Hyperspherical Coulomb spheroidal basis in the Coulomb three-body problem
International Nuclear Information System (INIS)
Abramov, D. I.
2013-01-01
A hyperspherical Coulomb spheroidal (HSCS) representation is proposed for the Coulomb three-body problem. This is a new expansion in the set of well-known Coulomb spheroidal functions. The orthogonality of Coulomb spheroidal functions on a constant-hyperradius surface ρ = const rather than on a constant-internuclear-distance surface R = const, as in the traditional Born-Oppenheimer approach, is a distinguishing feature of the proposed approach. Owing to this, the HSCS representation proves to be consistent with the asymptotic conditions for the scattering problem at energies below the threshold for three-body breakup: only a finite number of radial functions do not vanish in the limit of ρ→∞, with the result that the formulation of the scattering problem becomes substantially simpler. In the proposed approach, the HSCS basis functions are considerably simpler than those in the well-known adiabatic hyperspherical representation, which is also consistent with the asymptotic conditions. Specifically, the HSCS basis functions are completely factorized. Therefore, there arise no problems associated with avoided crossings of adiabatic hyperspherical terms.
Coulomb effects in deuteron stripping reactions as a three-body problem
International Nuclear Information System (INIS)
Osman, A.
1981-08-01
Deuteron stripping nuclear reactions are reconsidered as a three-body problem. The Coulomb effects between the proton and the target nucleus are investigated. The mathematical formalism introduces three-body integral equations which can be exactly calculated for such simple models. These coupled integral equations suitably include the Coulomb effects due to replusive or attractive Coulomb potential. Numerical calculations of the differential cross-sections of the reactions 28 Si(d,p) 29 Si and 40 Ca(d,p) 41 Ca are carried out showing the importance of the Coulomb effects. The angular distributions of these reactions are theoretically calculated and fitted to the experimental data. From this fitting, reasonable spectroscopic factors are obtained. Inclusion of Coulomb force in the three-body model are found to improve the results by a percentage of about 6.826%. (author)
Approximate Coulomb effects in the three-body scattering problem
International Nuclear Information System (INIS)
Haftel, M.I.; Zankel, H.
1981-01-01
From the momentum space Faddeev equations we derive approximate expressions which describe the Coulomb-nuclear interference in the three-body elastic scattering, rearrangement, and breakup problems and apply the formalism to p-d elastic scattering. The approximations treat the Coulomb interference as mainly a two-body effect, but we allow for the charge distribution of the deuteron in the p-d calculations. Real and imaginary parts of the Coulomb correction to the elastic scattering phase shifts are described in terms of on-shell quantities only. In the case of pure Coulomb breakup we recover the distorted-wave Born approximation result. Comparing the derived approximation with the full Faddeev p-d elastic scattering calculation, which includes the Coulomb force, we obtain good qualitative agreement in S and P waves, but disagreement in repulsive higher partial waves. The on-shell approximation investigated is found to be superior to other current approximations. The calculated differential cross sections at 10 MeV raise the question of whether there is a significant Coulomb-nuclear interference at backward angles
Muonic molecules as three-body Coulomb problem in adiabatic approximation
International Nuclear Information System (INIS)
Decker, M.
1994-04-01
The three-body Coulomb problem is treated within the framework of the hyperspherical adiabatic approach. The surface functions are expanded into Faddeev-type components in order to ensure the equivalent representation of all possible two-body contributions. It is shown that this decomposition reduces the numerical effort considerably. The remaining radial equations are solved both in the extreme and the uncoupled adiabatic approximation to determine the binding energies of the systems (dtμ) and (d 3 Heμ). Whereas the ground state is described very well in the uncoupled adiabatic approximation, the excited states should be treated within the coupled adiabatic approximation to obtain good agreement with variational calculations. (orig.)
Solving the three-body Coulomb breakup problem using exterior complex scaling
Energy Technology Data Exchange (ETDEWEB)
McCurdy, C.W.; Baertschy, M.; Rescigno, T.N.
2004-05-17
Electron-impact ionization of the hydrogen atom is the prototypical three-body Coulomb breakup problem in quantum mechanics. The combination of subtle correlation effects and the difficult boundary conditions required to describe two electrons in the continuum have made this one of the outstanding challenges of atomic physics. A complete solution of this problem in the form of a ''reduction to computation'' of all aspects of the physics is given by the application of exterior complex scaling, a modern variant of the mathematical tool of analytic continuation of the electronic coordinates into the complex plane that was used historically to establish the formal analytic properties of the scattering matrix. This review first discusses the essential difficulties of the three-body Coulomb breakup problem in quantum mechanics. It then describes the formal basis of exterior complex scaling of electronic coordinates as well as the details of its numerical implementation using a variety of methods including finite difference, finite elements, discrete variable representations, and B-splines. Given these numerical implementations of exterior complex scaling, the scattering wave function can be generated with arbitrary accuracy on any finite volume in the space of electronic coordinates, but there remains the fundamental problem of extracting the breakup amplitudes from it. Methods are described for evaluating these amplitudes. The question of the volume-dependent overall phase that appears in the formal theory of ionization is resolved. A summary is presented of accurate results that have been obtained for the case of electron-impact ionization of hydrogen as well as a discussion of applications to the double photoionization of helium.
International Nuclear Information System (INIS)
Tolstikhin, Oleg I.; Namba, Chusei
2003-08-01
A program to solve the quantum-mechanical collinear three-body Coulomb problem is described and illustrated by calculations for a number of representative systems and processes. In the internal region, the Schroedinger equation is solved in hyperspherical coordinates using the slow/smooth variable discretization method. In asymptotic regions, the solution is obtained in Jacobi coordinates using the asymptotic package GAILIT from the CPC library. Only bound states and scattering processes below the three-body disintegration threshold are considered here; resonances and fragmentation processes will be discussed in subsequent parts of this series. (author)
International Nuclear Information System (INIS)
Papp, Z.; Plessas, W.
1996-01-01
We demonstrate the feasibility and efficiency of the Coulomb-Sturmian separable expansion method for generating accurate solutions of the Faddeev equations. Results obtained with this method are reported for several benchmark cases of bosonic and fermionic three-body systems. Correct bound-state results in agreement with the ones established in the literature are achieved for short-range interactions. We outline the formalism for the treatment of three-body Coulomb systems and present a bound-state calculation for a three-boson system interacting via Coulomb plus short-range forces. The corresponding result is in good agreement with the answer from a recent stochastic-variational-method calculation. copyright 1996 The American Physical Society
Three-body Coulomb systems using generalized angular-momentum S states
Whitten, R. C.; Sims, J. S.
1974-01-01
An expansion of the three-body Coulomb potential in generalized angular-momentum eigenfunctions developed earlier by one of the authors is used to compute energy eigenvalues and eigenfunctions of bound S states of three-body Coulomb systems. The results for He, H(-), e(-)e(+)e(-), and pmu(-)p are compared with the results of other computational approaches.
International Nuclear Information System (INIS)
Bray, I.; Stelbovics, A.T.
1992-01-01
Convergence as a function of the number of states is studied and demonstrated for the Poet-Temkin model of electron-hydrogen scattering. In this Coulomb three-body problem only the l=0 partial waves are treated. By taking as many as thirty target states, obtained by diagonalizing the target Hamiltonian in a Laguerre basis, complete agreement with the smooth results of Poet is obtained at all energies. We show that the often-encountered pseudoresonance features in the cross sections are simply an indication of an inadequate target state representation
Coulomb two-body problem with internal structure
International Nuclear Information System (INIS)
Kuperin, Yu.A.; Makarov, K.A.; Mel'nikov, Yu.B.
1988-01-01
The methods of the theory of extensions to an enlarged Hilbert space are used to construct a model of the interaction of the external (Coulomb) and internal (quark) channels in the two-body problem. The mutual influence of the spectra of the corresponding channel Hamiltonians is studied: it leads, in particular, to a rearrangement of the spectra of hadronic atoms. An explicit representation is obtained for the S matrix, and its singularities on the energy shell are studied
Coulomb Fourier transformation: A novel approach to three-body scattering with charged particles
International Nuclear Information System (INIS)
Alt, E.O.; Levin, S.B.; Yakovlev, S.L.
2004-01-01
A unitary transformation of the three-body Hamiltonian which describes a system of two charged and one neutral particles is constructed such that the Coulomb potential which acts between the charged particles is explicitly eliminated. The transformed Hamiltonian and, in particular, the transformed short-range pair interactions are worked out in detail. Thereby it is found that, after transformation, the short-range potentials acting between the neutral and either one of the charged particles become simply Fourier transformed but, in addition, multiplied by a function that represents the Coulombic three-body correlations originating from the action of the other charged particle on the considered pair. This function which is universal as it does not depend on any property of the short-range interaction is evaluated explicitly and its singularity structure is described in detail. In contrast, the short-range potential between the charged particles remains of two-body type but occurs now in the 'Coulomb representation'. Specific applications to Yukawa and Gaussian potentials are given. Since the Coulomb-Fourier-transformed Hamiltonian does no longer contain the Coulomb potential or any other effective interaction of long range, standard methods of short-range few-body scattering theory are applicable
Incorporation of threshold phenomena in the three-body Coulomb continuum wavefunctions
International Nuclear Information System (INIS)
Berakdar, J.
1996-01-01
In this work a three-body Coulomb wavefunction for the description of two continuum electrons moving in the field of a nucleus is constructed such that the Wannier threshold law for double escape is reproduced and the asymptotic Coulomb boundary conditions as well as the Kato cusp conditions are satisfied. It is shown that the absolute value of the total cross section, as well as the spin asymmetry, are well described by the present approach. Further, the excess-energy sharing between the two escaping electrons is calculated and analysed in light of the Wannier theory predictions. This is the first time an analytical three-body wavefunction is presented which is asymptotically exact and capable of describing threshold phenomena. 37 refs., 3 figs
Three-body Coulomb breakup of 11Li in the complex scaling method
International Nuclear Information System (INIS)
Myo, Takayuki; Aoyama, Shigeyoshi; Kato, Kiyoshi; Ikeda, Kiyomi
2003-01-01
Coulomb breakup strengths of 11 Li into a three-body 9 Li+n+n system are studied in the complex scaling method. We decompose the transition strengths into the contributions from three-body resonances, two-body '' 10 Li+n'' and three-body '' 9 Li+n+n'' continuum states. In the calculated results, we cannot find the dipole resonances with a sharp decay width in 11 Li. There is a low energy enhancement in the breakup strength, which is produced by both the two- and three-body continuum states. The enhancement given by the three-body continuum states is found to have a strong connection to the halo structure of 11 Li. The calculated breakup strength distribution is compared with the experimental data from MSU, RIKEN and GSI
Stability of the three-body Coulomb systems with J=1 in the oscillator representation
International Nuclear Information System (INIS)
Dinejkhan, M.D.; Efimov, G.V.
