Staruszkiewicz, A.

    2008-01-01

    Professor Jan Weyssenhoff was Myron Mathisson's sponsor and collaborator. He introduced a class of objects known in Cracow as '' kreciolki Weyssenhoffa '', '' Weyssenhoff's rotating little beasts ''. The Author describes a particularly simple object from this class. The relativistic rotator described in the paper is such that its both Casimir invariants are parameters rather than constants of motion. (author)

  5. 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)

  6. 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

  7. 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.

  8. 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.

  9. 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.))

  10. Validity of various approximations for the Bethe-Salpeter equation and their WKB quantization

    International Nuclear Information System (INIS)

    Silvestre-Brac, B.; Bilal, A.; Gignoux, C.; Schuck, P.

    1984-01-01

    The validity of the instantaneous approximation for the Bethe-Salpeter equation is questioned within the framework of the simple scalar-scalar model of Cutkosky. Detailed numerous results for various approximations are compared to the exact ones. WKB quantization is applied to these relativistic approximations. An unexpected question arises: is the currently used Bethe-Salpeter equation (i.e., the ladder approximation) well suited to describe two interacting relativistic particles

  11. Relativistic effects in elastic scattering of electrons in TEM

    International Nuclear Information System (INIS)

    Rother, Axel; Scheerschmidt, Kurt

    2009-01-01

    Transmission electron microscopy typically works with highly accelerated thus relativistic electrons. Consequently the scattering process is described within a relativistic formalism. In the following, we will examine three different relativistic formalisms for elastic electron scattering: Dirac, Klein-Gordon and approximated Klein-Gordon, the standard approach. This corresponds to a different consideration of spin effects and a different coupling to electromagnetic potentials. A detailed comparison is conducted by means of explicit numerical calculations. For this purpose two different formalisms have been applied to the approaches above: a numerical integration with predefined boundary conditions and the multislice algorithm, a standard procedure for such simulations. The results show a negligibly small difference between the different relativistic equations in the vicinity of electromagnetic potentials, prevailing in the electron microscope. The differences between the two numeric approaches are found to be small for small-angle scattering but eventually grow large for large-angle scattering, recorded for instance in high-angle annular dark field.

  12. 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.)

  13. 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

  14. The L1-shell ionisation of atoms by relativistic particles

    International Nuclear Information System (INIS)

    Moiseiwitsch, B.L.; Norrington, P.H.

    1979-01-01

    An expression for the L 1 -shell ionisation cross sections of atoms by high-energy particles has been derived using the relativistic plane-wave Born approximation. The incident and scattered particles are described by Dirac plane waves while Darwin hydrogenic wavefunctions are used for the atomic electrons. A comparison is made with experimental total cross sections for incident electrons in the energy range 1-2 MeV. The agreement is a considerable improvement on that obtained using the non-relativistic planewave Born approximation. (author)

  15. Hydrodynamics of ultra-relativistic bubble walls

    Directory of Open Access Journals (Sweden)

    Leonardo Leitao

    2016-04-01

    Full Text Available In cosmological first-order phase transitions, gravitational waves are generated by the collisions of bubble walls and by the bulk motions caused in the fluid. A sizeable signal may result from fast-moving walls. In this work we study the hydrodynamics associated to the fastest propagation modes, namely, ultra-relativistic detonations and runaway solutions. We compute the energy injected by the phase transition into the fluid and the energy which accumulates in the bubble walls. We provide analytic approximations and fits as functions of the net force acting on the wall, which can be readily evaluated for specific models. We also study the back-reaction of hydrodynamics on the wall motion, and we discuss the extrapolation of the friction force away from the ultra-relativistic limit. We use these results to estimate the gravitational wave signal from detonations and runaway walls.

  16. Hydrodynamics of ultra-relativistic bubble walls

    Energy Technology Data Exchange (ETDEWEB)

    Leitao, Leonardo, E-mail: lleitao@mdp.edu.ar; Mégevand, Ariel, E-mail: megevand@mdp.edu.ar

    2016-04-15

    In cosmological first-order phase transitions, gravitational waves are generated by the collisions of bubble walls and by the bulk motions caused in the fluid. A sizeable signal may result from fast-moving walls. In this work we study the hydrodynamics associated to the fastest propagation modes, namely, ultra-relativistic detonations and runaway solutions. We compute the energy injected by the phase transition into the fluid and the energy which accumulates in the bubble walls. We provide analytic approximations and fits as functions of the net force acting on the wall, which can be readily evaluated for specific models. We also study the back-reaction of hydrodynamics on the wall motion, and we discuss the extrapolation of the friction force away from the ultra-relativistic limit. We use these results to estimate the gravitational wave signal from detonations and runaway walls.

  17. Relativistic gravitational instabilities

    International Nuclear Information System (INIS)

    Schutz, B.F.

    1987-01-01

    The purpose of these lectures is to review and explain what is known about the stability of relativistic stars and black holes, with particular emphases on two instabilities which are due entirely to relativistic effects. The first of these is the post-Newtonian pulsational instability discovered independently by Chandrasekhar (1964) and Fowler (1964). This effectively ruled out the then-popular supermassive star model for quasars, and it sets a limit to the central density of white dwarfs. The second instability was also discovered by Chandrasekhar (1970): the gravitational wave induced instability. This sets an upper bound on the rotation rate of neutron stars, which is near that of the millisecond pulsar PSR 1937+214, and which is beginning to constrain the equation of state of neutron matter. 111 references, 5 figures

  18. Relativistic studies in actinides

    International Nuclear Information System (INIS)

    Weinberger, P.; Gonis, A.

    1987-01-01

    In this review the theoretical background is given for a relativistic description for actinide systems. A short introduction is given of the density functional theory which forms the basis for a fully relativistic single-particle theory. A section on the Dirac Hamiltonian is followed by a brief summary on group theoretical concepts. Single site scattering is presented such that formal extensions to the case of the presence of an internal (external) magnetic field and/or anisotropic scattering are evident. Multiple scattering is discussed such that it can readily be applied also to the problem of dislocations. In connection with the problem of selfconsistency particular attention is drawn to the use of complex energies. Finally the various theoretical aspects discussed are illustrated through the results of numerical calculations. 101 refs.; 37 figs.; 5 tabs

  19. Relativistic charged Bose gas

    International Nuclear Information System (INIS)

    Hines, D.F.; Frankel, N.E.

    1979-01-01

    The charged Bose has been previously studied as a many body problem of great intrinsic interest which can also serve as a model of some real physical systems, for example, superconductors, white dwarf stars and neutron stars. In this article the excitation spectrum of a relativistic spin-zero charged Bose gas is obtained in a dielectric response formulation. Relativity introduces a dip in the spectrum and consequences of this dip for the thermodynamic functions are discussed

  20. Relativistic heavy ion reactions

    Energy Technology Data Exchange (ETDEWEB)

    Brink, D M

    1989-08-01

    The theory of quantum chromodynamics predicts that if nuclear matter is heated to a sufficiently high temperature then quarks might become deconfined and a quark-gluon plasma could be produced. One of the aims of relativistic heavy ion experiments is to search for this new state of matter. These lectures survey some of the new experimental results and give an introduction to the theories used to interpret them. 48 refs., 4 tabs., 11 figs.

  1. Relativistic Ideal Clock

    OpenAIRE

    Bratek, Łukasz

    2015-01-01

    Two particularly simple ideal clocks exhibiting intrinsic circular motion with the speed of light and opposite spin alignment are described. The clocks are singled out by singularities of an inverse Legendre transformation for relativistic rotators of which mass and spin are fixed parameters. Such clocks work always the same way, no matter how they move. When subject to high accelerations or falling in strong gravitational fields of black holes, the clocks could be used to test the clock hypo...

  2. Relativistic heavy ion reactions

    International Nuclear Information System (INIS)

    Brink, D.M.

    1989-08-01

    The theory of quantum chromodynamics predicts that if nuclear matter is heated to a sufficiently high temperature then quarks might become deconfined and a quark-gluon plasma could be produced. One of the aims of relativistic heavy ion experiments is to search for this new state of matter. These lectures survey some of the new experimental results and give an introduction to the theories used to interpret them. 48 refs., 4 tabs., 11 figs

  3. Gravitationally confined relativistic neutrinos

    Science.gov (United States)

    Vayenas, C. G.; Fokas, A. S.; Grigoriou, D.

    2017-09-01

    Combining special relativity, the equivalence principle, and Newton’s universal gravitational law with gravitational rather than rest masses, one finds that gravitational interactions between relativistic neutrinos with kinetic energies above 50 MeV are very strong and can lead to the formation of gravitationally confined composite structures with the mass and other properties of hadrons. One may model such structures by considering three neutrinos moving symmetrically on a circular orbit under the influence of their gravitational attraction, and by assuming quantization of their angular momentum, as in the Bohr model of the H atom. The model contains no adjustable parameters and its solution, using a neutrino rest mass of 0.05 eV/c2, leads to composite state radii close to 1 fm and composite state masses close to 1 GeV/c2. Similar models of relativistic rotating electron - neutrino pairs give a mass of 81 GeV/c2, close to that of W bosons. This novel mechanism of generating mass suggests that the Higgs mass generation mechanism can be modeled as a latent gravitational field which gets activated by relativistic neutrinos.

  4. The relativistic rotation of spin and asymptotic behaviour of the form factor of the composite system

    International Nuclear Information System (INIS)

    Trubnikov, S.V.

    1984-01-01

    The relativistic rotation of nucleon spin in addition to deuteron spin leads to the appearance of the new term in the deuteron charge form factor (DCFF). This term is absent in the traditional approaches and essentially influences the asymptotic behaviour of DCFF. General formulae are obtained for the DCFF asymptotics in the relativistic and nonrelativistic impulse approximation

  5. Point form relativistic quantum mechanics and relativistic SU(6)

    Science.gov (United States)

    Klink, W. H.

    1993-01-01

    The point form is used as a framework for formulating a relativistic quantum mechanics, with the mass operator carrying the interactions of underlying constituents. A symplectic Lie algebra of mass operators is introduced from which a relativistic harmonic oscillator mass operator is formed. Mass splittings within the degenerate harmonic oscillator levels arise from relativistically invariant spin-spin, spin-orbit, and tensor mass operators. Internal flavor (and color) symmetries are introduced which make it possible to formulate a relativistic SU(6) model of baryons (and mesons). Careful attention is paid to the permutation symmetry properties of the hadronic wave functions, which are written as polynomials in Bargmann spaces.

  6. The Gaussian formula and spherical aberrations of static and relativistic curved mirrors from Fermat's principle

    International Nuclear Information System (INIS)

    Sutanto, Sylvia H; Tjiang, Paulus C

    2011-01-01

    The Gaussian formula and spherical aberrations of static and relativistic curved mirrors are analyzed using the optical path length (OPL) and Fermat's principle. The geometrical figures generated by the rotation of conic sections about their symmetry axes are considered for the shapes of the mirrors. By comparing the results in static and relativistic cases, it is shown that the focal lengths and the spherical aberration relations of the relativistic mirrors obey the Lorentz contraction. Further analysis of the spherical aberrations for both static and relativistic cases have resulted in information about the limits for the paraxial approximation, as well as for the minimum speed of the systems to reduce the spherical aberrations

  7. On the classification of the spectrally stable standing waves of the Hartree problem

    Science.gov (United States)

    Georgiev, Vladimir; Stefanov, Atanas

    2018-05-01

    We consider the fractional Hartree model, with general power non-linearity and arbitrary spatial dimension. We construct variationally the "normalized" solutions for the corresponding Choquard-Pekar model-in particular a number of key properties, like smoothness and bell-shapedness are established. As a consequence of the construction, we show that these solitons are spectrally stable as solutions to the time-dependent Hartree model. In addition, we analyze the spectral stability of the Moroz-Van Schaftingen solitons of the classical Hartree problem, in any dimensions and power non-linearity. A full classification is obtained, the main conclusion of which is that only and exactly the "normalized" solutions (which exist only in a portion of the range) are spectrally stable.

  8. Order 1/N corrections to the time-dependent Hartree approximation for a system of N+1 oscillators

    International Nuclear Information System (INIS)

    Mihaila, B.; Dawson, J.F.; Cooper, F.