1995-01-01
The oscillator representation is applied to calculate the energy spectrum of three-body Coulomb systems with J total angular momentum. For the three-body Coulomb systems with J=1 and arbitrary masses the region of stability is determined. For the systems (A + A - e - ), (pe - C + ), (pB - e - ) and (D + e - e + ), the values for the critical masses of A-, B-, C- and D-particles are obtained: m A =2.22m e , m B =1.49m e , m C =2.11m e and m D =4.15m e . 18 refs., 1 fig., 3 tabs
International Nuclear Information System (INIS)
Musielak, Z E; Quarles, B
2014-01-01
The three-body problem, which describes three masses interacting through Newtonian gravity without any restrictions imposed on the initial positions and velocities of these masses, has attracted the attention of many scientists for more than 300 years. In this paper, we present a review of the three-body problem in the context of both historical and modern developments. We describe the general and restricted (circular and elliptic) three-body problems, different analytical and numerical methods of finding solutions, methods for performing stability analysis and searching for periodic orbits and resonances. We apply the results to some interesting problems of celestial mechanics. We also provide a brief presentation of the general and restricted relativistic three-body problems, and discuss their astronomical applications. (review article)
Coulomb Effects in Few-Body Reactions
Directory of Open Access Journals (Sweden)
Deltuva A.
2010-04-01
Full Text Available The method of screening and renormalization is used to include the Coulomb interaction between the charged particles in the momentum-space description of three- and four-body nuclear reactions. The necessity for the renormalization of the scattering amplitudes and the reliability of the method is demonstrated. The Coulomb eﬀect on observables is discussed.
Eikonal representation of N-body Coulomb scattering amplitudes
International Nuclear Information System (INIS)
Fried, H.M.; Kang, K.; McKellar, B.H.J.
1983-01-01
A new technique for the construction of N-body Coulomb scattering amplitudes is proposed, suggested by the simplest case of N = 2: Calculate the scattering amplitude in eikonal approximation, discard the infinite phase factors which appear upon taking the limit of a Coulomb potential, and treat the remainder as an amplitude whose absolute value squared produces the exact, Coulomb differential cross section. The method easily generalizes to the N-body Coulomb problem for elastic scattering, and for inelastic rearrangement scattering of Coulomb bound states. We give explicit results for N = 3 and 4; in the N = 3 case we extract amplitudes for the processes (12)+3->1+2+3 (breakup), (12)+3->1+(23) (rearrangement), and (12)+3→(12)'+3 (inelastic scattering) as residues at the appropriate poles in the free-free amplitude. The method produces scattering amplitudes f/sub N/ given in terms of explicit quadratures over (N-2) 2 distinct integrands
International Nuclear Information System (INIS)
Zaytsev, S A
2010-01-01
The possibility of using straight-line paths of integration in computing the integral representation of the three-body Coulomb Green's function is discussed. In our numerical examples two different kinds of integration contours in the complex energy planes are considered. It is demonstrated that straight-line paths, which cross the positive real axis, are suitable for numerical computation.
Quadratic and coulomb terms for the spectrum of a three-electron quantum dot
International Nuclear Information System (INIS)
Hassanabadi, H.; Hamzavi, M.; Zarrinkamar, S.; Rajabi, A.A.
2010-01-01
We consider the Hamiltonian of a three-electron quantum dot composed of quadratic plus Coulomb terms and calculate the system's spectra. We next apply the hyperradius to reduce the three-body Schroedinger equation into a one-variable differential equation that is solvable. To avoid the complexity, the Taylor expansion of the effective potential is enters the problem and thereby a solution is found for the eigenvalues of the corresponding three-body Schroedinger equation in terms of the Wigner parameter. Using a quasi-analytical approach, we have calculated the energy eigenvalues of the Schroedinger equation corresponding to a three-electron quantum dot. In addition to the hyperspherical coordinates, much of mathematical complexity has been avoided using the idea of Taylor expansion for the potential. For the potential, we have considered quadratic plus Coulomb terms. The obtained energy eigenvalues in terms of the Wigner parameter are given in tabular form. (author)
Marchal, Christian
1990-01-01
Recent research on the theory of perturbations, the analytical approach and the quantitative analysis of the three-body problem have reached a high degree of perfection. The use of electronics has aided developments in quantitative analysis and has helped to disclose the extreme complexity of the set of solutions. This accelerated progress has given new orientation and impetus to the qualitative analysis that is so complementary to the quantitative analysis. The book begins with the various formulations of the three-body problem, the main classical results and the important questions and conje
Directory of Open Access Journals (Sweden)
Yurii M. Streliaiev
2016-06-01
Full Text Available Three-dimensional quasistatic contact problem of two linearly elastic bodies' interaction with Coulomb friction taken into account is considered. The boundary conditions of the problem have been simplified by the modification of the Coulomb's law of friction. This modification is based on the introducing of a delay in normal contact tractions that bound tangent contact tractions in the Coulomb's law of friction expressions. At this statement the problem is reduced to a sequence of similar systems of nonlinear integral equations describing bodies' interaction at each step of loading. A method for an approximate solution of the integral equations system corresponded to each step of loading is applied. This method consists of system regularization, discretization of regularized system and iterative process application for solving the discretized system. A numerical solution of a contact problem of an elastic sphere with an elastic half-space interaction under increasing and subsequently decreasing normal compressive force has been obtained.
Three-body unitary transformations, three-body forces, and trinucleon bound state properties
International Nuclear Information System (INIS)
Haftel, M.I.
1976-01-01
A three-body unitary transformation method for the study of three-body forces is presented. Starting with a three-body Hamiltonian with two-body forces, unitary transformations are introduced to generate Hamiltonians that have both two- and three-body forces. For cases of physical interest, the two-body forces of the altered Hamiltonians are phase equivalent (for two-body scattering) to the original and the three-body force vanishes when any interparticle distance is large. Specific examples are presented. Applications for studying the possible role of three-body forces in accounting for trinucleon bound state properties are examined. Calculations of the 3 He and 3 H charge form factors and Coulomb energy difference with hyperspherical radial transformations and with conventional N-N potentials are performed. The form factor calculations demonstrate how the proposed method can help obtain improved agreement with experiment by the introduction of appropriate three-body forces. Calculations of the Coulomb energy difference confirm previous estimates concerning charge symmetry breaking in the N-N interaction
The exact solution of a four-body Coulomb problem
Ray, Hasi
2018-03-01
The elastic collision between two H-like atoms utilizing an ab initio static-exchange model (SEM) in the center of mass (CM) frame considering the system as a four-body Coulomb problem where all the Coulomb interaction terms in the direct and exchange channels are treated exactly, is studied thoroughly. A coupled-channel methodology in momentum space is used to solve Lippman-Schwinger equation following the integral approach. The new SEM code [Ray, Pramana 83, 907 (2014)] in which the Born-Oppenheimer (BO) scattering amplitude acts as input to derive the SEM amplitude using partial wave analysis, is utilized to study the s-, p-, d-wave elastic phase shifts and the corresponding partial cross sections. An augmented-Born approximation is used to include the contribution of higher partial waves more accurately to determine the total/integrated elastic cross sections. The effective range theory is used to determine the scattering lengths and effective ranges in the s-wave elastic scattering. The systems studied are Ps-Ps, Ps-Mu, Ps-H, Ps-D, Ps-T, Mu-Mu, Mu-H, Mu-D, Mu-T, H-H, H-D, H-T, D-D, D-T, T-T. The SEM includes the non-adiabatic short-range effects due to exchange. The MSEM code [Ray, Pramana 83, 907 (2014)] is used to study the effect of the long-range van der Waals interaction due to induced dipole polarizabilities of the atoms in H(1s)-H(1s) elastic collision. The dependence of scattering length on the reduced mass of the system and the dependence of scattering length on the strength of long-range van der Waals interaction that varies with the minimum interatomic distance are observed. Contribution to the Topical Issue "Low Energy Positron and Electron Interactions", edited by James Sullivan, Ron White, Michael Bromley, Ilya Fabrikant, and David Cassidy.
The role of three-body coulomb fields versus final state interactions in the decay of 12C-α-12C
International Nuclear Information System (INIS)
Quebert, J.L.; Bertault, D.; Scheurer, J.N.; Fouan, J.P.
1980-01-01
The alpha emission in 16 O + 12 C→ 12 C + α + 12 C has been thoroughly studied in the region of the rapidity plot: Ysub(α)=Ysub(c.m.). The three-body coulomb fields, as well as configurations close to alignment, account for the alpha yield which is observed. The apparent competition between direct and sequential decays is well explained by the coulomb break-up
A non-orthogonal harmonic-oscillator basis for three-body problems
International Nuclear Information System (INIS)
Agrello, D.A.; Aguilera-Navarro, V.C.; Chacon, E.
1979-01-01
A set of harmonic-oscillator states suitable for the representation of the wave function of the bound states of a system of three identical particles, is presented. As an illustration of the possibilities of the states defined in this paper, they are applied in a variational determination of the lowest symmetric S state of 12 C, in the model of three structureless α particles interacting through the Coulomb force plus a phenomenological two-body force. (author) [pt
Integral equation for Coulomb problem
International Nuclear Information System (INIS)
Sasakawa, T.
1986-01-01
For short range potentials an inhomogeneous (homogeneous) Lippmann-Schwinger integral equation of the Fredholm type yields the wave function of scattering (bound) state. For the Coulomb potential, this statement is no more valid. It has been felt difficult to express the Coulomb wave function in a form of an integral equation with the Coulomb potential as the perturbation. In the present paper, the author shows that an inhomogeneous integral equation of a Volterra type with the Coulomb potential as the perturbation can be constructed both for the scattering and the bound states. The equation yielding the binding energy is given in an integral form. The present treatment is easily extended to the coupled Coulomb problems
Poincaré and the three body problem
Barrow-Green, June
1997-01-01
The idea of chaos figures prominently in mathematics today. It arose in the work of one of the greatest mathematicians of the late 19th century, Henri Poincaré, on a problem in celestial mechanics: the three body problem. This ancient problem-to describe the paths of three bodies in mutual gravitational interaction-is one of those which is simple to pose but impossible to solve precisely. Poincaré's famous memoir on the three body problem arose from his entry in the competition celebrating the 60th birthday of King Oscar of Sweden and Norway. His essay won the prize and was set up in print as a paper in Acta Mathematica when it was found to contain a deep and critical error. In correcting this error Poincaré discovered mathematical chaos, as is now clear from Barrow-Green's pioneering study of a copy of the original memoir annotated by Poincaré himself, recently discovered in the Institut Mittag-Leffler in Stockholm. Poincaré and the Three Body Problem opens with a discussion of the development of the th...