    1997-01-01

    We solve numerically to order 1/N the time evolution of a quantum dynamical system of N oscillators of mass m coupled quadratically to a massless dynamic variable. We use Schwingers closed time path formalism to derive the equations. We compare two methods which differ by terms of order 1/N 2 . The first method is a direct perturbation theory in 1/N using the path integral. The second solves exactly the theory defined by the effective action to order 1/N. We compare the results of both methods as a function of N. At N=1, where we expect the expansion to be quite innacurate, we compare our results to an exact numerical solution of the Schroedinger equation. In this case we find that when the two methods disagree they also diverge from the exact answer. We also find at N=1 that the 1/N corrected evolutions track the exact answer for the expectation values much longer than the mean field (N=∞) result. copyright 1997 The American Physical Society

  9. Renormalization of self-consistent approximation schemes at finite temperature. II. Applications to the sunset diagram

    International Nuclear Information System (INIS)

    Hees, Hendrik van; Knoll, Joern

    2002-01-01

    The theoretical concepts for the renormalization of self-consistent Dyson resummations, devised in the first paper of this series, are applied to first example cases of φ 4 theory. In addition to the tadpole (Hartree) approximation, as a novel part the numerical solutions are presented, which include the sunset self-energy diagram into the self-consistent scheme based on the Φ-derivable approximation or the two-particle irreducible effective action concept

  10. Renormalization of self-consistent approximation schemes at finite temperature II: applications to the sunset diagram

    International Nuclear Information System (INIS)

    Hees, H. van; Knoll, J.

    2001-01-01

    The theoretical concepts for the renormalization of self-consistent Dyson resummations, deviced in the first paper of this series, are applied to first example cases for the φ 4 -theory. Besides the tadpole (Hartree) approximation as a novel part the numerical solutions are presented which includes the sunset self-energy diagram into the self-consistent scheme based on the Φ-derivable approximation or 2PI effective action concept. (orig.)

  11. Diophantine approximation and badly approximable sets

    DEFF Research Database (Denmark)

    Kristensen, S.; Thorn, R.; Velani, S.

    2006-01-01

    . The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension...

  12. On the relativistic calculation of spontaneous emission

    International Nuclear Information System (INIS)

    Boudet, R.

    1993-01-01

    In a recent work, Barut and Salamin (1988) have derived a method for calculating the relativistic decay rates in atoms, in a formulation of quantum electrodynamics based upon the electron's self-energy. The decay rate appears as the imaginary part of a formula giving a complex energy shift, the real part of the formula being the Lamb shift. The presence of the the decay rate in the imaginary part of a formula, giving an energy in its real part, may appear a bit strange. A confirmation of the Barut and Alamin calculation, by means of a quite different point of view, would be useful. Therefore in this work the Einstein A coefficients are calculated, in all cases of degeneracies of the Dirac transition currents, by means of the energy balance method. This point of view is based on the balance between the energy released during the transitions of electrons from a higher state to a lower one, and the flux of the Poynting vector of the classical electromagnetic field, created by the electrons, through a sphere a large radius. The particularity of the present work lies in the direct calculation of the relativistic Dirac transition currents and the fact that the dipole and Pauli approximations are avoided. The quantum part of the relativistic calculation is based on the determination of the transition charge currents in the Darwin solutions of the Dirac equation. 13 refs

  13. Relativistic twins or sextuplets?

    International Nuclear Information System (INIS)

    Sheldon, Eric

    2003-01-01

    A recent study of the relativistic twin 'paradox' by Soni in this journal affirmed that 'A simple solution of the twin paradox also shows anomalous behaviour of rigidly connected distant clocks' but entailed a pedagogic hurdle which the present treatment aims to surmount. Two scenarios are presented: the first 'flight-plan' is akin to that depicted by Soni, with constant-velocity segments, while the second portrays an alternative mission undertaken with sustained acceleration and deceleration, illustrated quantitatively for a two-way spacecraft flight from Earth to Polaris (465.9 light years distant) and back

  14. Relativistic twins or sextuplets?

    CERN Document Server

    Sheldon, E S

    2003-01-01

    A recent study of the relativistic twin 'paradox' by Soni in this journal affirmed that 'A simple solution of the twin paradox also shows anomalous behaviour of rigidly connected distant clocks' but entailed a pedagogic hurdle which the present treatment aims to surmount. Two scenarios are presented: the first 'flight-plan' is akin to that depicted by Soni, with constant-velocity segments, while the second portrays an alternative mission undertaken with sustained acceleration and deceleration, illustrated quantitatively for a two-way spacecraft flight from Earth to Polaris (465.9 light years distant) and back.

  15. Relativistic quantum cryptography

    Science.gov (United States)

    Kaniewski, Jedrzej

    Special relativity states that information cannot travel faster than the speed of light, which means that communication between agents occupying distinct locations incurs some minimal delay. Alternatively, we can see it as temporary communication constraints between distinct agents and such constraints turn out to be useful for cryptographic purposes. In relativistic cryptography we consider protocols in which interactions occur at distinct locations at well-defined times and we investigate why such a setting allows to implement primitives which would not be possible otherwise. (Abstract shortened by UMI.).

  16. Relativistic distances, sizes, lengths

    International Nuclear Information System (INIS)

    Strel'tsov, V.N.

    1992-01-01

    Such notion as light or retarded distance, field size, formation way, visible size of a body, relativistic or radar length and wave length of light from a moving atom are considered. The relation between these notions is cleared up, their classification is given. It is stressed that the formation way is defined by the field size of a moving particle. In the case of the electromagnetic field, longitudinal sizes increase proportionally γ 2 with growing charge velocity (γ is the Lorentz-factor). 18 refs

  17. Localization of relativistic particles

    International Nuclear Information System (INIS)

    Omnes, R.

    1997-01-01

    In order to discuss localization experiments and also to extend the consistent history interpretation of quantum mechanics to relativistic properties, the techniques introduced in a previous paper [J. Math. Phys. 38, 697 (1997)] are applied to the localization of a photon in a given region of space. An essential requirement is to exclude arbitrarily large wavelengths. The method is valid for a particle with any mass and spin. Though there is no proper position operator for a photon, one never needs one in practice. Causality is valid up to exponentially small corrections. copyright 1997 American Institute of Physics

  18. Relativistic wave mechanics

    CERN Document Server

    Corinaldesi, Ernesto

    1963-01-01

    Geared toward advanced undergraduate and graduate students of physics, this text provides readers with a background in relativistic wave mechanics and prepares them for the study of field theory. The treatment originated as a series of lectures from a course on advanced quantum mechanics that has been further amplified by student contributions.An introductory section related to particles and wave functions precedes the three-part treatment. An examination of particles of spin zero follows, addressing wave equation, Lagrangian formalism, physical quantities as mean values, translation and rotat

  19. Relativistic quarkonium dynamics

    International Nuclear Information System (INIS)

    Sazdjian, H.

    1985-06-01

    We present, in the framework of relativistic quantum mechanics of two interacting particles, a general model for quarkonium systems satisfying the following four requirements: confinement, spontaneous breakdown of chiral symmetry, soft explicit chiral symmetry breaking, short distance interactions of the vector type. The model is characterized by two arbitrary scalar functions entering in the large and short distance interaction potentials, respectively. Using relationships with corresponding quantities of the Bethe-Salpeter equation, we also present the normalization condition of the wave functions, as well as the expressions of the meson decay coupling constants. The quark masses appear in this model as free parameters

  20. Proton relativistic model

    International Nuclear Information System (INIS)

    Araujo, Wilson Roberto Barbosa de

    1995-01-01

    In this dissertation, we present a model for the nucleon, which is composed by three relativistic quarks interacting through a contract force. The nucleon wave-function was obtained from the Faddeev equation in the null-plane. The covariance of the model under kinematical null-plane boots is discussed. The electric proton form-factor, calculated from the Faddeev wave-function, was in agreement with the data for low-momentum transfers and described qualitatively the asymptotic region for momentum transfers around 2 GeV. (author)

  1. Relativistic nuclear collisions: theory

    International Nuclear Information System (INIS)

    Gyulassy, M.

    1980-07-01

    Some of the recent theoretical developments in relativistic (0.5 to 2.0-GeV/nucleon) nuclear collisions are reviewed. The statistical model, hydrodynamic model, classical equation of motion calculations, billiard ball dynamics, and intranuclear cascade models are discussed in detail. Inclusive proton and pion spectra are analyzed for a variety of reactions. Particular attention is focused on how the complex interplay of the basic reaction mechanism hinders attempts to deduce the nuclear matter equation of state from data. 102 references, 19 figures

  2. [Relativistic heavy ion research

    International Nuclear Information System (INIS)

    1991-01-01

    The present document describes our second-year application for a continuation grant on relativistic heavy-ion research at Nevis Laboratories, Columbia University, over the two-year period starting from November 15, 1990. The progress during the current budget year is presented. This year, construction of RHIC officially began. As a result, the entire Nevis nuclear physics group has made a coherent effort to create new proposal for an Open Axially Symmetric Ion Spectrometer (OASIS) proposal. Future perspectives and our plans for this proposal are described

  3. 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.

  4. Relativistic dynamics without conservation laws

    OpenAIRE

    Rothenstein, Bernhard; Popescu, Stefan

    2006-01-01

    We show that relativistic dynamics can be approached without using conservation laws (conservation of momentum, of energy and of the centre of mass). Our approach avoids collisions that are not easy to teach without mnemonic aids. The derivations are based on the principle of relativity and on its direct consequence, the addition law of relativistic velocities.

  5. Relativistic non-Hamiltonian mechanics

    International Nuclear Information System (INIS)

    Tarasov, Vasily E.

    2010-01-01

    Relativistic particle subjected to a general four-force is considered as a nonholonomic system. The nonholonomic constraint in four-dimensional space-time represents the relativistic invariance by the equation for four-velocity u μ u μ + c 2 = 0, where c is the speed of light in vacuum. In the general case, four-forces are non-potential, and the relativistic particle is a non-Hamiltonian system in four-dimensional pseudo-Euclidean space-time. We consider non-Hamiltonian and dissipative systems in relativistic mechanics. Covariant forms of the principle of stationary action and the Hamilton's principle for relativistic mechanics of non-Hamiltonian systems are discussed. The equivalence of these principles is considered for relativistic particles subjected to potential and non-potential forces. We note that the equations of motion which follow from the Hamilton's principle are not equivalent to the equations which follow from the variational principle of stationary action. The Hamilton's principle and the principle of stationary action are not compatible in the case of systems with nonholonomic constraint and the potential forces. The principle of stationary action for relativistic particle subjected to non-potential forces can be used if the Helmholtz conditions are satisfied. The Hamilton's principle and the principle of stationary action are equivalent only for a special class of relativistic non-Hamiltonian systems.

  6. Relativistic energy loss in a dispersive medium

    DEFF Research Database (Denmark)

    Houlrik, Jens Madsen

    2002-01-01

    The electron energy loss in a dispersive medium is obtained using macroscopic electrodynamics taking advantage of a static frame of reference. Relativistic corrections are described in terms of a dispersive Lorentz factor obtained by replacing the vacuum velocity c by the characteristic phase...... velocity c/n, where n is the complex index of refraction. The angle-resolved energy-loss spectrum of a Drude conductor is analyzed in detail and it is shown that the low-energy peak due to Ohmic losses is enhanced compared to the classical approximation....

  7. Contraint's theory and relativistic dynamics

    International Nuclear Information System (INIS)

    Longhi, G.; Lusanna, L.

    1987-01-01

    The purpose of this Workshop was to examine the current situation of relativistic dynamics. In particular, Dirac-Bergmann's theory of constraints, which lies at the heart of gauge theories, general relativity, relativistic mechanics and string theories, was chosen as the unifying theoretical framework best suited to investigate such a field. The papers discussed were on general relativity; relativistic mechanics; particle physics and mathematical physics. Also discussed were the problems of classical and quantum level, namely the identification of the classical observables of constrained systems, the equivalence of the nonequivalence of the various ways to quantize such systems; the problem of the anomalies; the best geometrical approach to the theory of constraints; the possibility of unifying all the treatments of relativistic mechanics. This book compiles the papers presented at proceedings of relativistic dynamics and constraints theory

  8. Relativistic centrifugal instability

    Science.gov (United States)

    Gourgouliatos, Konstantinos N.; Komissarov, Serguei S.

    2018-03-01

    Near the central engine, many astrophysical jets are expected to rotate about their axis. Further out they are expected to go through the processes of reconfinement and recollimation. In both these cases, the flow streams along a concave surface and hence, it is subject to the centrifugal force. It is well known that such flows may experience the centrifugal instability (CFI), to which there are many laboratory examples. The recent computer simulations of relativistic jets from active galactic nuclei undergoing the process of reconfinement show that in such jets CFI may dominate over the Kelvin-Helmholtz instability associated with velocity shear (Gourgouliatos & Komissarov). In this letter, we generalize the Rayleigh criterion for CFI in rotating fluids to relativistic flows using a heuristic analysis. We also present the results of computer simulations which support our analytic criterion for the case of an interface separating two uniformly rotating cylindrical flows. We discuss the difference between CFI and the Rayleigh-Taylor instability in flows with curved streamlines.

  9. Relativistic heavy ion physics

    International Nuclear Information System (INIS)

    Hill, J.C.; Wohn, F.K.

    1992-01-01

    In 1992 a proposal by the Iowa State University experimental nuclear physics group entitled ''Relativistic Heavy Ion Physics'' was funded by the US Department of Energy, Office of Energy Research, for a three-year period beginning November 15, 1991. This is a progress report for the first six months of that period but, in order to give a wider perspective, we report here on progress made since the beginning of calendar year 1991. In the first section, entitled ''Purpose and Trends,'' we give some background on the recent trends in our research program and its evolution from an emphasis on nuclear structure physics to its present emphasis on relativistic heavy ion and RHIC physics. The next section, entitled, ''Physics Research Programs,'' is divided into three parts. First, we discuss our participation in the program to develop a large detector named PHENIX for the RHIC accelerator. Second, we outline progress made in the study of electromagnetic dissociation (ED). A highlight of this endeavor is experiments carried out with the 197 Au beam from the AGS accelerator in April 1991. Third, we discuss progress in completion of our nuclear structure studies. In the final section a list of publications, invited talks and contributed talks starting in 1991 is given

  10. 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

  11. 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

  12. 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

  13. 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.

  14. Numerical studies of the g-hartree density functional in the Thomas-Fermi scaling limit

    International Nuclear Information System (INIS)

    Millack, T.; Weymans, G.

    1986-02-01

    Methods of finite temperature quantum field theory are used to construct the g-Hartree density functional for atoms. Low and high temperature expansions are discussed in detail. Numerical studies for atomic ground-state configurations are presented in the Thomas-Fermi-Scaling limit. (orig.)

  15. 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

  16. 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.)

  17. Relativistic plasma dielectric tensor evaluation based on the exact plasma dispersion functions concept

    International Nuclear Information System (INIS)

    Castejon, F.; Pavlov, S. S.

    2006-01-01

    The fully relativistic plasma dielectric tensor for any wave and plasma parameter is estimated on the basis of the exact plasma dispersion functions concept. The inclusion of this concept allows one to write the tensor in a closed and compact form and to reduce the tensor evaluation to the calculation of those functions. The main analytical properties of these functions are studied and two methods are given for their evaluation. The comparison between the exact dielectric tensor with the weakly relativistic approximation, widely used presently in plasma waves calculations, is given as well as the range of plasma temperature, harmonic number, and propagation angle in which the weakly relativistic approximation is valid

  18. Relativistic description of the Fermi motion effects on deuterium targets

    International Nuclear Information System (INIS)

    Kusno, D.

    1979-12-01

    A comprehensive analysis of the inconsistencies of the conventional, non-relativistic approach, which has been used so far in the extraction of neutron data from deuterium targets, is given. A new approach dealing with the smearing effects, due to the nucleon's Fermi motion inside the deuteron, is developed as an alternative to the conventional one. This new approach is a spin-less, relativistic, simple and consistent approach. A new covariant model of the elastic electromagnetic form factors of the deuteron in the impulse approximation is also presented. The treatment includes spin and allows for a possibility of determining completely the two elastic structure functions

  19. The K-shell ionisation of atoms by relativistic protons

    International Nuclear Information System (INIS)

    Davidovic, D.M.; Moiseiwitsch, B.L.; Norrington, P.H.

    1978-01-01

    The K-shell ionisation of atoms by protons travelling with relativistic velocities is investigated using an extension of the first-order time-dependent perturbation-theory treatment of Moeller (Ann. Phys. Lpz.; 14:531 (1932)), taking Dirac plane waves for the description of the incident and scattered protons and the Darwin approximation for the relativistic wavefunctions of the K-shell atomic electrons and the ejected electron. The differential cross sections and total cross sections are calculated. Results are compared with those of earlier workers. (author)

  20. Relativistic calculation of dielectronic recombination for He-like krypton

    Institute of Scientific and Technical Information of China (English)

    Shi Xi-Heng; Wang Yan-Sen; Chen Chong-Yang; Gu Ming-Feng

    2005-01-01

    Dielectronic recombination (DR) cross sections and rate coefficients of He-like Kr are calculated employing the relativistic flexible atomic code, in which autoionization rates are calculated based on the relativistic distorted-wave approximation and the configuration interaction is considered. The Auger and total radiative rates of some strong resonances are listed and compared with the results from multiconfiguration Dirac-Fock and Hebrew University Lawrence Livermore Atomic Code methods. The n-3 scaling law is checked and used to extrapolate rate coefficients. We also show the variation of DR branching ratio with different DR resonances or atomic number Z. The effect of radiative cascades on DR cross sections are studied.

  1. General Relativistic Mean Field Theory for rotating nuclei

    Energy Technology Data Exchange (ETDEWEB)

    Madokoro, Hideki [Kyushu Univ., Fukuoka (Japan). Dept. of Physics; Matsuzaki, Masayuki

    1998-03-01

    The {sigma}-{omega} model Lagrangian is generalized to an accelerated frame by using the technique of general relativity which is known as tetrad formalism. We apply this model to the description of rotating nuclei within the mean field approximation, which we call General Relativistic Mean Field Theory (GRMFT) for rotating nuclei. The resulting equations of motion coincide with those of Munich group whose formulation was not based on the general relativistic transformation property of the spinor fields. Some numerical results are shown for the yrast states of the Mg isotopes and the superdeformed rotational bands in the A {approx} 60 mass region. (author)

  2. Towards an exact relativistic theory of Earth's geoid undulation

    Science.gov (United States)

    Kopeikin, Sergei M.; Mazurova, Elena M.; Karpik, Alexander P.

    2015-08-01

    The present paper extends the Newtonian concept of the geoid in classic geodesy towards the realm of general relativity by utilizing the covariant geometric methods of the perturbation theory of curved manifolds. It yields a covariant definition of the anomalous (disturbing) gravity potential and formulates differential equation for it in the form of a covariant Laplace equation. The paper also derives the Bruns equation for calculation of geoid's height with full account for relativistic effects beyond the Newtonian approximation. A brief discussion of the relativistic Bruns formula is provided.

  3. Relativistic Energy Density Functionals: Exotic modes of excitation

    International Nuclear Information System (INIS)

    Vretenar, D.; Paar, N.; Marketin, T.

    2008-01-01

    The framework of relativistic energy density functionals has been applied to the description of a variety of nuclear structure phenomena, not only in spherical and deformed nuclei along the valley of β-stability, but also in exotic systems with extreme isospin values and close to the particle drip-lines. Dynamical aspects of exotic nuclear structure have been investigated with the relativistic quasiparticle random-phase approximation. We present results for the evolution of low-lying dipole (pygmy) strength in neutron-rich nuclei, and charged-current neutrino-nucleus cross sections.

  4. Elementary relativistic atoms

    International Nuclear Information System (INIS)

    Nemenov, L.

    2001-01-01

    The Coulomb interaction which occurs in the final state between two particles with opposite charges allows for creation of the bound state of these particles. In the case when particles are generated with large momentum in lab frame, the Lorentz factors of the bound state will also be much larger than one. The relativistic velocity of the atoms provides the opportunity to observe bound states of (π + μ - ), (π + π - ) and (π + K - ) with a lifetime as short as 10 -16 s, and to measure their parameters. The ultrarelativistic positronium atoms (A 2e ) allow us to observe the e.ect of superpenetration in matter, to study the effects caused by the formation time of A 2e from virtual e + e - pairs and to investigate the process of transformation of two virtual particles into the bound state

  5. Photoionization at relativistic energies

    International Nuclear Information System (INIS)

    Ionescu, D.C.; Technische Univ. Dresden; Soerensen, A.H.; Belkacem, A.

    2000-11-01

    At MeV energies and beyond the inner-shell vacancy production cross section associated with the photoelectric and Compton effect decrease with increasing photon energy. However, when the photon energy exceeds twice the rest energy of the electron, ionization of a bound electron may be catalyzed by the creation of an electron-positron pair. Distinctly different from all other known mechanisms for inner-shell vacancy production by photons, we show that the cross section for this ''vacuum-assisted photoionization'' increases with increasing photon energy and then saturates. As a main result, we predict that vacuum-assisted photoionization will dominate the other known photoionization mechanisms in the highly relativistic energy regime. (orig.)

  6. Relativistic thermodynamics of fluids

    International Nuclear Information System (INIS)

    Souriau, J.-M.

    1977-05-01

    The relativistic covariant definition of a statistical equilibrium, applied to a perfect gas, involves a 'temperature four-vector', whose direction is the mean velocity of the fluid, and whose length is the reciprocal temperature. The hypothesis of this 'temperature four-vector' being a relevant variable for the description of the dissipative motions of a simple fluid is discussed. The kinematics is defined by using a vector field and measuring the number of molecules. Such a dissipative fluid is subject to motions involving null entropy generation; the 'temperature four-vector' is then a Killing vector; the equations of motion can be completely integrated. Perfect fluids can be studied by this way and the classical results of Lichnerowicz are obtained. In weakly dissipative motions two viscosity coefficient appear together with the heat conductibility coefficient. Two other coefficients perharps measurable on real fluids. Phase transitions and shock waves are described with using the model [fr

  7. Relativistic heavy ion physics

    International Nuclear Information System (INIS)

    Hill, J.C.; Wohn, F.K.

    1993-01-01

    This is a progress report for the period May 1992 through April 1993. The first section, entitled ''Purpose and Trends, gives background on the recent trends in the research program and its evolution from an emphasis on nuclear structure physics to its present emphasis on relativistic heavy ion and RHIC physics. The next section, entitled ''Physics Research Progress'', is divided into four parts: participation in the program to develop a large detector named PHENIX for the RHIC accelerator; joining E864 at the AGS accelerator and the role in that experiment; progress made in the study of electromagnetic dissociation highlight of this endeavor is an experiment carried out with the 197 Au beam from the AGS accelerator in April 1992; progress in completion of the nuclear structure studies. In the final section a list of publications, invited talks, and contributed talks is given

  8. Relativistic Light Sails

    Energy Technology Data Exchange (ETDEWEB)

    Kipping, David, E-mail: dkipping@astro.columbia.edu [Department of Astronomy, Columbia University, 550 W. 120th St., New York, NY 10027 (United States)

    2017-06-01

    One proposed method for spacecraft to reach nearby stars is by accelerating sails using either solar radiation pressure or directed energy. This idea constitutes the thesis behind the Breakthrough Starshot project, which aims to accelerate a gram-mass spacecraft up to one-fifth the speed of light toward Proxima Centauri. For such a case, the combination of the sail’s low mass and relativistic velocity renders previous treatments incorrect at the 10% level, including that of Einstein himself in his seminal 1905 paper introducing special relativity. To address this, we present formulae for a sail’s acceleration, first in response to a single photon and then extended to an ensemble. We show how the sail’s motion in response to an ensemble of incident photons is equivalent to that of a single photon of energy equal to that of the ensemble. We use this principle of ensemble equivalence for both perfect and imperfect mirrors, enabling a simple analytic prediction of the sail’s velocity curve. Using our results and adopting putative parameters for Starshot , we estimate that previous relativistic treatments underestimate the spacecraft’s terminal velocity by ∼10% for the same incident energy. Additionally, we use a simple model to predict the sail’s temperature and diffraction beam losses during the laser firing period; this allows us to estimate that, for firing times of a few minutes and operating temperatures below 300°C (573 K), Starshot will require a sail that absorbs less than one in 260,000 photons.