The three-body problem from Pythagoras to Hawking
Valtonen, Mauri; Kholshevnikov, Konstantin; Mylläri, Aleksandr; Orlov, Victor; Tanikawa, Kiyotaka
2016-01-01
This book, written for a general readership, reviews and explains the three-body problem in historical context reaching to latest developments in computational physics and gravitation theory. The three-body problem is one of the oldest problems in science and it is most relevant even in today’s physics and astronomy. The long history of the problem from Pythagoras to Hawking parallels the evolution of ideas about our physical universe, with a particular emphasis on understanding gravity and how it operates between astronomical bodies. The oldest astronomical three-body problem is the question how and when the moon and the sun line up with the earth to produce eclipses. Once the universal gravitation was discovered by Newton, it became immediately a problem to understand why these three-bodies form a stable system, in spite of the pull exerted from one to the other. In fact, it was a big question whether this system is stable at all in the long run. Leading mathematicians attacked this problem over more than...
Shape Optimization in Three-Dimensional Contact Problems with Coulomb Friction
Czech Academy of Sciences Publication Activity Database
Beremlijski, P.; Haslinger, J.; Kočvara, Michal; Kučera, R.; Outrata, Jiří
2009-01-01
Roč. 20, č. 1 (2009), s. 416-444 ISSN 1052-6234 R&D Projects: GA AV ČR IAA100750802; GA AV ČR IAA1075402 Grant - others:European Commision(XE) FP6 - 30717; GA ČR(CZ) GA201/07/0294 Institutional research plan: CEZ:AV0Z10750506 Keywords : shape optimization * contact problems * Coulomb friction Subject RIV: BA - General Mathematics Impact factor: 1.429, year: 2009
Lavine method applied to three body problems
International Nuclear Information System (INIS)
Mourre, Eric.
1975-09-01
The methods presently proposed for the three body problem in quantum mechanics, using the Faddeev approach for proving the asymptotic completeness, come up against the presence of new singularities when the potentials considered v(α)(x(α)) for two-particle interactions decay less rapidly than /x(α)/ -2 ; and also when trials are made for solving the problem with a representation space whose dimension for a particle is lower than three. A method is given that allows the mathematical approach to be extended to three body problem, in spite of singularities. Applications are given [fr
International Nuclear Information System (INIS)
Kar, S.; Ho, Y.K.
2009-01-01
We have investigated the doubly excited 1 D e resonance states of Ps - interacting with pure Coulomb and screened Coulomb (Yukawa) potentials employing highly correlated wave functions. For pure Coulomb interaction, in the framework of stabilization method and complex coordinate rotation method we have obtained two resonances below the n = 2 threshold of the Ps atom. For screened Coulomb interaction, we employ the stabilization method to extract resonance parameters. Resonance energies and widths for the 1 D e resonance states of Ps - for different screening parameter ranging from infinity (pure Coulomb case) to a small value are also reported. (author)
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
The three body problem with energy dependent potentials
International Nuclear Information System (INIS)
Kim, Y.E.; McKay, C.M.; McKellar, B.H.J.
1975-10-01
It is shown how to generalize the three body equations of Faddeev, and of Karlsson and Zeiger, to include the case when the two body potential is energy dependent. Such generalizations will prove useful in the three nucleon problem and in three body models of nuclear reactions. (author)
International Nuclear Information System (INIS)
Minesaki, Yukitaka
2013-01-01
For the restricted three-body problem, we propose an accurate orbital integration scheme that retains all conserved quantities of the two-body problem with two primaries and approximately preserves the Jacobi integral. The scheme is obtained by taking the limit as mass approaches zero in the discrete-time general three-body problem. For a long time interval, the proposed scheme precisely reproduces various periodic orbits that cannot be accurately computed by other generic integrators
Dynamics in few body Coulomb problems
International Nuclear Information System (INIS)
Ovchinnikov, S.Y.; Macek, J.H.; Tantawi, R.S.; Sabbah, A.S.
1999-01-01
We develop the 'positive energy Sturmian technique' for the solution of time-dependent Schroedinger equations which describe few Coulomb centers with scattering initial conditions. The 'positive energy Sturmian technique' is based on the following main steps: (i) time-dependent scaled transformation; (ii) Fourier transformation into the frequency domain; (iii) outgoing wave Sturmian expansions; and (iv) solution of coupled equations. The technique has been applied in electron-atom and ion-atom collisions for calculations of energy and angular distributions of emitted electrons and excitations of atoms. Refs. 2 (author)
Generalized coherent states for the Coulomb problem in one dimension
International Nuclear Information System (INIS)
Nouri, S.
2002-01-01
A set of generalized coherent states for the one-dimensional Coulomb problem in coordinate representation is constructed. At first, we obtain a mapping for proper transformation of the one-dimensional Coulomb problem into a nonrotating four-dimensional isotropic harmonic oscillator in the hyperspherical space, and the generalized coherent states for the one-dimensional Coulomb problem is then obtained in exact closed form. This exactly soluble model can provide an adequate means for a quantum coherency description of the Coulomb problem in one dimension, sample for coherent aspects of the exciton model in one-dimension example in high-temperature superconductivity, semiconductors, and polymers. Also, it can be useful for investigating the coherent scattering of the Coulomb particles in one dimension
Poisson equation in the Kohn-Sham Coulomb problem
Manby, F. R.; Knowles, Peter James
2001-01-01
We apply the Poisson equation to the quantum mechanical Coulomb problem for many-particle systems. By introducing a suitable basis set, the two-electron Coulomb integrals become simple overlaps. This offers the possibility of very rapid linear-scaling treatment of the Coulomb contribution to Kohn-Sham theory.
Many-Body Coulomb Gauge Exotic and Charmed Hybrids
Llanes-Estrada, Felipe J.; Cotanch, Stephen R.
2000-01-01
Utilizing a QCD Coulomb gauge Hamiltonian with linear confinement specified by lattice, we report a relativistic many-body calculation for the light exotic and charmed hybrid mesons. The Hamiltonian successfully describes both quark and gluon sectors, with vacuum and quasiparticle properties generated by a BCS transformation and more elaborate TDA and RPA diagonalizations for the meson ($q\\bar{q}$) and glueball ($gg$) masses. Hybrids entail a computationally intense relativistic three quasipa...
Comment on "Calculations for the one-dimensional soft Coulomb problem and the hard Coulomb limit".
Carrillo-Bernal, M A; Núñez-Yépez, H N; Salas-Brito, A L; Solis, Didier A
2015-02-01
In the referred paper, the authors use a numerical method for solving ordinary differential equations and a softened Coulomb potential -1/√[x(2)+β(2)] to study the one-dimensional Coulomb problem by approaching the parameter β to zero. We note that even though their numerical findings in the soft potential scenario are correct, their conclusions do not extend to the one-dimensional Coulomb problem (β=0). Their claims regarding the possible existence of an even ground state with energy -∞ with a Dirac-δ eigenfunction and of well-defined parity eigenfunctions in the one-dimensional hydrogen atom are questioned.
Two-center Coulomb problem with Calogero interaction
Energy Technology Data Exchange (ETDEWEB)
Hakobyan, T., E-mail: tigran.hakobyan@ysu.am; Nersessian, A., E-mail: arnerses@ysu.am [Armenia Tomsk Polytechnic University, Yerevan State University (Russian Federation)
2017-03-15
We show that the Calogero-type perturbation preserves the integrability and partial separation of variables for the Stark–Coulomb and two-center Coulomb problems, and present the explicit expressions of their constants of motion. We reveal that this perturbation preserves the spectra of initial systems, but leads to the change of degree of degeneracy.
Gebremedhin, Daniel H; Weatherford, Charles A
2015-02-01
This is a response to the comment we received on our recent paper "Calculations for the one-dimensional soft Coulomb problem and the hard Coulomb limit." In that paper, we introduced a computational algorithm that is appropriate for solving stiff initial value problems, and which we applied to the one-dimensional time-independent Schrödinger equation with a soft Coulomb potential. We solved for the eigenpairs using a shooting method and hence turned it into an initial value problem. In particular, we examined the behavior of the eigenpairs as the softening parameter approached zero (hard Coulomb limit). The commenters question the existence of the ground state of the hard Coulomb potential, which we inferred by extrapolation of the softening parameter to zero. A key distinction between the commenters' approach and ours is that they consider only the half-line while we considered the entire x axis. Based on mathematical considerations, the commenters consider only a vanishing solution function at the origin, and they question our conclusion that the ground state of the hard Coulomb potential exists. The ground state we inferred resembles a δ(x), and hence it cannot even be addressed based on their argument. For the excited states, there is agreement with the fact that the particle is always excluded from the origin. Our discussion with regard to the symmetry of the excited states is an extrapolation of the soft Coulomb case and is further explained herein.
Spectral sum rules for the three-body problem
International Nuclear Information System (INIS)
Bolle, D.; Osborn, T.A.
1982-01-01
This paper derives a number of sum rules for nonrelativistic three-body scattering. These rules are valid for any finite region μ in the six-dimensional coordinate space. They relate energy moments of the trace of the onshell time-delay operator to the energy-weighted probability for finding the three-body bound-state wave functions in the region μ. If μ is all of the six-dimensional space, the global form of the sum rules is obtained. In this form the rules constitute higher-order Levinson's theorems for the three-body problem. Finally, the sum rules are extended to allow the energy momtns have complex powers
Continuum capture in the three-body problem
International Nuclear Information System (INIS)
Sellin, I.A.
1980-01-01
The three-body problem, especially the problem of electron capture to the continuum in heavy particle collisions is reviewed. Major topics covered include: second born-induced asymmetry in electron capture to the continuum; historical context, links to other tests of atomic scattering theory; experiments characterizing the velocity distribution of ECC electrons; other atomic physics tests of high velocity Born expansions; atom capture; capture by positrons; and pion capture to the continuum
International Nuclear Information System (INIS)
Amado, R.D.
1975-01-01
An overview of the formal theory of the three-body problem as it has developed in the past twelve years is given. The formal structure of the theory, some of the techniques that have developed for handling the theory, and some results on how general quantum mechanical principles structure the results, are presented. The discussion is held entirely in the context of non-relativistic quantum mechanics with short-range forces. In this presentation the main outline of the theory is stressed, often at the expense of mathematical rigour [pt
Nuclear three-body problem and energy-dependent potentials
International Nuclear Information System (INIS)
Abdurakhmanov, A.; Akhmadkhodzhaev, B.; Zubarev, A.L.; Irgaziev, B.F.