  9. Relativistic Light Sails

    International Nuclear Information System (INIS)

    Kipping, David

    2017-01-01

    One proposed method for spacecraft to reach nearby stars is by accelerating sails using either solar radiation pressure or directed energy. This idea constitutes the thesis behind the Breakthrough Starshot project, which aims to accelerate a gram-mass spacecraft up to one-fifth the speed of light toward Proxima Centauri. For such a case, the combination of the sail’s low mass and relativistic velocity renders previous treatments incorrect at the 10% level, including that of Einstein himself in his seminal 1905 paper introducing special relativity. To address this, we present formulae for a sail’s acceleration, first in response to a single photon and then extended to an ensemble. We show how the sail’s motion in response to an ensemble of incident photons is equivalent to that of a single photon of energy equal to that of the ensemble. We use this principle of ensemble equivalence for both perfect and imperfect mirrors, enabling a simple analytic prediction of the sail’s velocity curve. Using our results and adopting putative parameters for Starshot , we estimate that previous relativistic treatments underestimate the spacecraft’s terminal velocity by ∼10% for the same incident energy. Additionally, we use a simple model to predict the sail’s temperature and diffraction beam losses during the laser firing period; this allows us to estimate that, for firing times of a few minutes and operating temperatures below 300°C (573 K), Starshot will require a sail that absorbs less than one in 260,000 photons.

  10. Some problems in relativistic thermodynamics

    International Nuclear Information System (INIS)

    Veitsman, E. V.

    2007-01-01

    The relativistic equations of state for ideal and real gases, as well as for various interface regions, have been derived. These dependences help to eliminate some controversies in the relativistic thermodynamics based on the special theory of relativity. It is shown, in particular, that the temperature of system whose velocity tends to the velocity of light in vacuum varies in accordance with the Ott law T = T 0 /√1 - v 2 /c 2 . Relativistic dependences for heat and mass transfer, for Ohm's law, and for a viscous flow of a liquid have also been derived

  11. Electron-deuteron scattering in a relativistic theory of hadrons

    International Nuclear Information System (INIS)

    Phillips, D.

    1998-11-01

    The author reviews a three-dimensional formalism that provides a systematic way to include relativistic effects including relativistic kinematics, the effects of negative-energy states, and the boosts of the two-body system in calculations of two-body bound-states. He then explains how to construct a conserved current within this relativistic three-dimensional approach. This general theoretical framework is specifically applied to electron-deuteron scattering both in impulse approximation and when the ρπγ meson-exchange current is included. The experimentally-measured quantities A, B, and T 20 are calculated over the kinematic range that is probed in Jefferson Lab experiments. The role of both negative-energy states and meson retardation appears to be small in the region of interest

  12. Relativistic three-particle dynamical equations: I. Theoretical development

    International Nuclear Information System (INIS)

    Adhikari, S.K.; Tomio, L.; Frederico, T.

    1993-11-01

    Starting from the two-particle Bethe-Salpeter equation in the ladder approximation and integrating over the time component of momentum, three dimensional scattering integral equations satisfying constrains of relativistic unitarity and covariance are rederived. These equations were first derived by Weinberg and by Blankenbecler and Sugar. These two-particle equations are shown to be related by a transformation of variables. Hence it is shown to perform and relate dynamical calculation using these two equations. Similarly, starting from the Bethe-Salpeter-Faddeev equation for the three-particle system and integrating over the time component of momentum, several three dimensional three-particle scattering equations satisfying constraints of relativistic unitary and covariance are derived. Two of these three-particle equations are related by a transformation of variables as in the two-particle case. The three-particle equations obtained are very practical and suitable for performing relativistic scattering calculations. (author)

  13. Heavy-ion interactions in relativistic mean-field models

    International Nuclear Information System (INIS)

    Rashdan, M.

    1996-01-01

    The interaction potential between spherical nuclei and the elastic scattering cross section are calculated within relativistic mean-field (linear and non-linear) models, using a generalized relativistic local density approximation. The nuclear densities are calculated self-consistently from the solution of the relativistic mean-field equations. It is found that both the linear and non-linear models predict the characteristic switching-over phenomenon of the heavy-ion nuclear potential, where the potential gets attraction with increasing energy up to some value where it reverses this behaviour. The non-linear NLC model predicts a deeper potential than the linear LW model. The elastic scattering cross section calculated within the non-linear NLC model is in better agreement with experiments than that calculated within the linear LW model. (orig.)

  14. Properties of Doubly Heavy Baryons in the Relativistic Quark Model

    International Nuclear Information System (INIS)

    Ebert, D.; Faustov, R.N.; Galkin, V.O.; Martynenko, A.P.

    2005-01-01

    Mass spectra and semileptonic decay rates of baryons consisting of two heavy (b or c) and one light quark are calculated in the framework of the relativistic quark model. The doubly heavy baryons are treated in the quark-diquark approximation. The ground and excited states of both the diquark and quark-diquark bound systems are considered. The quark-diquark potential is constructed. The light quark is treated completely relativistically, while the expansion in the inverse heavy-quark mass is used. The weak transition amplitudes of heavy diquarks bb and bc going, respectively, to bc and cc are explicitly expressed through the overlap integrals of the diquark wave functions in the whole accessible kinematic range. The relativistic baryon wave functions of the quark-diquark bound system are used for the calculation of the decay matrix elements, the Isgur-Wise function, and decay rates in the heavy-quark limit

  15. On the injection of relativistic particles into the Crab Nebula

    International Nuclear Information System (INIS)

    Shklovskij, I.S.

    1977-01-01

    It is shown that a flux of relativistic electrons from the NP 0532 pulsar magnetosphere, responsible for its synchrotron emission, cannot provide the necessary energy pumping to the Crab Nebula. A conclusion is reached that such a pumping can be effectuated by a flow of relativistic electrons leaving the NP 0532 magnetosphere at small pitch angles and giving therefore no appreciable contribution to the synchrotron emission of the pulsar. An interpretation of the Crab Nebula synchrotron spectrum is given on the assumption of secular ''softening'' of the energy spectrum of the relativistic electrons injected into the Nebula. A possibility of explanation of the observed rapid variability of some features in the central part of the Nebula by ejection of free - neutron - rich dense gas clouds from the pulsar surface during ''starquakes'' is discussed. The clouds of rather dense (nsub(e) approximately 10 7 cm -3 ) plasma, thus formed at about 10 13 cm from pulsar, will be accelerated up to relativistic velocities by the pressure of the magneto-dipole radiation of NP 0532 and will deform the magnetic field in the inner part (R 17 cm) of the Crab Nebula, that is the cause of the variability observed. In this case, favourable conditions for the acceleration of the particles in the cloud up to relativistic energies are realized; that may be an additional source of injection

  16. Strong-field relativistic processes in highly charged ions

    Energy Technology Data Exchange (ETDEWEB)

    Postavaru, Octavian

    2010-12-08

    In this thesis we investigate strong-field relativistic processes in highly charged ions. In the first part, we study resonance fluorescence of laser-driven highly charged ions in the relativistic regime by solving the time-dependent master equation in a multi-level model. Our ab initio approach based on the Dirac equation allows for investigating highly relativistic ions, and, consequently, provides a sensitive means to test correlated relativistic dynamics, bound-state quantum electrodynamic phenomena and nuclear effects by applying coherent light with x-ray frequencies. Atomic dipole or multipole moments may be determined to unprecedented accuracy by measuring the interference-narrowed fluorescence spectrum. Furthermore, we investigate the level structure of heavy hydrogenlike ions in laser beams. Interaction with the light field leads to dynamic shifts of the electronic energy levels, which is relevant for spectroscopic experiments. We apply a fully relativistic description of the electronic states by means of the Dirac equation. Our formalism goes beyond the dipole approximation and takes into account non-dipole effects of retardation and interaction with the magnetic field components of the laser beam. We predicted cross sections for the inter-shell trielectronic recombination (TR) and quadruelectronic recombination processes which have been experimentally confirmed in electron beam ion trap measurements, mainly for C-like ions, of Ar, Fe and Kr. For Kr{sup 30}+, inter-shell TR contributions of nearly 6% to the total resonant photorecombination rate were found. (orig.)

  17. Relativistic ''potential model'' for N-particle systems

    International Nuclear Information System (INIS)

    Noyes, H.P.

    1986-08-01

    Neither quantum field theory nor S-Matrix theory have a well defined procedure for going over to an approximation that can be reliably used in non-relativistic models for nuclear physics. We meet the problem here by constructing a finite particle number relativistic scattering theory for (scalar) particles and mesons using integral equations of the Faddeev-Yakubovsky type. Restricted to N particles and one meson, we can go from the relativistic theory to a ''potential theory'' in the integral equation formulation by using boundary states which do not contain the meson asymptotically. The meson-particle input amplitudes contain a pole at the particle mass, and the particle-particle input amplitudes are null. This gives unique definition (numerically calculable) to the particle-particle off-shell amplitude, and hence to the covariant ''scattering potential'' (but not to the noninvariant concept of ''potential energy''). As we have commented before, if we take these scattering amplitudes as iput for relativistic Faddeev equations, the results are identical to those obtained from the same model starting from three particles and one meson. In this paper we explore how far we can extend this relativistic ''potential model'' to higher numbers of particles and mesons. 10 refs

  18. Conductivity of a relativistic plasma

    Energy Technology Data Exchange (ETDEWEB)

    Braams, B.J.; Karney, C.F.F.

    1989-03-01

    The collision operator for a relativistic plasma is reformulated in terms of an expansion in spherical harmonics. This formulation is used to calculate the electrical conductivity. 13 refs., 1 fig., 1 tab.

  19. Relativistic description of atomic nuclei

    International Nuclear Information System (INIS)

    Krutov, V.A.

    1985-01-01

    Papers on the relativistic description of nuclei are reviewed. The Brown and Rho ''small'' bag'' model is accepted for hardrons. Meson exchange potentials of the nucleon-nucleon interaction have been considered. Then the transition from a system of two interacting nucleons has been performed to the relativistic nucleus description as a multinucleon system on the basis of OBEP (one-boson exchange potential). The proboem of OPEP (one-pion-exchange potential) inclusion to a relativistic scheme is discussed. Simplicity of calculations and attractiveness of the Walecka model for specific computations and calculations was noted. The relativistic model of nucleons interacting through ''effective'' scalar and vector boson fields was used in the Walacka model for describing neutronaand nuclear mater matters

  20. Conductivity of a relativistic plasma

    International Nuclear Information System (INIS)

    Braams, B.J.; Karney, C.F.F.

    1989-03-01

    The collision operator for a relativistic plasma is reformulated in terms of an expansion in spherical harmonics. This formulation is used to calculate the electrical conductivity. 13 refs., 1 fig., 1 tab

  1. Relativistic heavy-ion physics

    CERN Document Server

    Herrera Corral, G

    2010-01-01

    The study of relativistic heavy-ion collisions is an important part of the LHC research programme at CERN. This emerging field of research focuses on the study of matter under extreme conditions of temperature, density, and pressure. Here we present an introduction to the general aspects of relativistic heavy-ion physics. Afterwards we give an overview of the accelerator facility at CERN and then a quick look at the ALICE project as a dedicated experiment for heavy-ion collisions.

  2. Radiation dominated relativistic current sheets

    International Nuclear Information System (INIS)

    Jaroschek, C.H.

    2008-01-01

    Relativistic Current Sheets (RCS) feature plasma instabilities considered as potential key to magnetic energy dissipation and non-thermal particle generation in Poynting flux dominated plasma flows. We show in a series of kinetic plasma simulations that the physical nature of non-linear RCS evolution changes in the presence of incoherent radiation losses: In the ultra-relativistic regime (i.e. magnetization parameter sigma = 104 defined as the ratio of magnetic to plasma rest frame energy density) the combination of non-linear RCS dynamics and synchrotron emission introduces a temperature anisotropy triggering the growth of the Relativistic Tearing Mode (RTM). As direct consequence the RTM prevails over the Relativistic Drift Kink (RDK) Mode as competitive RCS instability. This is in contrast to the previously studied situation of weakly relativistic RCS (sigma ∼ 1) where the RDK is dominant and most of the plasma is thermalized. The simulations witness the typical life cycle of ultra-relativistic RCS evolving from a violent radiation induced collapse towards a radiation quiescent state in rather classical Sweet-Parker topology. Such a transition towards Sweet-Parker configuration in the late non-linear evolution has immediate consequences for the efficiency of magnetic energy dissipation and non-thermal particle generation. Ceasing dissipation rates directly affect our present understanding of non-linear RCS evolution in conventional striped wind scenarios. (author)

  3. Radiative electron capture studied in relativistic heavy-ion atom collisions

    International Nuclear Information System (INIS)

    Stoehlker, T.; Kozhuharov, C.; Mokler, P.H.; Warczak, A.; Bosch, F.; Geissel, H.; Moshammer, R.; Scheidenberger, C.; Eichler, J.; Shirai, T.; Stachura, Z.; Rymuza, P.

    1994-08-01

    The process of Radiative Electron Capture (REC) in relativistic collisions of high-Z ions with low-Z gaseous and solid targets is studied experimentally and theoretically. The observed X-ray spectra are analysed with respect to photon angular distributions as well as to total K-REC cross sections. The experimental results for angle-differential cross sections are well-reproduced by exact relativistic calculations which yield significant deviations from standard sin 2 θ distributions. Total cross sections for K-REC are shown to follow a simple scaling rule obtained from exact relativistic calculations as well as from a non-relativistic dipole approximation. The agreement between these different theoretical approaches must be regarded as fortuitous, but it lends support to the use of the non-relativistic approach for practical purposes. (orig.)

  4. Pramana – Journal of Physics | Indian Academy of Sciences

    Indian Academy of Sciences (India)

    pp 815-826 Research Articles. Soliton dynamics in a modified Yakushevich model · P C Dash M Panigrahi · More Details Fulltext PDF. pp 827-839 Research Articles. Shape change in Hf, W and Os-isotopes: A non-relativistic Hartree-Fock versus relativistic Hartree approximation · Z Naik B K Sharma T K Jha P Arumugam ...

  5. 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.

  6. 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.

  7. 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.

  8. Relativistic theory of gravitation

    International Nuclear Information System (INIS)

    Logunov, A.A.; Mestvirishvili, M.A.

    1986-01-01

    In the present paper a relativistic theory of gravitation (RTG) is unambiguously constructed on the basis of the special relativity and geometrization principle. In this a gravitational field is treated as the Faraday--Maxwell spin-2 and spin-0 physical field possessing energy and momentum. The source of a gravitational field is the total conserved energy-momentum tensor of matter and of a gravitational field in Minkowski space. In the RTG the conservation laws are strictly fulfilled for the energy-moment and for the angular momentum of matter and a gravitational field. The theory explains the whole available set of experiments on gravity. By virtue of the geometrization principle, the Riemannian space in our theory is of field origin, since it appears as an effective force space due to the action of a gravitational field on matter. The RTG leads to an exceptionally strong prediction: The universe is not closed but just ''flat.'' This suggests that in the universe a ''missing mass'' should exist in a form of matter

  9. Relativistic theory of gravitation

    International Nuclear Information System (INIS)

    Logunov, A.A.; Mestvirishvilli, M.A.

    1985-01-01

    In the present paper a relativistic theory of gravitation (RTG) is constructed in a unique way on the basis of the special relativity and geometrization principle. In this, a gravitational field is treated as the Faraday-Maxwell spin-2 and spin-0 physical field possessing energy and momentum. The source of a gravitational field is the total conserved energy-momentum tensor of matter and of a gravitational field in Minkowski space. In the RTG, the conservation laws are strictly fulfilled for the energy-momentum and for the angular momentum of matter and a gravitational field. The theory explains the whole available set of experiments on gravitation. In virtue of the geometrization principle, the Riemannian space in our theory is of field origin, since it appears as an effective force space due to the action of a gravitational field on matter. The RTg leads to an exceptionally strong prediction: The Universe is not closed but just ''flat''. This suggests that in the Universe a ''hidden mass'' should exist in some form of matter

  10. Relativistic gravitation theory

    International Nuclear Information System (INIS)

    Logunov, A.A.; Mestvirishvili, M.A.

    1984-01-01

    On the basis of the special relativity and geometrization principle a relativistic gravitation theory (RGT) is unambiguously constructed with the help of a notion of a gravitational field as a physical field in Faraday-Maxwell spirit, which posesses energy momentum and spins 2 and 0. The source of gravitation field is a total conserved energy-momentum tensor for matter and for gravitation field in Minkowski space. In the RGT conservation laws for the energy momentum and angular momentum of matter and gravitational field hold rigorously. The theory explains the whole set of gravitation experiments. Here, due to the geometrization principle the Riemannian space is of a field origin since this space arises effectively as a result of the gravitation field origin since this space arises effectively as a result of the gravitation field action on the matter. The RGT astonishing prediction is that the Universe is not closed but ''flat''. It means that in the Universe there should exist a ''missing'' mass in some form of matter

  11. 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

  12. Global existence of solutions to the Cauchy problem for time-dependent Hartree equations

    International Nuclear Information System (INIS)

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

    1975-01-01

    The existence of global solutions to the Cauchy problem for time-dependent Hartree equations for N electrons is established. The solution is shown to have a uniformly bounded H 1 (R 3 ) norm and to satisfy an estimate of the form two parallel PSI (t) two parallel/sub H 2 ; less than or equal to c exp(kt). It is shown that ''negative energy'' solutions do not converge uniformly to zero as t → infinity. (U.S.)

  13. 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.

  14. 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.

  15. 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)

  16. 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.)

  17. 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

  18. 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)

  19. 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

  20. 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

  1. Relativistic positioning systems: perspectives and prospects

    Science.gov (United States)

    Coll Bartolomé

    2013-11-01

    Relativistic positioning systems are interesting technical objects for applications around the Earth and in the Solar system. But above all else, they are basic scientific objects allowing developing relativity from its own concepts. Some past and future features of relativistic positioning sys- tems, with special attention to the developments that they suggest for an epistemic relativity (relativistic experimental approach to physics), are analyzed. This includes relativistic stereometry, which, together with relativistic positioning systems, allows to introduce the general relativistic notion of (finite) laboratory (space-time region able to perform experiments of finite size).

  2. Newtonian hydrodynamic equations with relativistic pressure and velocity

    Energy Technology Data Exchange (ETDEWEB)

    Hwang, Jai-chan [Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu 702-701 (Korea, Republic of); Noh, Hyerim [Korea Astronomy and Space Science Institute, Daejeon 305-348 (Korea, Republic of); Fabris, Júlio; Piattella, Oliver F.; Zimdahl, Winfried, E-mail: jchan@knu.ac.kr, E-mail: hr@kasi.re.kr, E-mail: fabris@pq.cnpq.br, E-mail: oliver.piattella@pq.cnpq.br, E-mail: winfried.zimdahl@pq.cnpq.br [Departamento de Fisica, Universidade Federal do Espirito Santo, Vitória (Brazil)

    2016-07-01

    We present a new approximation to include fully general relativistic pressure and velocity in Newtonian hydrodynamics. The energy conservation, momentum conservation and two Poisson's equations are consistently derived from Einstein's gravity in the zero-shear gauge assuming weak gravity and action-at-a-distance limit. The equations show proper special relativity limit in the absence of gravity. Our approximation is complementary to the post-Newtonian approximation and the equations are valid in fully nonlinear situations.

  3. Current status of relativistic core collapse simulations

    Energy Technology Data Exchange (ETDEWEB)

    Font, Jose A [Departamento de Astronomia y Astrofisica, Universidad de Valencia, Dr. Moliner 50, 46100 Burjassot (Valencia) (Spain)

    2007-05-15

    With the first generation of ground-based gravitational wave laser interferometers already taking data, the availability of reliable waveform templates from astrophysical sources, which may help extract the signal from the anticipated noisy data, is urgently required. Gravitational stellar core collapse supernova has traditionally been considered among the most important astrophysical sources of potentially detectable gravitational radiation. Only very recently the first multidimensional simulations of relativistic rotational core collapse have been possible (albeit for models with simplified input physics), thanks to the use of conservative formulations of the hydrodynamics equations and advanced numerical methodology, as well as stable formulations of Einstein's equations. In this paper, the current status of relativistic core collapse simulations is discussed, with the emphasis given to the modelling of the collapse dynamics and to the computation of the gravitational radiation in the existing numerical approaches. Work employing the conformally-flat approximation (CFC) of the 3+1 Einstein's equations is reported, as well as extensions of this approximation (CFC+) and investigations within the framework of the so-called BSSN formulation of the 3+1 gravitational field equations (with no approximation for the spacetime dynamics). On the other hand, the incorporation of magnetic fields and the MHD equations in numerical codes to improve the realism of core collapse simulations in general relativity, is currently an emerging field where significant progress is bound to be soon achieved. The paper also contains a brief discussion of magneto-rotational simulations of core collapse, aiming at addressing the effects of magnetic fields on the collapse dynamics and on the gravitational waveforms.

  4. Current status of relativistic core collapse simulations

    International Nuclear Information System (INIS)

    Font, Jose A

    2007-01-01

    With the first generation of ground-based gravitational wave laser interferometers already taking data, the availability of reliable waveform templates from astrophysical sources, which may help extract the signal from the anticipated noisy data, is urgently required. Gravitational stellar core collapse supernova has traditionally been considered among the most important astrophysical sources of potentially detectable gravitational radiation. Only very recently the first multidimensional simulations of relativistic rotational core collapse have been possible (albeit for models with simplified input physics), thanks to the use of conservative formulations of the hydrodynamics equations and advanced numerical methodology, as well as stable formulations of Einstein's equations. In this paper, the current status of relativistic core collapse simulations is discussed, with the emphasis given to the modelling of the collapse dynamics and to the computation of the gravitational radiation in the existing numerical approaches. Work employing the conformally-flat approximation (CFC) of the 3+1 Einstein's equations is reported, as well as extensions of this approximation (CFC+) and investigations within the framework of the so-called BSSN formulation of the 3+1 gravitational field equations (with no approximation for the spacetime dynamics). On the other hand, the incorporation of magnetic fields and the MHD equations in numerical codes to improve the realism of core collapse simulations in general relativity, is currently an emerging field where significant progress is bound to be soon achieved. The paper also contains a brief discussion of magneto-rotational simulations of core collapse, aiming at addressing the effects of magnetic fields on the collapse dynamics and on the gravitational waveforms

  5. μ- and tau-pair production from relativistic heavy-ion collisions

    International Nuclear Information System (INIS)

    Bottcher, C.; Strayer, M.R.

    1986-01-01

    The question is addressed of μ- and tau-pair production from the motional Coulomb fields available at the new relativistic heavy-ion accelerators. A semiclassical field theory is developed which is appropriate for families of leptons which are coupled electromagnetically. The field equations are mapped on to a lattice of collocation points using basis spline methods, and techniques for solving the resulting lattice equations are outlined. The properties of the transverse electromagnetic field near the heavy-ion beam are examined and physical arguments are given as to the feasibility of pair creation under a variety of circumstances. Using the Dirac-Hartree equations developed in part one, we shall dynamically evolve the vacuum, using the appropriate fields, and compute μ-pair and tau-pair production cross sections. 16 refs., 10 figs

  6. Relativistic corrections to one-particle neutron levels in the harmonic oscillator well

    International Nuclear Information System (INIS)

    Yanavichyus, A.I.

    1983-01-01

    Relativistic corrections to mass and potential energy for one-particle levels in the harmonic oscillator well are calculated in the first approximation of the perturbation theory. These corrections are, mainly negliqible, but they sharply increase with growth of the head and orbital quantum numbers. For the state 1s the relativistic correction is of the order of 0.01 MeV, and for 3p it is equal to 0.4 MeV. Thus, the relativistic correction for certain states approaches the energy of spin-orbital interactions and it should be taken into account in calculating the energy of one-particle levels

  7. Relativistic theory of gravity

    International Nuclear Information System (INIS)

    Logunov, A.A.; Mestvirishvili, M.A.