1985-01-01
Energy-dependent potentials in the three-body problem are being considered. Three-particle equations for the case of pairing energy-dependent potentials are generalized and the problems related to this ambiguous generalization are investigated. In terms of the equations obtained the tritium binding energy and vertex coupling constants (Tdn) and (Tdν) are evaluated. The binding energy and, especially, coupling constants are shown to be sensitive to a shape of the energy-dependent potential
Non-integrability of the Anisotropic Stormer Problem and the Isosceles Three-Body Problem
Nomikos, D. G.; Papageorgiou, V. G.
2009-02-01
We study the Anisotropic Stormer Problem (ASP) and the Isosceles Three-Body Problem (IP), from the viewpoint of integrability, using Morales-Ramis theory and its generalization. The study of their integrability presents particular interest since they model important physical phenomena. Both problems can be reduced with respect to the S1 symmetry. Almeida and Stuchi [M.A. Almeida, T.J. Stuchi, Non-integrability of the anisotropic Stormer problem with angular momentum, Physica D 189 (2004) 219-233] proved that the reduced ASP is non-integrable for almost all values of the parameters. In this paper we establish the non-integrability (in the extended Liouville sense) of the remaining cases. The IP is a special case of the three-body problem and it can be considered as a generalization of the Sitnikov problem. Here we prove that the complexified reduced IP does not admit an additional independent meromorphic first integral.
Coulomb oscillations in three-layer graphene nanostructures
International Nuclear Information System (INIS)
Guettinger, J; Stampfer, C; Molitor, F; Graf, D; Ihn, T; Ensslin, K
2008-01-01
We present transport measurements on a tunable three-layer graphene single electron transistor (SET). The device consists of an etched three-layer graphene flake with two narrow constrictions separating the island from source and drain contacts. Three lateral graphene gates are used to electrostatically tune the device. An individual three-layer graphene constriction has been investigated separately showing a transport gap near the charge neutrality point. The graphene tunneling barriers show a strongly nonmonotonic coupling as a function of gate voltage indicating the presence of localized states in the constrictions. We show Coulomb oscillations and Coulomb diamond measurements proving the functionality of the graphene SET. A charging energy of ∼0.6 meV is extracted.
A cluster expansion for bound three-alpha particles as a three-body problem
International Nuclear Information System (INIS)
Osman, A.
1981-08-01
A three-body model is proposed to study the nuclear bound states. The nucleus is described as a bound state of three clusters. A cluster expansion is introduced for the three cluster bound state problem. The present integral equations are treated by simple approximate solutions, which lead to effective potentials by using the present cluster expansion. The 12 C nucleus is described as a three-alpha particle bound state. The binding energy of 12 C is calculated numerically using the present cluster expansion as bound three-alpha clusters. The present three-body cluster expansion calculations are very near to the exact three-body calculations using separable potentials. The present theoretical calculations are in good agreement with the experimental measurements. (author)
LAGRANGE SOLUTIONS TO THE DISCRETE-TIME GENERAL THREE-BODY PROBLEM
International Nuclear Information System (INIS)
Minesaki, Yukitaka
2013-01-01
There is no known integrator that yields exact orbits for the general three-body problem (G3BP). It is difficult to verify whether a numerical procedure yields the correct solutions to the G3BP because doing so requires knowledge of all 11 conserved quantities, whereas only six are known. Without tracking all of the conserved quantities, it is possible to show that the discrete general three-body problem (d-G3BP) yields the correct orbits corresponding to Lagrange solutions of the G3BP. We show that the d-G3BP yields the correct solutions to the G3BP for two special cases: the equilateral triangle and collinear configurations. For the triangular solution, we use the fact that the solution to the three-body case is a superposition of the solutions to the three two-body cases, and we show that the three bodies maintain the same relative distances at all times. To obtain the collinear solution, we assume a specific permutation of the three bodies arranged along a straight rotating line, and we show that the d-G3BP maintains the same distance ratio between two bodies as in the G3BP. Proving that the d-G3BP solutions for these cases are equivalent to those of the G3BP makes it likely that the d-G3BP and G3BP solutions are equivalent in other cases. To our knowledge, this is the first work that proves the equivalence of the discrete solutions and the Lagrange orbits.
Diffusion Monte Carlo calculation of three-body systems
International Nuclear Information System (INIS)
Lu Mengjiao; Lin Qihu; Ren Zhongzhou
2012-01-01
The application of the diffusion Monte Carlo algorithm in three-body systems is studied. We develop a program and use it to calculate the property of various three-body systems. Regular Coulomb systems such as atoms, molecules, and ions are investigated. The calculation is then extended to exotic systems where electrons are replaced by muons. Some nuclei with neutron halos are also calculated as three-body systems consisting of a core and two external nucleons. Our results agree well with experiments and others' work. (authors)
The electron-atom ionization problem
International Nuclear Information System (INIS)
McCarthy, I.E.
1995-02-01
Methods of calculating electron-atom ionization as a three-body problem with Coulomb boundary conditions are considered. In the absence of a fully-valid computational method for a time-independent experiment the approximation is made that the incident electron experiences a screened potential. Approximations involving a final state that obeys the three-body Coulomb boundary condition are compared with the distorted-wave Born approximation and the convergent close-coupling method. 24 refs., 6 figs
Three-dimensional oscillator and Coulomb systems reduced from Kaehler spaces
International Nuclear Information System (INIS)
Nersessian, Armen; Yeranyan, Armen
2004-01-01
We define the oscillator and Coulomb systems on four-dimensional spaces with U(2)-invariant Kaehler metric and perform their Hamiltonian reduction to the three-dimensional oscillator and Coulomb systems specified by the presence of Dirac monopoles. We find the Kaehler spaces with conic singularity, where the oscillator and Coulomb systems on three-dimensional sphere and two-sheet hyperboloid originate. Then we construct the superintegrable oscillator system on three-dimensional sphere and hyperboloid, coupled to a monopole, and find their four-dimensional origins. In the latter case the metric of configuration space is a non-Kaehler one. Finally, we extend these results to the family of Kaehler spaces with conic singularities
The three-body problem and equivariant Riemannian geometry
Alvarez-Ramírez, M.; García, A.; Meléndez, J.; Reyes-Victoria, J. G.
2017-08-01
We study the planar three-body problem with 1/r2 potential using the Jacobi-Maupertuis metric, making appropriate reductions by Riemannian submersions. We give a different proof of the Gaussian curvature's sign and the completeness of the space reported by Montgomery [Ergodic Theory Dyn. Syst. 25, 921-947 (2005)]. Moreover, we characterize the geodesics contained in great circles.
Multivariable hypergeometric solutions for three charged particles
Energy Technology Data Exchange (ETDEWEB)
Gasaneo, G.; Colavecchia, F.D.; Garibotti, C.R. [Comision Nacional de Energia Atomica, San Carlos de Bariloche (Argentina). Centro Atomico Bariloche]|[Consejo Nacional de Investigaciones Cientificas y Tecnicas, San Carlos de Bariloche (Argentina); Miraglia, J.E.; Macri, P. [IAFE, Consejo de Investigaciones Cientificas y Tecnicas, Buenos Aires (Argentina)
1997-04-28
We present a new wavefunction which describes the ion-atom problem above the ionization threshold. This is an approximate solution of the Schrodinger equation for the three-body Coulomb problem that can be expressed in terms of a confluent hypergeometric function of two variables. The proposed wavefunction includes correlation among the motions of the three particles and verifies the correct Coulombic asymptotic behaviours. (author).
Analytic solution of the relativistic Coulomb problem for a spinless Salpeter equation
International Nuclear Information System (INIS)
Durand, B.; Durand, L.
1983-01-01
We construct an analytic solution to the spinless S-wave Salpeter equation for two quarks interacting via a Coulomb potential, [2(-del 2 +m 2 )/sup 1/2/-M-α/r] psi(r) = 0, by transforming the momentum-space form of the equation into a mapping or boundary-value problem for analytic functions. The principal part of the three-dimensional wave function is identical to the solution of a one-dimensional Salpeter equation found by one of us and discussed here. The remainder of the wave function can be constructed by the iterative solution of an inhomogeneous singular integral equation. We show that the exact bound-state eigenvalues for the Coulomb problem are M/sub n/ = 2m/(1+α 2 /4n 2 )/sup 1/2/, n = 1,2,..., and that the wave function for the static interaction diverges for r→0 as C(mr)/sup -nu/, where #betta# = (α/π)(1+α/π+...) is known exactly
The convergent close-coupling method for a Coulomb three-body problem
International Nuclear Information System (INIS)
Bray, I.; Stelbovics, A.T.
1994-09-01
The close-coupling method relies on the reformulation of the Schroedinger equation into an infinite set of coupled-channel equations by expanding over the complete set of target states. The difficulty in applying this approach is that the continuum channels are known to be very important in the intermediate-energy region and coupling to them must be included with little approximation. The application of the Convergent Close-Coupling (CCC) method is discussed which allows the continuum to be treated in a systematic manner via the use of square-integrable states. The CCC method utilizes an expansion of the target in a complete set of orthogonal L 2 functions which form a basis for the underlying Hilbert space. The utility of the method relies on being able to demonstrate convergence in the scattering amplitudes of interest as the basis size is increased. Numerical examples for the well known Temkin-Poet problem are used to illustrate the method. It is estimated the methods may be readily applied to full electron-atom scattering problem. 17 refs., 4 figs
Some studies in scatering by Coulomb modified nuclear potentials
International Nuclear Information System (INIS)
Laha, U.
1988-01-01
Recently, there has been a surge of interest in theoretical questions concerning the Coulomb nuclear problems with the main emphasis on their off-shell behaviour. Earlier approaches to the problem made use of a version of the two-potential formula as used by Bajzer. A slightly different point of view is presented here. An expression for the interacting Green's function for motion in the Coulomb plus Graz potential is constructed and used to obtain the half-off-shell T matrix in the ''maximal reduced form''. Similar results were also derived for the off-shell Jost functions. It is explicitly demonstrated that Coulomb and Coulomb-like potentials the half-off-shell T matrix can be expressed in terms of on-and off-shell Jost functions in the same way as one does for a purely short range interaction. In presenting the results for T matrix and other related quantities, the Coulomb effect is included rigorously. Results clearly delineate the branch point singularities originating from the long range nature of the Coulomb interaction and thus provide a better understanding of the off-shell two-body Coulomb-like T matrices. It is hoped that these results will form an adequate starting point for rigorous calculations on few-body systems with charges. (author). 16 refs
Nuclear Astrophysics from View Point of Few-Body Problems
International Nuclear Information System (INIS)
Tumino, A.; Spitaleri, C.; Bertulani, C.; Mukhamedzhanov, A.M.