    1985-01-01

    This work presents an unambiguous construction of the relativistic theory of gravity (RTG) in the framework of relativity and the geometrization principle. The gauge principle has been formulated, and the Lagrangian density of the gravitational field has thus been constructed. This theory explains the totality of the available experimental data on the solar system and predicts the existence of gravitational waves of the Faraday-Maxwell type. According to the RTG, the Universe is infinite and ''flat'', hence it follows that its matter density should be equal to its critical density. Therefore, an appreciable ''hidden mass'' exceeding the presently observed mass of the matter almost 40-fold should exist in the Universe in some form of the matter or other. In accordance with the RTG, a massive body having a finite density ceases to contract under gravitational forces within a finite interval of proper time. From the viewpoint of an external reference frame, the brightness of the body decreases exponentially (it is getting darker), but nothing extraordinary happens in this case because its density always remains finite and, for example, for a body with the mass of about 10 8 M 0 it is equal to 2 g/cm 3 . That is why it follows from the RTG that there could be no object whatsoever (black holes) in which gravitational collapse of matter develops to an infinite density. As has been shown, the presence of a cosmological term necessarily requires the introduction of a term with an explicit dependence on the Minkowski metrics. For the long-range gravitational forces the cosmological constant vanishes

  8. Radiatively driven relativistic spherical winds under relativistic radiative transfer

    Science.gov (United States)

    Fukue, J.

    2018-05-01

    We numerically investigate radiatively driven relativistic spherical winds from the central luminous object with mass M and luminosity L* under Newtonian gravity, special relativity, and relativistic radiative transfer. We solve both the relativistic radiative transfer equation and the relativistic hydrodynamical equations for spherically symmetric flows under the double-iteration processes, to obtain the intensity and velocity fields simultaneously. We found that the momentum-driven winds with scattering are quickly accelerated near the central object to reach the terminal speed. The results of numerical solutions are roughly fitted by a relation of \\dot{m}=0.7(Γ _*-1)\\tau _* β _* β _out^{-2.6}, where \\dot{m} is the mass-loss rate normalized by the critical one, Γ* the central luminosity normalized by the critical one, τ* the typical optical depth, β* the initial flow speed at the central core of radius R*, and βout the terminal speed normalized by the speed of light. This relation is close to the non-relativistic analytical solution, \\dot{m} = 2(Γ _*-1)\\tau _* β _* β _out^{-2}, which can be re-expressed as β _out^2/2 = (Γ _*-1)GM/c^2 R_*. That is, the present solution with small optical depth is similar to that of the radiatively driven free outflow. Furthermore, we found that the normalized luminosity (Eddington parameter) must be larger than unity for the relativistic spherical wind to blow off with intermediate or small optical depth, i.e. Γ _* ≳ \\sqrt{(1+β _out)^3/(1-β _out)}. We briefly investigate and discuss an isothermal wind.

  9. Relativistic numerical cosmology with silent universes

    Science.gov (United States)

    Bolejko, Krzysztof

    2018-01-01

    Relativistic numerical cosmology is most often based either on the exact solutions of the Einstein equations, or perturbation theory, or weak-field limit, or the BSSN formalism. The silent universe provides an alternative approach to investigate relativistic evolution of cosmological systems. The silent universe is based on the solution of the Einstein equations in 1  +  3 comoving coordinates with additional constraints imposed. These constraints include: the gravitational field is sourced by dust and cosmological constant only, both rotation and magnetic part of the Weyl tensor vanish, and the shear is diagnosable. This paper describes the code simsilun (free software distributed under the terms of the reposi General Public License), which implements the equations of the silent universe. The paper also discusses applications of the silent universe and it uses the Millennium simulation to set up the initial conditions for the code simsilun. The simulation obtained this way consists of 16 777 216 worldlines, which are evolved from z  =  80 to z  =  0. Initially, the mean evolution (averaged over the whole domain) follows the evolution of the background ΛCDM model. However, once the evolution of cosmic structures becomes nonlinear, the spatial curvature evolves from ΩK =0 to ΩK ≈ 0.1 at the present day. The emergence of the spatial curvature is associated with ΩM and Ω_Λ being smaller by approximately 0.05 compared to the ΛCDM.

  10. Relativistic direct interaction and hadron models

    International Nuclear Information System (INIS)

    Biswas, T.

    1984-01-01

    Direct interaction theories at a nonrelativistic level have been used successfully in several areas earlier (e.g. nuclear physics). But for hadron spectroscopy relativistic effects are important and hence the need for a relativistic direct interaction theory arises. It is the goal of this thesis to suggest such a theory which has the simplicity and the flexibility required for phenomenological model building. In general the introduction of relativity in a direct interaction theory is shown to be non-trivial. A first attempt leads to only an approximate form for allowed interactions. Even this is far too complex for phenomenological applicability. To simplify the model an extra spacelike particle called the vertex is introduced in any set of physical (timelike) particles. The vertex model is successfully used to fit and to predict experimental data on hadron spectra, γ and psi states fit very well with an interaction function inspired by QCD. Light mesons also fit reasonably well. Better forms of hyperfine interaction functions would be needed to improve the fitting of light mesons. The unexpectedly low pi meson mass is partially explained. Baryon ground states are fitted with unprecedented accuracy with very few adjustable parameters. For baryon excited states it is shown that better QCD motivated interaction functions are needed for a fit. Predictions for bb states in e + e - experiments are made to assist current experiments

  11. Scattering in relativistic particle mechanics

    International Nuclear Information System (INIS)

    De Bievre, S.

    1986-01-01

    The problem of direct interaction in relativistic particle mechanics has been extensively studied and a variety of models has been proposed avoiding the conclusions of the so-called no-interaction theorems. In this thesis the authors studied scattering in the relativistic two-body problem. He uses the results to analyze gauge invariance in Hamiltonian constraint models and the uniqueness of the symplectic structure in manifestly covariant relativistic particle mechanics. A general geometric framework that underlies approaches to relativistic particle mechanics is presented and the kinematic properties of the scattering transformation, i.e., those properties that arise solely from the invariance of the theory under the Poincare group are studied. The second part of the analysis of the relativistic two-body scattering problem is devoted to the dynamical properties of the scattering process. Using general geometric arguments, gauge invariance of the scattering transformation in the Todorov-Komar Hamiltonian constraint model is proved. Finally, quantization of the models is discussed

  12. Relativistic two-fermion equations with form factors and anomalous magnetic moment interactions

    International Nuclear Information System (INIS)

    Ahmed, S.

    1977-04-01

    Relativistic equations for two-fermion systems are derived from quantum field theory taking into account the form factors of the particles. When the q 2 dependence of the form factors is disregarded, in the static approximation, the two-fermion equations with Coulomb and anomalous magnetic moment interactions are obtained. Separating the angular variables, a sixteen-component relativistic radial equation are finally given

  13. K-Vacancy Production in the Collision of Highly Charged Relativistic Ions With Heavy Atoms

    OpenAIRE

    KHABIBULLAEV, P. K.

    2014-01-01

    A general expression for the cross section of the inelastic collision of relativistic highly charged ion with heavy (relativistic) atoms is obtained using the generalized eikonal approximation. In the ultrarelativistic limit, the obtained formula coincides with a known exact one. As an application of the obtained result, probability and cross section of the K-vacany production in the U92+ - U91+ collision are calculated.

  14. Finite pt contribution to relativistic Coulomb excitation: A possible explanation for the clean fission puzzle

    International Nuclear Information System (INIS)

    Galetti, D.; Kodama, T.; Nemes, M.C.

    1986-10-01

    The quantum relativistic Coulomb excitation process including reccil effects is studied in the plane wave Born approximation. Quantum and relativistic recoil effects allow for relatively large transverse momentum transfers, usually neglected. This specific feature is shown to modify the angular distribution of Coulomb induced fission fragmentation in an essential manner. In contrast with usual treatments it is found that these results compare favourably with recent data. (Authors) [pt

  15. Relativistic approach to the near-threshold phenomena in the nucleon-antinucleon interactions

    International Nuclear Information System (INIS)

    Shapiro, I.S.; Smirnov, A.V.

    1997-01-01

    It is shown that the strongest (∝r -3 ) singularities at small interparticle distances, arising from the spin-tensor forces in the standard nonrelativistic one-boson-exchange (OBE) potentials, disappear in the relativistic treatment of the NN- and NN-interactions. The partial wave analysis is performed in the framework of a relativistic OBE quasipotential model, and the results are compared with those obtained in the nonrelativistic approximation. (orig.)

  16. Quantum Geometry: Relativistic energy approach to cooperative electron-nucleary-transition spectrum

    Directory of Open Access Journals (Sweden)

    Ольга Юрьевна Хецелиус

    2014-11-01

    Full Text Available An advanced relativistic energy approach is presented and applied to calculating parameters of electron-nuclear 7-transition spectra of nucleus in the atom. The intensities of the spectral satellites are defined in the relativistic version of the energy approach (S-matrix formalism, and gauge-invariant quantum-electrodynamical perturbation theory with the Dirac-Kohn-Sham density-functional zeroth approximation.

  17. Relativistic density functional theory with picture-change corrected electron density based on infinite-order Douglas-Kroll-Hess method

    Science.gov (United States)

    Oyama, Takuro; Ikabata, Yasuhiro; Seino, Junji; Nakai, Hiromi

    2017-07-01

    This Letter proposes a density functional treatment based on the two-component relativistic scheme at the infinite-order Douglas-Kroll-Hess (IODKH) level. The exchange-correlation energy and potential are calculated using the electron density based on the picture-change corrected density operator transformed by the IODKH method. Numerical assessments indicated that the picture-change uncorrected density functional terms generate significant errors, on the order of hartree for heavy atoms. The present scheme was found to reproduce the energetics in the four-component treatment with high accuracy.

  18. RPA correlations and nuclear densities in relativistic mean field approach

    International Nuclear Information System (INIS)

    Van Giai, N.; Liang, H.Z.; Meng, J.

    2007-02-01

    The relativistic mean field approach (RMF) is well known for describing accurately binding energies and nucleon distributions in atomic nuclei throughout the nuclear chart. The random phase approximation (RPA) built on top of the RMF is also a good framework for the study of nuclear excitations. Here, we examine the consequences of long range correlations brought about by the RPA on the neutron and proton densities as given by the RMF approach. (authors)

  19. Relativistic scattering theory of two charged spinless particles

    International Nuclear Information System (INIS)

    Alt, E.O.; Hannemann

    1985-01-01

    In the framework of a relativistic quantum mechanics, the authors calculate for two spinless particles with Coulomb interaction exactly the partial-wave S-matrix and the full scattering amplitude. From the former they can extract the exact binding energies which, when expanded in powers of α, reproduce in the hydrogenic case the fourth-order result of a previous study. In the weak field limit, the latter coincides with the amplitude derived by another study from QED in eikonal approximation

  20. Relativistic theory of the Lamb shift based on self energy

    International Nuclear Information System (INIS)

    Barut, A.O.; Salamin, Y.I.

    1987-07-01

    A study is made to evaluate the Lamb shift to all orders in (Zα) using relativistic Dirac Coulomb wavefunctions and without resorting to the dipole approximation. Use is made of the angular integrals and spins sums performed elsewhere exactly. A regularization procedure is given that makes the sum over the positive and negative energy states finite. Finally, the energy shift ΔE n LS is given in terms of an integral that may be done numerically. (author). 19 refs

  1. Scale-relativistic cosmology

    International Nuclear Information System (INIS)

    Nottale, Laurent

    2003-01-01

    The principle of relativity, when it is applied to scale transformations, leads to the suggestion of a generalization of fundamental dilations laws. These new special scale-relativistic resolution transformations involve log-Lorentz factors and lead to the occurrence of a minimal and of a maximal length-scale in nature, which are invariant under dilations. The minimal length-scale, that replaces the zero from the viewpoint of its physical properties, is identified with the Planck length l P , and the maximal scale, that replaces infinity, is identified with the cosmic scale L=Λ -1/2 , where Λ is the cosmological constant.The new interpretation of the Planck scale has several implications for the structure and history of the early Universe: we consider the questions of the origin, of the status of physical laws at very early times, of the horizon/causality problem and of fluctuations at recombination epoch.The new interpretation of the cosmic scale has consequences for our knowledge of the present universe, concerning in particular Mach's principle, the large number coincidence, the problem of the vacuum energy density, the nature and the value of the cosmological constant. The value (theoretically predicted ten years ago) of the scaled cosmological constant Ω Λ =0.75+/-0.15 is now supported by several different experiments (Hubble diagram of Supernovae, Boomerang measurements, gravitational lensing by clusters of galaxies).The scale-relativity framework also allows one to suggest a solution to the missing mass problem, and to make theoretical predictions of fundamental energy scales, thanks to the interpretation of new structures in scale space: fractal/classical transitions as Compton lengths, mass-coupling relations and critical value 4π 2 of inverse couplings. Among them, we find a structure at 3.27+/-0.26x10 20 eV, which agrees closely with the observed highest energy cosmic rays at 3.2+/-0.9x10 20 eV, and another at 5.3x10 -3 eV, which corresponds to the

  2. Methods in relativistic nuclear physics

    International Nuclear Information System (INIS)

    Danos, M.; Gillet, V.; Cauvin, M.

    1984-01-01

    This book is intended to provide the methods and tools for performing actual calculations for finite many-body systems of bound relativistic constituent particles. The aim is to cover thoroughly the methodological aspects of the relativistic many-body problem for bound states while avoiding the presentation of specific models. The many examples contained in the later part of the work are meant to give concrete illustrations of how to actually apply the methods which are given in the first part. The basic framework of the approach is the lagrangian field theory solved in the time-independent Schroedinger picture. (Auth.)

  3. Frontiers in relativistic celestial mechanics

    CERN Document Server

    2014-01-01

    Relativistic celestial mechanics – investigating the motion celestial bodies under the influence of general relativity – is a major tool of modern experimental gravitational physics. With a wide range of prominent authors from the field, this two-volume series consists of reviews on a multitude of advanced topics in the area of relativistic celestial mechanics – starting from more classical topics such as the regime of asymptotically-flat spacetime, light propagation and celestial ephemerides, but also including its role in cosmology and alternative theories of gravity as well as modern experiments in this area.

  4. Superheavy nuclei: a relativistic mean field outlook

    International Nuclear Information System (INIS)

    Afanasjev, A.V.

    2006-01-01

    The analysis of quasi-particle spectra in the heaviest A∼250 nuclei with spectroscopic data provides an additional constraint for the choice of effective interaction for the description of superheavy nuclei. It strongly suggests that only the parametrizations which predict Z = 120 and N = 172 as shell closures are reliable for superheavy nuclei within the relativistic mean field theory. The influence of the central depression in the density distribution of spherical superheavy nuclei on the shell structure is studied. A large central depression produces large shell gaps at Z = 120 and N = 172. The shell gaps at Z = 126 and N = 184 are favoured by a flat density distribution in the central part of the nucleus. It is shown that approximate particle number projection (PNP) by means of the Lipkin-Nogami (LN) method removes pairing collapse seen at these gaps in the calculations without PNP

  5. Dielectric response of planar relativistic quantum plasmas

    International Nuclear Information System (INIS)

    Bardos, D.C.; Frankel, N.E.

    1991-01-01

    The dielectric response of planar relativistic charged particle-antiparticle plasmas is investigated, treating Fermi and Bose plasmas. The conductivity tensor in each case is derived in the self-consistent Random Phase Approximation. The tensors are then evaluated at zero temperature for the case of no external fields, leading to explicit dispersion relations for the electrodynamic modes of the plasma. The longitudinal and transverse modes are in general coupled for plasma layers. This coupling vanishes, however, in the zero field case, allowing 'effective' longitudinal and transverse dielectric functions to be defined in terms of components of the conductivity tensor. Solutions to the longitudinal mode equations (i.e. plasmon modes) are exhibited, while purely transverse modes are found not to exist. In the case of the Bose plasma the screening of a test charge is investigated in detail. 41 refs., 1 fig

  6. Multiwavelength Observations of Relativistic Jets from General Relativistic Magnetohydrodynamic Simulations

    Directory of Open Access Journals (Sweden)

    Richard Anantua

    2018-03-01

    Full Text Available This work summarizes a program intended to unify three burgeoning branches of the high-energy astrophysics of relativistic jets: general relativistic magnetohydrodynamic (GRMHD simulations of ever-increasing dynamical range, the microphysical theory of particle acceleration under relativistic conditions, and multiwavelength observations resolving ever-decreasing spatiotemporal scales. The process, which involves converting simulation output into time series of images and polarization maps that can be directly compared to observations, is performed by (1 self-consistently prescribing models for emission, absorption, and particle acceleration and (2 performing time-dependent polarized radiative transfer. M87 serves as an exemplary prototype for this investigation due to its prominent and well-studied jet and the imminent prospect of learning much more from Event Horizon Telescope (EHT observations this year. Synthetic observations can be directly compared with real observations for observational signatures such as jet instabilities, collimation, relativistic beaming, and polarization. The simplest models described adopt the standard equipartition hypothesis; other models calculate emission by relating it to current density or shear. These models are intended for application to the radio jet instead of the higher frequency emission, the disk and the wind, which will be subjects of future investigations.

  7. Apparent unambiguousness of relativistic time dilation

    International Nuclear Information System (INIS)

    Strel'tsov, V.N.

    1992-01-01

    It is indicated on the definite analogy between the dependence of visible sizes of relativistic objects and period of the wave, emitted by the moving source from the observation conditions ('retradition factor'). It is noted that the definition of time for moving extended objects, led to relativistic dilation, corresponds to the definition of the relativistic (radar) length led to the 'elongation formula'. 10 refs

  8. Relativistic generalization of strong plasma turbulence

    International Nuclear Information System (INIS)

    Chian, A.C.-L.

    1982-01-01

    Two fundamental electrostatic modes of an unmagnetized plasma, namely, ion acoustic mode and Langumir mode are studied. Previous theories are generalized to include the effect of relativistic mass variations. The existence of relativistic ion acoustic solitons is demonstrated. In addition, it is shown that simple, relativistic Langumir solitons do not exist in a infinite plasma. (L.C.) [pt

  9. Quantum gates via relativistic remote control

    Energy Technology Data Exchange (ETDEWEB)

    Martín-Martínez, Eduardo, E-mail: emartinm@uwaterloo.ca [Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, N2L 3G1 (Canada); Dept. Applied Math., University of Waterloo, Ontario, N2L 3G1 (Canada); Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5 (Canada); Sutherland, Chris [Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, N2L 3G1 (Canada)

    2014-12-12

    We harness relativistic effects to gain quantum control on a stationary qubit in an optical cavity by controlling the non-inertial motion of a different probe atom. Furthermore, we show that by considering relativistic trajectories of the probe, we enhance the efficiency of the quantum control. We explore the possible use of these relativistic techniques to build 1-qubit quantum gates.

  10. Modulated Pade approximant

    International Nuclear Information System (INIS)

    Ginsburg, C.A.

    1980-01-01

    In many problems, a desired property A of a function f(x) is determined by the behaviour of f(x) approximately equal to g(x,A) as x→xsup(*). In this letter, a method for resuming the power series in x of f(x) and approximating A (modulated Pade approximant) is presented. This new approximant is an extension of a resumation method for f(x) in terms of rational functions. (author)

  11. Collapse of the random-phase approximation: Examples and counter-examples from the shell model

    International Nuclear Information System (INIS)

    Johnson, Calvin W.; Stetcu, Ionel

    2009-01-01

    The Hartree-Fock approximation to the many-fermion problem can break exact symmetries, and in some cases by changing a parameter in the interaction one can drive the Hartree-Fock minimum from a symmetry-breaking state to a symmetry-conserving state (also referred to as a 'phase transition' in the literature). The order of the transition is important when one applies the random-phase approximation (RPA) to the of the Hartree-Fock wave function: if first order, RPA is stable through the transition, but if second-order, then the RPA amplitudes become large and lead to unphysical results. The latter is known as 'collapse' of the RPA. While the difference between first- and second-order transitions in the RPA was first pointed out by Thouless, we present for the first time nontrivial examples of both first- and second-order transitions in a uniform model, the interacting shell-model, where we can compare to exact numerical results.

  12. Proof of the Spin Statistics Connection 2: Relativistic Theory

    Science.gov (United States)

    Santamato, Enrico; De Martini, Francesco

    2017-12-01

    The traditional standard theory of quantum mechanics is unable to solve the spin-statistics problem, i.e. to justify the utterly important "Pauli Exclusion Principle" but by the adoption of the complex standard relativistic quantum field theory. In a recent paper (Santamato and De Martini in Found Phys 45(7):858-873, 2015) we presented a proof of the spin-statistics problem in the nonrelativistic approximation on the basis of the "Conformal Quantum Geometrodynamics". In the present paper, by the same theory the proof of the spin-statistics theorem is extended to the relativistic domain in the general scenario of curved spacetime. The relativistic approach allows to formulate a manifestly step-by-step Weyl gauge invariant theory and to emphasize some fundamental aspects of group theory in the demonstration. No relativistic quantum field operators are used and the particle exchange properties are drawn from the conservation of the intrinsic helicity of elementary particles. It is therefore this property, not considered in the standard quantum mechanics, which determines the correct spin-statistics connection observed in Nature (Santamato and De Martini in Found Phys 45(7):858-873, 2015). The present proof of the spin-statistics theorem is simpler than the one presented in Santamato and De Martini (Found Phys 45(7):858-873, 2015), because it is based on symmetry group considerations only, without having recourse to frames attached to the particles. Second quantization and anticommuting operators are not necessary.

  13. Big Data Meets Quantum Chemistry Approximations: The Δ-Machine Learning Approach.

    Science.gov (United States)

    Ramakrishnan, Raghunathan; Dral, Pavlo O; Rupp, Matthias; von Lilienfeld, O Anatole

    2015-05-12

    Chemically accurate and comprehensive studies of the virtual space of all possible molecules are severely limited by the computational cost of quantum chemistry. We introduce a composite strategy that adds machine learning corrections to computationally inexpensive approximate legacy quantum methods. After training, highly accurate predictions of enthalpies, free energies, entropies, and electron correlation energies are possible, for significantly larger molecular sets than used for training. For thermochemical properties of up to 16k isomers of C7H10O2 we present numerical evidence that chemical accuracy can be reached. We also predict electron correlation energy in post Hartree-Fock methods, at the computational cost of Hartree-Fock, and we establish a qualitative relationship between molecular entropy and electron correlation. The transferability of our approach is demonstrated, using semiempirical quantum chemistry and machine learning models trained on 1 and 10% of 134k organic molecules, to reproduce enthalpies of all remaining molecules at density functional theory level of accuracy.

  14. Quantum mechanics of the fractional-statistics gas: Random-phase approximation

    International Nuclear Information System (INIS)

    Dai, Q.; Levy, J.L.; Fetter, A.L.; Hanna, C.B.; Laughlin, R.B.

    1992-01-01

    A description of the fractional-statistics gas based on the complete summation of Hartree, Fock, ladder and bubble diagrams is presented. The superfluid properties identified previously in the random-phase-approximation (RPA) calculation of Fetter, Hanna, and Laughlin [Phys. Rev. B 39, 9679 (1989)] are substantially confirmed. The discrepancy between the RPA sound speed and the Hartree-Fock bulk modulus is found to be eliminated. The unusual Hall-effect behavior is found to vanish for the Bose gas test case but not for the fractional-statistics gas, implying that it is physically correct. Excellent agreement is obtained with the collective-mode dispersion obtained numerically by Xie, He, and Das Sarma [Phys. Rev. Lett. 65, 649 (1990)

  15. When Density Functional Approximations Meet Iron Oxides.

    Science.gov (United States)

    Meng, Yu; Liu, Xing-Wu; Huo, Chun-Fang; Guo, Wen-Ping; Cao, Dong-Bo; Peng, Qing; Dearden, Albert; Gonze, Xavier; Yang, Yong; Wang, Jianguo; Jiao, Haijun; Li, Yongwang; Wen, Xiao-Dong

    2016-10-11

    Three density functional approximations (DFAs), PBE, PBE+U, and Heyd-Scuseria-Ernzerhof screened hybrid functional (HSE), were employed to investigate the geometric, electronic, magnetic, and thermodynamic properties of four iron oxides, namely, α-FeOOH, α-Fe 2 O 3 , Fe 3 O 4 , and FeO. Comparing our calculated results with available experimental data, we found that HSE (a = 0.15) (containing 15% "screened" Hartree-Fock exchange) can provide reliable values of lattice constants, Fe magnetic moments, band gaps, and formation energies of all four iron oxides, while standard HSE (a = 0.25) seriously overestimates the band gaps and formation energies. For PBE+U, a suitable U value can give quite good results for the electronic properties of each iron oxide, but it is challenging to accurately get other properties of the four iron oxides using the same U value. Subsequently, we calculated the Gibbs free energies of transformation reactions among iron oxides using the HSE (a = 0.15) functional and plotted the equilibrium phase diagrams of the iron oxide system under various conditions, which provide reliable theoretical insight into the phase transformations of iron oxides.