2013-01-01
Few-body systems provide very useful tools to solve different problems for nuclear astrophysics. This is the case of indirect techniques, developed to overcome some of the limits of direct measurements at astrophysical energies. Here the Coulomb dissociation, the asymptotic normalization coefficient and the Trojan Horse method are discussed. (author)
On the libration collinear points in the restricted three – body problem
Directory of Open Access Journals (Sweden)
Alzahrani F.
2017-03-01
Full Text Available In the restricted problem of three bodies when the primaries are triaxial rigid bodies, the necessary and sufficient conditions to find the locations of the three libration collinear points are stated. In addition, the Linear stability of these points is studied for the case of the Euler angles of rotational motion being θi = 0, ψi + φi = π/2, i = 1, 2 accordingly. We underline that the model studied in this paper has special importance in space dynamics when the third body moves in gravitational fields of planetary systems and particularly in a Jupiter model or a problem including an irregular asteroid.
Generating families in the restricted three-body problem
Hénon, Michel
The classical restricted three-body problem is of fundamental importance because of its applications in astronomy and space navigation, and also as a simple model of a non-integrable Hamiltonian dynamical system. A central role is played by periodic orbits, of which many have been computed numerically. This is the second volume of an attempt to explain and organize the material through a systematic study of generating families, the limits of families of periodic orbits when the mass ratio of the two main bodies becomes vanishingly small. We use quantitative analysis in the vicinity of bifurcations of types 1 and 2. In most cases the junctions between branches can now be determined. A first-order approximation of families of periodic orbits in the vicinity of a bifurcation is also obtained. This book is intended for scientists and students interested in the restricted problem, in its applications to astronomy and space research, and in the theory of dynamical systems.
Precise numerical results for limit cycles in the quantum three-body problem
International Nuclear Information System (INIS)
Mohr, R.F.; Furnstahl, R.J.; Hammer, H.-W.; Perry, R.J.; Wilson, K.G.
2006-01-01
The study of the three-body problem with short-range attractive two-body forces has a rich history going back to the 1930s. Recent applications of effective field theory methods to atomic and nuclear physics have produced a much improved understanding of this problem, and we elucidate some of the issues using renormalization group ideas applied to precise nonperturbative calculations. These calculations provide 11-12 digits of precision for the binding energies in the infinite cutoff limit. The method starts with this limit as an approximation to an effective theory and allows cutoff dependence to be systematically computed as an expansion in powers of inverse cutoffs and logarithms of the cutoff. Renormalization of three-body bound states requires a short range three-body interaction, with a coupling that is governed by a precisely mapped limit cycle of the renormalization group. Additional three-body irrelevant interactions must be determined to control subleading dependence on the cutoff and this control is essential for an effective field theory since the continuum limit is not likely to match physical systems (e.g., few-nucleon bound and scattering states at low energy). Leading order calculations precise to 11-12 digits allow clear identification of subleading corrections, but these corrections have not been computed
Three-body scattering problem in the fixed center approximation: The case of attraction
Energy Technology Data Exchange (ETDEWEB)
Kudryavtsev, Alexander E. [National Research Center Kurchatov Institute, Institute for Theoretical and Experimental Physics, Moscow (Russian Federation); Gani, Vakhid A. [National Research Center Kurchatov Institute, Institute for Theoretical and Experimental Physics, Moscow (Russian Federation); National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow (Russian Federation); Romanov, Alexander I. [National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow (Russian Federation)
2016-12-15
We study the scattering of a light particle on a bound pair of heavy particles (e.g., the deuteron) within the fixed center approximation in the case of light-heavy attraction, solving the integral equation for the three-body Green's function both in the coordinate and in the momentum space. The results for the three-body scattering amplitude appear to be ambiguous -they depend on a single real parameter. This parameter may be fixed by a three-body input, e.g., the three-body scattering length. We also solve the integral equation for the three-body Green function in the momentum space, introducing a finite cut-off. We show that all three approaches are equivalent. We also discuss how our approach to the problem matches with the introduction of three-body contact interaction as done by other authors. (orig.)
Existence for viscoplastic contact with Coulomb friction problems
Directory of Open Access Journals (Sweden)
Amina Amassad
2002-01-01
frictional contact between an elastic-viscoplastic body and a rigid obstacle. We model the frictional contact both by a Tresca's friction law and a regularized Coulomb's law. We assume, in a first part, that the contact is bilateral and that no separation takes place. In a second part, we consider the Signorini unilateral contact conditions. Proofs are based on a time-discretization method, Banach and Schauder fixed point theorems.
Extended Kepler–Coulomb quantum superintegrable systems in three dimensions
International Nuclear Information System (INIS)
Kalnins, E G; Kress, J M; Miller, W Jr
2013-01-01
The quantum Kepler–Coulomb system in three dimensions is well known to be second order superintegrable, with a symmetry algebra that closes polynomially under commutators. This polynomial closure is also typical for second order superintegrable systems in 2D and for second order systems in 3D with nondegenerate (four-parameter) potentials. However, the degenerate three-parameter potential for the 3D Kepler–Coulomb system (also second order superintegrable) is an exception, as its symmetry algebra does not close polynomially. The 3D four-parameter potential for the extended Kepler–Coulomb system is not even second order superintegrable, but Verrier and Evans (2008 J. Math. Phys. 49 022902) showed it was fourth order superintegrable, and Tanoudis and Daskaloyannis (2011 arXiv:11020397v1) showed that, if a second fourth order symmetry is added to the generators, the symmetry algebra closes polynomially. Here, based on the Tremblay, Turbiner and Winternitz construction, we consider an infinite class of quantum extended Kepler–Coulomb three- and four-parameter systems indexed by a pair of rational numbers (k 1 , k 2 ) and reducing to the usual systems when k 1 = k 2 = 1. We show these systems to be superintegrable of arbitrarily high order and determine the structure of their symmetry algebras. We demonstrate that the symmetry algebras close algebraically; only for systems admitting extra discrete symmetries is polynomial closure achieved. Underlying the structure theory is the existence of raising and lowering operators, not themselves symmetry operators or even defined independent of basis, that can be employed to construct the symmetry operators and their structure relations. (paper)
The three-body problem in quantum mechanics
International Nuclear Information System (INIS)
Antunes, A.C.B.
1973-01-01
Different methods used in the analysis of the scattering of an elementary particle by a system of two bound particles are compared. All particles are considered spinless and distinguishable from each other. Two approaches are used in the treatment of the problem. In the first method we build an effective - potential which accounts for the interaction of the incident particle with the bound system. The second approach consists in treating the target as a system of two particles, whose momentum distribution is given by the bound state wavefunction. The three body system is then treated by the techniques of the multiple scattering series and of Glauber theory. (author)
Realizing all reduced syzygy sequences in the planar three-body problem
International Nuclear Information System (INIS)
Moeckel, Richard; Montgomery, Richard
2015-01-01
The configuration space of the planar three-body problem, reduced by rotations and with collisions excluded, has a rich topology which supports a large set of free homotopy classes. These classes have a simple description in terms of syzygy (or eclipse) sequences. Each homotopy class corresponds to a unique ‘reduced’ syzygy sequence. We prove that each reduced syzygy sequence is realized by a periodic solution of the rotation-reduced Newtonian planar three-body problem. The realizing solutions have small, nonzero angular momentum, repeatedly come very close to triple collision, and have lots of ‘stutters’—repeated syzygies of the same type, which cancel out up to homotopy. The heart of the proof stems from the work by one of us on symbolic dynamics arising out of the central configurations after the triple collision is blown up using McGehee's method. We end with a list of open problems. (paper)
Lyapunov vs. geometrical stability analysis of the Kepler and the restricted three body problems
International Nuclear Information System (INIS)
Yahalom, A.; Levitan, J.; Lewkowicz, M.; Horwitz, L.
2011-01-01
In this Letter we show that although the application of standard Lyapunov analysis predicts that completely integrable Kepler motion is unstable, the geometrical analysis of Horwitz et al. predicts the observed stability. This seems to us to provide evidence for both the incompleteness of the standard Lyapunov analysis and the strength of the geometrical analysis. Moreover, we apply this approach to the three body problem in which the third body is restricted to move on a circle of large radius which induces an adiabatic time dependent potential on the second body. This causes the second body to move in a very interesting and intricate but periodic trajectory; however, the standard Lyapunov analysis, as well as methods based on the parametric variation of curvature associated with the Jacobi metric, incorrectly predict chaotic behavior. The geometric approach predicts the correct stable motion in this case as well. - Highlights: → Lyapunov analysis predicts Kepler motion to be unstable. → Geometrical analysis predicts the observed stability. → Lyapunov analysis predicts chaotic behavior in restricted three body problem. → The geometric approach predicts the correct stable motion in restricted three body problem.
Modified Strum functions method in the nuclear three body problem
International Nuclear Information System (INIS)
Nasyrov, M.; Abdurakhmanov, A.; Yunusova, M.
1997-01-01
Fadeev-Hahn equations in the nuclear three-body problem were solved by modified Sturm functions method. Numerical calculations were carried out the square well potential. It was shown that the convergence of the method is high and the binding energy value is in agreement with experimental one (A.A.D.)
Lagrangian relative equilibria for a gyrostat in the three-body problem: bifurcations and stability
Energy Technology Data Exchange (ETDEWEB)
Guirao, Juan L G; Vera, Juan A, E-mail: juan.garcia@upct.e, E-mail: juanantonio.vera@upct.e [Departamento de Matematica Aplicada y EstadIstica, Universidad Politecnica de Cartagena, Hospital de Marina, 30203 Cartagena, Region de Murcia (Spain)
2010-05-14
In this paper we consider the non-canonical Hamiltonian dynamics of a gyrostat in the frame of the three-body problem. Using geometric/mechanic methods we study the approximate dynamics of the truncated Legendre series representation of the potential of an arbitrary order. Working in the reduced problem, we study the existence of relative equilibria that we refer to as Lagrange type following the analogy with the standard techniques. We provide necessary and sufficient conditions for the linear stability of Lagrangian relative equilibria if the gyrostat morphology form is close to a sphere. Thus, we generalize the classical results on equilibria of the three-body problem and many results on them obtained by the classic approach for the case of rigid bodies.
Coulomb Impurity Problem of Graphene in Strong Coupling Regime in Magnetic Fields.