  16. 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.

  17. 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.

  18. Instability in relativistic nuclear matter

    International Nuclear Information System (INIS)

    Tezuka, Hirokazu.

    1979-11-01

    The stability of the Fermi gas state in the nuclear matter which satisfies the saturation property is considered relativistically. It is shown that the Fermi gas state is stable at very low density and at high density, but it is unstable for density fluctuation in the intermediate density region including the normal density. (author)

  19. Cyberinfrastructure for Computational Relativistic Astrophysics

    OpenAIRE

    Ott, Christian

    2012-01-01

    Poster presented at the NSF Office of Cyberinfrastructure CyberBridges CAREER PI workshop. This poster discusses the computational challenges involved in the modeling of complex relativistic astrophysical systems. The Einstein Toolkit is introduced. It is an open-source community infrastructure for numerical relativity and computational astrophysics.

  20. Future relativistic heavy ion experiments

    International Nuclear Information System (INIS)

    Pugh, H.G.

    1980-12-01

    Equations of state for nuclear matter and ongoing experimental studies are discussed. Relativistic heavy ion physics is the only opportunity to study in the laboratory the properties of extended multiquark systems under conditions such that quarks might run together into new arrangements previously unobserved. Several lines of further study are mentioned

  1. A relativistic radiation transfer benchmark

    International Nuclear Information System (INIS)

    Munier, A.

    1988-01-01

    We use the integral form of the radiation transfer equation in an one dimensional slab to determine the time-dependent propagation of the radiation energy, flux and pressure in a collisionless homogeneous medium. First order v/c relativistic terms are included and the solution is given in the fluid frame and the laboratory frame

  2. Fundamental length and relativistic length

    International Nuclear Information System (INIS)

    Strel'tsov, V.N.

    1988-01-01

    It si noted that the introduction of fundamental length contradicts the conventional representations concerning the contraction of the longitudinal size of fast-moving objects. The use of the concept of relativistic length and the following ''elongation formula'' permits one to solve this problem

  3. Sparse approximation with bases

    CERN Document Server

    2015-01-01

    This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications.  The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...

  4. 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

  5. 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.)

  6. 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.

  7. 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

  8. 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)

  9. 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

  10. 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.

  11. Approximate symmetries of Hamiltonians

    Science.gov (United States)

    Chubb, Christopher T.; Flammia, Steven T.

    2017-08-01

    We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.

  12. Relativistic Descriptions of Few-Body Systems

    International Nuclear Information System (INIS)

    Karmanov, V. A.

    2011-01-01

    A brief review of relativistic effects in few-body systems, of theoretical approaches, recent developments and applications is given. Manifestations of relativistic effects in the binding energies, in the electromagnetic form factors and in three-body observables are demonstrated. The three-body forces of relativistic origin are also discussed. We conclude that relativistic effects in nuclei can be important in spite of small binding energy. At high momenta they clearly manifest themselves and are necessary to describe the deuteron e.m. form factors. At the same time, there is still a discrepancy in three-body observables which might be a result of less clarity in understanding the corresponding relativistic effects, the relativistic NN kernel and the three-body forces. Relativistic few-body physics remains to be a field of very intensive and fruitful researches. (author)

  13. A full-dimensional multilayer multiconfiguration time-dependent Hartree study on the ultraviolet absorption spectrum of formaldehyde oxide

    International Nuclear Information System (INIS)

    Meng, Qingyong; Meyer, Hans-Dieter

    2014-01-01

    Employing the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method in conjunction with the multistate multimode vibronic coupling Hamiltonian (MMVCH) model, we perform a full dimensional (9D) quantum dynamical study on the simplest Criegee intermediate, formaldehyde oxide, in five lower-lying singlet electronic states. The ultraviolet (UV) spectrum is then simulated by a Fourier transform of the auto-correlation function. The MMVCH model is built based on extensive MRCI(8e,8o)/aug-cc-pVTZ calculations. To ensure a fast convergence of the final calculations, a large number of ML-MCTDH test calculations is performed to find an appropriate multilayer separations (ML-trees) of the ML-MCTDH nuclear wave functions, and the dynamical calculations are carefully checked to ensure that the calculations are well converged. To compare the computational efficiency, standard MCTDH simulations using the same Hamiltonian are also performed. A comparison of the MCTDH and ML-MCTDH calculations shows that even for the present not-too-large system (9D here) the ML-MCTDH calculations can save a considerable amount of computational resources while producing identical spectra as the MCTDH calculations. Furthermore, the present theoretical B ~ 1 A ′ ←X ~ 1 A ′ UV spectral band and the corresponding experimental measurements [J. M. Beames, F. Liu, L. Lu, and M. I. Lester, J. Am. Chem. Soc. 134, 20045–20048 (2012); L. Sheps, J. Phys. Chem. Lett. 4, 4201–4205 (2013); W.-L. Ting, Y.-H. Chen, W. Chao, M. C. Smith, and J. J.-M. Lin, Phys. Chem. Chem. Phys. 16, 10438–10443 (2014)] are discussed. To the best of our knowledge, this is the first theoretical UV spectrum simulated for this molecule including nuclear motion beyond an adiabatic harmonic approximation

  14. Approximating distributions from moments

    Science.gov (United States)

    Pawula, R. F.

    1987-11-01

    A method based upon Pearson-type approximations from statistics is developed for approximating a symmetric probability density function from its moments. The extended Fokker-Planck equation for non-Markov processes is shown to be the underlying foundation for the approximations. The approximation is shown to be exact for the beta probability density function. The applicability of the general method is illustrated by numerous pithy examples from linear and nonlinear filtering of both Markov and non-Markov dichotomous noise. New approximations are given for the probability density function in two cases in which exact solutions are unavailable, those of (i) the filter-limiter-filter problem and (ii) second-order Butterworth filtering of the random telegraph signal. The approximate results are compared with previously published Monte Carlo simulations in these two cases.

  15. Relativistic heavy-atom effects on heavy-atom nuclear shieldings

    Science.gov (United States)

    Lantto, Perttu; Romero, Rodolfo H.; Gómez, Sergio S.; Aucar, Gustavo A.; Vaara, Juha

    2006-11-01

    The principal relativistic heavy-atom effects on the nuclear magnetic resonance (NMR) shielding tensor of the heavy atom itself (HAHA effects) are calculated using ab initio methods at the level of the Breit-Pauli Hamiltonian. This is the first systematic study of the main HAHA effects on nuclear shielding and chemical shift by perturbational relativistic approach. The dependence of the HAHA effects on the chemical environment of the heavy atom is investigated for the closed-shell X2+, X4+, XH2, and XH3- (X =Si-Pb) as well as X3+, XH3, and XF3 (X =P-Bi) systems. Fully relativistic Dirac-Hartree-Fock calculations are carried out for comparison. It is necessary in the Breit-Pauli approach to include the second-order magnetic-field-dependent spin-orbit (SO) shielding contribution as it is the larger SO term in XH3-, XH3, and XF3, and is equally large in XH2 as the conventional, third-order field-independent spin-orbit contribution. Considering the chemical shift, the third-order SO mechanism contributes two-thirds of the difference of ˜1500ppm between BiH3 and BiF3. The second-order SO mechanism and the numerically largest relativistic effect, which arises from the cross-term contribution of the Fermi contact hyperfine interaction and the relativistically modified spin-Zeeman interaction (FC/SZ-KE), are isotropic and practically independent of electron correlation effects as well as the chemical environment of the heavy atom. The third-order SO terms depend on these factors and contribute both to heavy-atom shielding anisotropy and NMR chemical shifts. While a qualitative picture of heavy-atom chemical shifts is already obtained at the nonrelativistic level of theory, reliable shifts may be expected after including the third-order SO contributions only, especially when calculations are carried out at correlated level. The FC/SZ-KE contribution to shielding is almost completely produced in the s orbitals of the heavy atom, with values diminishing with the principal

  16. CONTRIBUTIONS TO RATIONAL APPROXIMATION,

    Science.gov (United States)

    Some of the key results of linear Chebyshev approximation theory are extended to generalized rational functions. Prominent among these is Haar’s...linear theorem which yields necessary and sufficient conditions for uniqueness. Some new results in the classic field of rational function Chebyshev...Furthermore a Weierstrass type theorem is proven for rational Chebyshev approximation. A characterization theorem for rational trigonometric Chebyshev approximation in terms of sign alternation is developed. (Author)

  17. 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.

  18. Approximation techniques for engineers

    CERN Document Server

    Komzsik, Louis

    2006-01-01

    Presenting numerous examples, algorithms, and industrial applications, Approximation Techniques for Engineers is your complete guide to the major techniques used in modern engineering practice. Whether you need approximations for discrete data of continuous functions, or you''re looking for approximate solutions to engineering problems, everything you need is nestled between the covers of this book. Now you can benefit from Louis Komzsik''s years of industrial experience to gain a working knowledge of a vast array of approximation techniques through this complete and self-contained resource.

  19. Towards an exact relativistic theory of Earth's geoid undulation

    International Nuclear Information System (INIS)

    Kopeikin, Sergei M.; Mazurova, Elena M.; Karpik, Alexander P.

    2015-01-01

    The present paper extends the Newtonian concept of the geoid in classic geodesy towards the realm of general relativity by utilizing the covariant geometric methods of the perturbation theory of curved manifolds. It yields a covariant definition of the anomalous (disturbing) gravity potential and formulates differential equation for it in the form of a covariant Laplace equation. The paper also derives the Bruns equation for calculation of geoid's height with full account for relativistic effects beyond the Newtonian approximation. A brief discussion of the relativistic Bruns formula is provided. - Highlights: • We apply general relativity to define the exact concept of relativistic geoid. • We derive relativistic equation of geoid and the reference level surface. • We employ the manifold perturbation theory to discuss geoid's undulation

  20. Towards an exact relativistic theory of Earth's geoid undulation

    Energy Technology Data Exchange (ETDEWEB)

    Kopeikin, Sergei M., E-mail: kopeikins@missouri.edu [Department of Physics & Astronomy, University of Missouri, Columbia, MO 65211 (United States); Siberian State Geodetic Academy, 10 Plakhotny St., Novosibirsk 630108 (Russian Federation); Mazurova, Elena M., E-mail: e_mazurova@mail.ru [Moscow State University of Geodesy and Cartography, 4 Gorokhovsky Alley, Moscow 105064 (Russian Federation); Siberian State Geodetic Academy, 10 Plakhotny St., Novosibirsk 630108 (Russian Federation); Karpik, Alexander P., E-mail: rector@ssga.ru [Siberian State Geodetic Academy, 10 Plakhotny St., Novosibirsk 630108 (Russian Federation)

    2015-08-14

    The present paper extends the Newtonian concept of the geoid in classic geodesy towards the realm of general relativity by utilizing the covariant geometric methods of the perturbation theory of curved manifolds. It yields a covariant definition of the anomalous (disturbing) gravity potential and formulates differential equation for it in the form of a covariant Laplace equation. The paper also derives the Bruns equation for calculation of geoid's height with full account for relativistic effects beyond the Newtonian approximation. A brief discussion of the relativistic Bruns formula is provided. - Highlights: • We apply general relativity to define the exact concept of relativistic geoid. • We derive relativistic equation of geoid and the reference level surface. • We employ the manifold perturbation theory to discuss geoid's undulation.