Kim, S C; Yang, S-R Eric
2015-10-01
We investigate the Coulomb impurity problem of graphene in strong coupling limit in the presence of magnetic fields. When the strength of the Coulomb potential is sufficiently strong the electron of the lowest energy boundstate of the n = 0 Landau level may fall to the center of the potential. To prevent this spurious effect the Coulomb potential must be regularized. The scaling function for the inverse probability density of this state at the center of the impurity potential is computed in the strong coupling regime. The dependence of the computed scaling function on the regularization parameter changes significantly as the strong coupling regime is approached.
Green function of a three-dimensional Wick problem
International Nuclear Information System (INIS)
Matveev, V.A.
1988-01-01
An exact solution of a three-dimensional Coulomb Wick-Cutkovsky problem has been obtained which possesses the hidden 0(4)-symmetry. Here we shell give the derivation of the corresponding Green function and consider its connection with the asymptoric behaviour of the scattering amplitude. 9 refs
Coulomb-Fourier representation approach to three-body scattering with charged particles
International Nuclear Information System (INIS)
Alt, E.O.; Levin, S.B.; Yakovlev, S.L.
2004-01-01
We present a novel approach for calculating charged-composite particle scattering. It consists in eliminating by means of a suitably chosen representation that part of the interaction which is of longest range and, hence, gives rise to all the troublesome features which plague charged particle scattering theories. In this paper only the simplest case is considered, namely that of two charged and one neutral particles which interact via pairwise strong potentials, and a repulsive Coulomb potential between the charged particles
Solution of the Chandler-Gibson equations for a three-body test problem
International Nuclear Information System (INIS)
Gibson, A.G.; Waters, A.J.; Berthold, G.H.; Chandler, C.
1991-01-01
The Chandler-Gibson (CG) N-body equations are tested by considering the problem of three nonrelativistic particles moving on a line and interacting through attractive delta-function potentials. In particular, the input Born and overlap matrix-valued functions are evaluated analytically, and the CG equations are solved using a B-spline collocation method. The computed scattering matrix elements are within 0.5% of the known exact solutions, and the corresponding scattering probabilities are within 0.001% of the exact probabilities, both below and above the 3-body breakup threshold. These results establish that the CG method is practical, as well as theoretically correct, and may be a valuable approach for solving certain more complicated N-body scattering problems
Free time minimizers for the three-body problem
Moeckel, Richard; Montgomery, Richard; Sánchez Morgado, Héctor
2018-03-01
Free time minimizers of the action (called "semi-static" solutions by Mañe in International congress on dynamical systems in Montevideo (a tribute to Ricardo Mañé), vol 362, pp 120-131, 1996) play a central role in the theory of weak KAM solutions to the Hamilton-Jacobi equation (Fathi in Weak KAM Theorem in Lagrangian Dynamics Preliminary Version Number 10, 2017). We prove that any solution to Newton's three-body problem which is asymptotic to Lagrange's parabolic homothetic solution is eventually a free time minimizer. Conversely, we prove that every free time minimizer tends to Lagrange's solution, provided the mass ratios lie in a certain large open set of mass ratios. We were inspired by the work of Da Luz and Maderna (Math Proc Camb Philos Soc 156:209-227, 1980) which showed that every free time minimizer for the N-body problem is parabolic and therefore must be asymptotic to the set of central configurations. We exclude being asymptotic to Euler's central configurations by a second variation argument. Central configurations correspond to rest points for the McGehee blown-up dynamics. The large open set of mass ratios are those for which the linearized dynamics at each Euler rest point has a complex eigenvalue.
International Nuclear Information System (INIS)
Hiratsuka, Y.; Oryu, S.; Gojuki, S.
2011-01-01
Reliability of the screened Coulomb renormalization method, which was proposed in an elegant way by Alt-Sandhas-Zankel-Ziegelmann (ASZZ), is discussed on the basis of 'two-potential theory' for the three-body AGS equations with the Coulomb potential. In order to obtain ASZZ's formula, we define the on-shell Moller function, and calculate it by using the Haeringen criterion, i. e. 'the half-shell Coulomb amplitude is zero'. By these two steps, we can finally obtain the ASZZ formula for a small Coulomb phase shift. Furthermore, the reliability of the Haeringen criterion is thoroughly checked by a numerically rigorous calculation for the Coulomb LS-type equation. We find that the Haeringen criterion can be satisfied only in the higher energy region. We conclude that the ASZZ method can be verified in the case that the on-shell approximation to the Moller function is reasonable, and the Haeringen criterion is reliable. (author)
Three-body calculations at Los Alamos
International Nuclear Information System (INIS)
Friar, J.L.
1986-01-01
This work was motivated by four goals: (1) by working in configuration space, where intuition is greatest, investigate graphically those trinucleon properties which are determined by specific features of wave functions; (2) produce benchmark calculations against which new techniques and numerical methods can be measured; (3) investigate the effect of the Coulomb interaction between the two protons in 3 He and in the p-d system; (4) systematically investigate the various trinucleon observables. Configuration space is particularly well-suited for investigating the Coulomb problem. The singularity and discontinuity problems associated with the Coulomb (momentum space) t-matrix are transformed into boundary condition problems in configuration space. One simply adds the Coulomb potential to the strong interaction. In order to produce accurate numerical solutions powerful techniques were adopted which have not frequently been used in nuclear physics. These spline methods together with collocation techniques combine the power of Gaussian quadrature procedures with the flexibility and strength of finite element approaches to solving partial differential equations. The union of these methods allows one to calculate wavefunctions at the same qualitative level of accuracy as the eigenvalues. Observables can therefore be calculated with considerable confidence. 30 refs., 6 figs
Three-body problem in d-dimensional space: Ground state, (quasi)-exact-solvability
Turbiner, Alexander V.; Miller, Willard; Escobar-Ruiz, M. A.
2018-02-01
As a straightforward generalization and extension of our previous paper [A. V. Turbiner et al., "Three-body problem in 3D space: Ground state, (quasi)-exact-solvability," J. Phys. A: Math. Theor. 50, 215201 (2017)], we study the aspects of the quantum and classical dynamics of a 3-body system with equal masses, each body with d degrees of freedom, with interaction depending only on mutual (relative) distances. The study is restricted to solutions in the space of relative motion which are functions of mutual (relative) distances only. It is shown that the ground state (and some other states) in the quantum case and the planar trajectories (which are in the interaction plane) in the classical case are of this type. The quantum (and classical) Hamiltonian for which these states are eigenfunctions is derived. It corresponds to a three-dimensional quantum particle moving in a curved space with special d-dimension-independent metric in a certain d-dependent singular potential, while at d = 1, it elegantly degenerates to a two-dimensional particle moving in flat space. It admits a description in terms of pure geometrical characteristics of the interaction triangle which is defined by the three relative distances. The kinetic energy of the system is d-independent; it has a hidden sl(4, R) Lie (Poisson) algebra structure, alternatively, the hidden algebra h(3) typical for the H3 Calogero model as in the d = 3 case. We find an exactly solvable three-body S3-permutationally invariant, generalized harmonic oscillator-type potential as well as a quasi-exactly solvable three-body sextic polynomial type potential with singular terms. For both models, an extra first order integral exists. For d = 1, the whole family of 3-body (two-dimensional) Calogero-Moser-Sutherland systems as well as the Tremblay-Turbiner-Winternitz model is reproduced. It is shown that a straightforward generalization of the 3-body (rational) Calogero model to d > 1 leads to two primitive quasi
Local Momenta and a Three-Body Gauge
Schillaci, Michael Jay
2000-06-01
Here I discuss position-dependent, phlocal momentum which depend upon the logarithmic gradient of a continuum Coulomb pair. These momenta have become increasingly important in the modeling of three-body scattering phenomena, while their precise mathematical and physical nature has remained unexplored. These momenta are analytic at all values of the radial separation, except possibly at zero, and can be used to illustrate why the reigning 3C wavefunction works so well in describing many phlight-atom ion processes. I calculate the contributions for several subsystems, and explain the schillaci/threebody/ momentum.html>asymmetric results achieved by Wiese(L.M. Wiese phet al.), PRL 25, 4982 (1997)., on the breakup of the (H_3^+) ion - a massive three-body system. I propose that the local momentum herein formulated become part of a three-body gauge constraint. When applied, a non-vanishing, position-dependent phase will modulate the resulting transition amplitude. The size of this modulation depends critically upon the system.
Nonunique and nonuniform mapping in few-body Coulomb-explosion imaging
Sayler, A. M.; Eckner, E.; McKenna, J.; Esry, B. D.; Carnes, K. D.; Ben-Itzhak, I.; Paulus, G. G.
2018-03-01
Much of our knowledge of molecular geometry and interaction dynamics comes from indirect measurements of the molecular fragments following breakup. This technique—Coulomb-explosion imaging (CEI), i.e., determining the initial molecular configuration of a system from the momenta of the resulting fragments using knowledge of the particle interactions—is one of the fundamental tools of molecular physics. Moreover, CEI has been a staple of molecular studies for decades. Here we show that one often cannot assign a unique initial configuration to the few-body breakup of a polyatomic molecule given the measurement of the resulting fragments' momenta. Specifically, multiple initial configurations can result in identical momenta for a molecule breaking into three or more parts. Further, the nonunique and nonuniform mapping from the initial configuration to the measured momenta also significantly complicates the determination of molecular alignment at the time of breakup.
Generalized ladder operators for the Dirac-Coulomb problem via SUSY QM
International Nuclear Information System (INIS)
Rodrigues, R. de Lima; Universidade Federal de Campina Grande, PB
2003-12-01
The supersymmetry in quantum mechanics and shape invariance condition are applied as an algebraic method to solving the Dirac-Coulomb problem. The ground state and the excited states are investigated via new generalized ladder operators. (author)
Orbits of the n-dimensional Kepler-Coulomb problem and universality of the Kepler laws
International Nuclear Information System (INIS)
Oender, M; Vercin, A
2006-01-01
In the standard classical mechanics textbooks used at undergraduate and graduate levels, no attention is paid to the dimensional aspects of the Kepler-Coulomb problem. We have shown that the orbits of the n-dimensional classical Kepler-Coulomb problem are the usual conic sections in a fixed two-dimensional subspace and the Kepler laws with their well-known forms are valid independent of dimension. The basic characteristics of motion in a central force field are also established in an arbitrary dimension. The approach followed is easily accessible to late undergraduate and recent graduate students
Three-body problem in the ground-state representation
International Nuclear Information System (INIS)
Gonzalez, A.
1993-01-01
The ground-state probability density of a three-body system is used to construct a classical potential U whose minimum coincides exactly with the ground-state energy. The spectrum of excited states may approximately be obtained by imposing quasiclassical quantization conditions over the classical motion in U. We show nontrivial one-dimensional models in which either this quantization condition is exact or considerably improves the usual semiclassical quantization. For three-dimensional problems, the small-oscillation frequencies in states with total angular momentum L = 0 are computed. These frequencies could represent an improvement over the frequencies of triatomic molecules computed with the use of ordinary quasiclassics for the motion of the nuclei in the molecular term. By providing a semiclassical description of the first excited quantum states, the sketched approach rises some interesting questions such as, for example, the relevance (once again) of classical chaos to quantum mechanics
Energy Analysis in the Elliptic Restricted Three-body Problem
Qi, Yi; de Ruiter, Anton
2018-05-01
The gravity assist or flyby is investigated by analyzing the inertial energy of a test particle in the elliptic restricted three-body problem (ERTBP), where two primary bodies are moving in elliptic orbits. Firstly, the expression of the derivation of energy is obtained and discussed. Then, the approximate expressions of energy change in a circular neighborhood of the smaller primary are derived. Numerical computation indicates that the obtained expressions can be applied to study the flyby problem of the nine planets and the Moon in the solar system. Parameters related to the flyby are discussed analytically and numerically. The optimal conditions, including the position and time of the periapsis, for a flyby orbit are found to make a maximum energy gain or loss. Finally, the mechanical process of a flyby orbit is uncovered by an approximate expression in the ERTBP. Numerical computations testify that our analytical results well approximate the mechanical process of flyby orbits obtained by the numerical simulation in the ERTBP. Compared with the previous research established in the patched-conic method and numerical calculation, our analytical investigations based on a more elaborate derivation get more original results.
Three-body problem in quantum mechanics: Hyperspherical elliptic coordinates and harmonic basis sets
International Nuclear Information System (INIS)
Aquilanti, Vincenzo; Tonzani, Stefano
2004-01-01
Elliptic coordinates within the hyperspherical formalism for three-body problems were proposed some time ago [V. Aquilanti, S. Cavalli, and G. Grossi, J. Chem. Phys. 85, 1362 (1986)] and recently have also found application, for example, in chemical reaction theory [see O. I. Tolstikhin and H. Nakamura, J. Chem. Phys. 108, 8899 (1998)]. Here we consider their role in providing a smooth transition between the known 'symmetric' and 'asymmetric' parametrizations, and focus on the corresponding hyperspherical harmonics. These harmonics, which will be called hyperspherical elliptic, involve products of two associated Lame polynomials. We will provide an expansion of these new sets in a finite series of standard hyperspherical harmonics, producing a powerful tool for future applications in the field of scattering and bound-state quantum-mechanical three-body problems
Solvability of Static Contact Problems with Coulomb Friction for Orthotropic Material
Czech Academy of Sciences Publication Activity Database
Eck, C.; Jarušek, Jiří
2008-01-01
Roč. 93, č. 1 (2008), s. 93-104 ISSN 0374-3535 R&D Projects: GA AV ČR IAA1075402 Institutional research plan: CEZ:AV0Z10190503 Keywords : contact problem * Coulomb friction * orthotropic elasticity Subject RIV: BA - General Mathematics Impact factor: 1.277, year: 2008
Electron induced break-up of helium. Benchmark experiments on a dynamical four-body Coulomb system
International Nuclear Information System (INIS)
Duerr, M.
2006-01-01
This work presents an experimental study of fragmentation of helium by electron impact, in which absolute fully differential cross sections for single ionization, ionization-excitation and double ionization were determined. By applying a charged-particle imaging technique, the so-called 'reaction microscope', a large fraction of the final-state momentum space is covered, and the major limitations of previous experimental methods applied in this field could be overcome. Decisive modifications of the previous reaction microscope were undertaken, the most important one being the arrangement of the projectile beam parallel to the imaging-fields. For single ionization on helium an enhanced electron emission outside the projectile scattering plane is observed at both considered impact energies (102 eV and 1 keV), which is similar to the result found for ion-impact (M. Schulz et al., Nature (London) 422, 48 (2003)). The angle resolved cross sections obtained for double ionization at 105 eV impact energy reveal, that the process is dominated by the mutual repulsion of the three final-state continuum electrons. However, signatures of more complex dynamics are also observed. The data provide an ultimate benchmark for recently developed theories treating the dynamical three- and four-body Coulomb problem. (orig.)
Electron induced break-up of helium. Benchmark experiments on a dynamical four-body Coulomb system
Energy Technology Data Exchange (ETDEWEB)
Duerr, M.
2006-07-05
This work presents an experimental study of fragmentation of helium by electron impact, in which absolute fully differential cross sections for single ionization, ionization-excitation and double ionization were determined. By applying a charged-particle imaging technique, the so-called 'reaction microscope', a large fraction of the final-state momentum space is covered, and the major limitations of previous experimental methods applied in this field could be overcome. Decisive modifications of the previous reaction microscope were undertaken, the most important one being the arrangement of the projectile beam parallel to the imaging-fields. For single ionization on helium an enhanced electron emission outside the projectile scattering plane is observed at both considered impact energies (102 eV and 1 keV), which is similar to the result found for ion-impact (M. Schulz et al., Nature (London) 422, 48 (2003)). The angle resolved cross sections obtained for double ionization at 105 eV impact energy reveal, that the process is dominated by the mutual repulsion of the three final-state continuum electrons. However, signatures of more complex dynamics are also observed. The data provide an ultimate benchmark for recently developed theories treating the dynamical three- and four-body Coulomb problem. (orig.)
A method for solving a three-body problem with energy-dependent interactions
International Nuclear Information System (INIS)
Safronov, A.N.
1994-01-01
A method is proposed for solving a three-body problem with energy-dependent interactions. This method is based on introducing the dependence of scattering operators and state vectors on an additional external parameter. Effects caused by the energy dependence of the interaction operator are investigated by using the unitary condition for the amplitude of the 2 → 2 and 2 → 3 transitions. It is shown, in particular, that taking this dependence into account leads to a change in the relation between the asymptotic normalization factor of the wave function of the three-body bound state and the vertex constant of virtual dissociation (synthesis) of the system into two fragments. 15 refs
Derivation of a configuration space Hamiltonian for heavy atoms: three body potentials
International Nuclear Information System (INIS)
Mittleman, M.H.
1981-01-01
A brief history of the difficulties associated with the derivation of a configuration space Hamiltonian is presented. One of the problems encountered is the definition of the projection operators which must occur. A variational definition is obtained and, with simplifying assumptions, the optimum projection operators are those which project onto Hartree-Fock orbitals. This puts many previously performed numerical calculations on a firm footing. The form of the two body interactions is discussed in the context of the gauge freedom. The Coulomb gauge is the favored one but it is pointed out that it has never been proven to be the best one. Finally a form for the relativistic three election potential is given and the possibility of its observation is discussed
Regularization of the Coulomb scattering problem
International Nuclear Information System (INIS)
Baryshevskii, V.G.; Feranchuk, I.D.; Kats, P.B.
2004-01-01
The exact solution of the Schroedinger equation for the Coulomb potential is used within the scope of both stationary and time-dependent scattering theories in order to find the parameters which determine the regularization of the Rutherford cross section when the scattering angle tends to zero but the distance r from the center remains finite. The angular distribution of the particles scattered in the Coulomb field is studied on rather a large but finite distance r from the center. It is shown that the standard asymptotic representation of the wave functions is inapplicable in the case when small scattering angles are considered. The unitary property of the scattering matrix is analyzed and the 'optical' theorem for this case is discussed. The total and transport cross sections for scattering the particle by the Coulomb center proved to be finite values and are calculated in the analytical form. It is shown that the effects under consideration can be important for the observed characteristics of the transport processes in semiconductors which are determined by the electron and hole scattering by the field of charged impurity centers
Separable expansions for local potentials with Coulomb interactions
International Nuclear Information System (INIS)
Adhikari, S.K.
1976-01-01
If two particles are interacting via a short range potential and a repulsive Coulomb potential the t matrix can be written as a sum of the Coulomb and the ''nuclear'' t matrices. In order to solve the three-nucleon problem with Coulomb interactions usually we need a separable representation of this ''nuclear'' t matrix. A recently proposed method for finding a separable expansion for local potentials is here extended to find a rapidly convergent separable expansion, with analytic form factors, for the ''nuclear'' part of the t matrix of a local potential, in the presence of Coulomb interactions. The method is illustrated for a two-term Malfliet-Tjon potential. In each rank the ''nuclear'' phase shift is close to the corresponding phase shift when the Coulomb interaction is switched off
Three-body Coulomb bound states
Bhatia, A. K.; Drachman, Richard J.
1987-01-01
The binding energies of three-particle systems containing two electrons and one positive particle of mass M are reexamined in an attempt to understand the approximate proportionality of the 1Se ground-state binding energies of the reduced masses, as pointed out by Botero and Green (1986). The contribution to the energy of the mass-polarization term is evaluated. No fundamental principle is involved, since the mass polarization merely decreases somewhat as the mass of the positive particle is reduced below the proton mass. In the case of the excited 3Pe state, this reduction is not sufficient to allow binding when M approaches the electron mass. Some properties of the recently observed negative muonium ion (e/-/ mu/+/ e/-/) are also computed.
Global regularization method for planar restricted three-body problem
Directory of Open Access Journals (Sweden)
Sharaf M.A.
2015-01-01
Full Text Available In this paper, global regularization method for planar restricted three-body problem is purposed by using the transformation z = x+iy = ν cos n(u+iv, where i = √−1, 0 < ν ≤ 1 and n is a positive integer. The method is developed analytically and computationally. For the analytical developments, analytical solutions in power series of the pseudotime τ are obtained for positions and velocities (u, v, u', v' and (x, y, x˙, y˙ in both regularized and physical planes respectively, the physical time t is also obtained as power series in τ. Moreover, relations between the coefficients of the power series are obtained for two consequent values of n. Also, we developed analytical solutions in power series form for the inverse problem of finding τ in terms of t. As typical examples, three symbolic expressions for the coefficients of the power series were developed in terms of initial values. As to the computational developments, the global regularized equations of motion are developed together with their initial values in forms suitable for digital computations using any differential equations solver. On the other hand, for numerical evolutions of power series, an efficient method depending on the continued fraction theory is provided.
A simple coordinate space approach to three-body problems ...
Indian Academy of Sciences (India)
We show how to treat the dynamics of an asymmetric three-body system consisting of one heavy and two identical light particles in a simple coordinate space variational approach. The method is constructive and gives an efﬁcient way of resolving a three-body system to an effective two-body system. It is illustrated by ...
The generalized parabolic Coulomb wavefunction in spherical coordinates
Energy Technology Data Exchange (ETDEWEB)
Gasaneo, G. [Consejo Nacional de Investigaciones Cientificas y Tecnicas, Departamento de Fisica, Universidad del Sur, Buenos Aires (Argentina); Colavecchia, F.D.; Garibotti, C.R. [Consejo Nacional de Investigaciones Cientificas y Tecnicas, Centro Atomico Bariloche, Rio Negro (Argentina); Otranto, S. [Consejo Nacional de Investigaciones Cientificas y Tecnicas, Departamento de Fisica, Universidad del Sur, Buenos Aires (Argentina); Consejo Nacional de Investigaciones Cientificas y Tecnicas, Centro Atomico Bariloche, Rio Negro (Argentina)
2001-10-19
In this work we present a detailed study of the recently introduced {delta}{sub m,n} basis for three Coulomb particles. We show that the scattering and generalized Coulomb problems as well as a {phi}{sub 2} approach can be viewed as particular cases of this basis. We derive a partial wave expansion for {delta}{sub m,n} functions and analyse the reduction to some of the precedent cases. (author)
Three-body calculation of two-body threshold electrodisintegration of 3He and 3H
International Nuclear Information System (INIS)
Heimbach, C.R.; Lehman, D.R.; O'Connell, J.S.
1977-01-01
Threshold two-body electrodisintegration of 3 He and 3 H is investigated within the context of exact three-body theory. The calculations performed are based on the formalism of Gibson and Lehman. Careful consideration is given to the singularities of the disintegration Born amplitude for this case, since the momentum transfer is not zero, to assure validity of the numerical methods. Calculated results are compared with all the latest threshold 3 He electrodisintegration data which samples a range of scattered-electron angles, 92.6 0 0 , and incident electron energies, 40 MeV 0 3 H electrodisintegration for some of the same kinematics. The mechanism for the sharp rise as a function of excitation energy in the (e,e') cross section for theta/sub e/ approx. 90 0 due to the 2 S → 2 S monopole transition from Coulomb scattering is singled out by examination of the contributions to the Coulomb doublet amplitude. A similar analysis is carried out for the doublet and quartet transverse amplitudes where the 2 S → 4 P magnetic quadrupole transition dominates for excitation energies less than 20 MeV
Exact Analytical Solutions in Three-Body Problems and Model of Neutrino Generator
Directory of Open Access Journals (Sweden)
Takibayev N.Zh.
2010-04-01
Full Text Available Exact analytic solutions are obtained in three-body problem for the scattering of light particle on the subsystem of two ﬁxed centers in the case when pair potentials have a separable form. Solutions show an appearance of new resonance states and dependence of resonance energy and width on distance between two ﬁxed centers. The approach of exact analytical solutions is expanded to the cases when two-body scattering amplitudes have the Breit-Wigner’s form and employed for description of neutron resonance scattering on subsystem of two heavy nuclei ﬁxed in nodes of crystalline lattice. It is shown that some resonance states have widths close to zero at the certain values of distance between two heavy scatterer centers, this gives the possibility of transitions between states. One of these transitions between three-body resonance states could be connected with process of electron capture by proton with formation of neutron and emission of neutrino. This exoenergic process leading to the cooling of star without nuclear reactions is discussed.
Application of Symplectic Algebraic Dynamics Algorithm to Circular Restricted Three-Body Problem
International Nuclear Information System (INIS)
Wei-Tao, Lu; Hua, Zhang; Shun-Jin, Wang
2008-01-01
Symplectic algebraic dynamics algorithm (SADA) for ordinary differential equations is applied to solve numerically the circular restricted three-body problem (CR3BP) in dynamical astronomy for both stable motion and chaotic motion. The result is compared with those of Runge–Kutta algorithm and symplectic algorithm under the fourth order, which shows that SADA has higher accuracy than the others in the long-term calculations of the CR3BP. (general)
An su(1, 1) algebraic approach for the relativistic Kepler-Coulomb problem
International Nuclear Information System (INIS)
Salazar-Ramirez, M; Granados, V D; MartInez, D; Mota, R D
2010-01-01
We apply the Schroedinger factorization method to the radial second-order equation for the relativistic Kepler-Coulomb problem. From these operators we construct two sets of one-variable radial operators which are realizations for the su(1, 1) Lie algebra. We use this algebraic structure to obtain the energy spectrum and the supersymmetric ground state for this system.
Tails and bridges in the parabolic restricted three-body problem
Barrabés, Esther; Cors, Josep M.; Garcia-Taberner, Laura; Ollé, Mercè
2017-12-01
After a close encounter of two galaxies, bridges and tails can be seen between or around them. A bridge would be a spiral arm between a galaxy and its companion, whereas a tail would correspond to a long and curving set of debris escaping from the galaxy. The goal of this paper is to present a mechanism, applying techniques of dynamical systems theory, that explains the formation of tails and bridges between galaxies in a simple model, the so-called parabolic restricted three-body problem, i.e. we study the motion of a particle under the gravitational influence of two primaries describing parabolic orbits. The equilibrium points and the final evolutions in this problem are recalled,and we show that the invariant manifolds of the collinear equilibrium points and the ones of the collision manifold explain the formation of bridges and tails. Massive numerical simulations are carried out and their application to recover previous results are also analysed.
Diffusion in Coulomb crystals.
Hughto, J; Schneider, A S; Horowitz, C J; Berry, D K
2011-07-01
Diffusion in Coulomb crystals can be important for the structure of neutron star crusts. We determine diffusion constants D from molecular dynamics simulations. We find that D for Coulomb crystals with relatively soft-core 1/r interactions may be larger than D for Lennard-Jones or other solids with harder-core interactions. Diffusion, for simulations of nearly perfect body-centered-cubic lattices, involves the exchange of ions in ringlike configurations. Here ions "hop" in unison without the formation of long lived vacancies. Diffusion, for imperfect crystals, involves the motion of defects. Finally, we find that diffusion, for an amorphous system rapidly quenched from Coulomb parameter Γ=175 to Coulomb parameters up to Γ=1750, is fast enough that the system starts to crystalize during long simulation runs. These results strongly suggest that Coulomb solids in cold white dwarf stars, and the crust of neutron stars, will be crystalline and not amorphous.
Leigh, Nathan W. C.; Wegsman, Shalma
2018-05-01
We present a formalism for constructing schematic diagrams to depict chaotic three-body interactions in Newtonian gravity. This is done by decomposing each interaction into a series of discrete transformations in energy- and angular momentum-space. Each time a transformation is applied, the system changes state as the particles re-distribute their energy and angular momenta. These diagrams have the virtue of containing all of the quantitative information needed to fully characterize most bound or unbound interactions through time and space, including the total duration of the interaction, the initial and final stable states in addition to every intervening temporary meta-stable state. As shown via an illustrative example for the bound case, prolonged excursions of one of the particles, which by far dominates the computational cost of the simulations, are reduced to a single discrete transformation in energy- and angular momentum-space, thereby potentially mitigating any computational expense. We further generalize our formalism to sequences of (unbound) three-body interactions, as occur in dense stellar environments during binary hardening. Finally, we provide a method for dynamically evolving entire populations of binaries via three-body scattering interactions, using a purely analytic formalism. In principle, the techniques presented here are adaptable to other three-body problems that conserve energy and angular momentum.
Three-body interactions in many-body effective field theory
International Nuclear Information System (INIS)
Furnstahl, R.J.
2004-01-01
This contribution is an advertisement for applying effective field theory (EFT) to many-body problems, including nuclei and cold atomic gases. Examples involving three-body interactions are used to illustrate how EFT's quantify and systematically eliminate model dependence, and how they make many-body calculations simpler and more powerful
Calculation of proton-deuteron phase parameters including the Coulomb force
International Nuclear Information System (INIS)
Alt, E.O.; Sandhas, W.; Ziegelmann, H.
1985-04-01
A previously proposed exact method for including the Coulomb force in three-body collisions is applied to proton-deuteron scattering. We present phase shifts for angular momenta up to L=9, from elastic threshold to 50 MeV proton laboratory energy. Separable rank-one potentials are taken for the nuclear interactions. A charge-independent and a charge-symmetric choise, while leading to different neutron-deuteron and proton-deuteron phase parameters, nevertheless yields practically the same Coulomb corrections. We, moreover, investigate the question of P-wave resonances.A critical comparison of our results with those obtained in a co-ordinate space formalism is performed. Furthermore, proposals for an approximate inclusion of the Coulomb potential are tested, and found unsatisfactory. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Ojeda-Guillén, D., E-mail: dogphysics@gmail.com [Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Ed. 9, Unidad Profesional Adolfo López Mateos, C.P. 07738, México D.F. (Mexico); Mota, R.D. [Escuela Superior de Ingeniería Mecánica y Eléctrica, Unidad Culhuacán, Instituto Politécnico Nacional, Av. Santa Ana No. 1000, Col. San Francisco Culhuacán, Delegación Coyoacán, C.P. 04430, México D.F. (Mexico); Granados, V.D. [Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Ed. 9, Unidad Profesional Adolfo López Mateos, C.P. 07738, México D.F. (Mexico)
2014-08-14
We decouple the Dirac's radial equations in D+1 dimensions with Coulomb-type scalar and vector potentials through appropriate transformations. We study each of these uncoupled second-order equations in an algebraic way by using an su(1,1) algebra realization. Based on the theory of irreducible representations, we find the energy spectrum and the radial eigenfunctions. We construct the Perelomov coherent states for the Sturmian basis, which is the basis for the unitary irreducible representation of the su(1,1) Lie algebra. The physical radial coherent states for our problem are obtained by applying the inverse original transformations to the Sturmian coherent states. - Highlights: • We solve the most general Dirac–Kepler–Coulomb problem. • The eigenfunctions and energy spectrum are obtained in a purely algebraic way. • We construct the radial SU(1,1) coherent states for the Kepler–Coulomb problem.
International Nuclear Information System (INIS)
Ojeda-Guillén, D.; Mota, R.D.; Granados, V.D.
2014-01-01
We decouple the Dirac's radial equations in D+1 dimensions with Coulomb-type scalar and vector potentials through appropriate transformations. We study each of these uncoupled second-order equations in an algebraic way by using an su(1,1) algebra realization. Based on the theory of irreducible representations, we find the energy spectrum and the radial eigenfunctions. We construct the Perelomov coherent states for the Sturmian basis, which is the basis for the unitary irreducible representation of the su(1,1) Lie algebra. The physical radial coherent states for our problem are obtained by applying the inverse original transformations to the Sturmian coherent states. - Highlights: • We solve the most general Dirac–Kepler–Coulomb problem. • The eigenfunctions and energy spectrum are obtained in a purely algebraic way. • We construct the radial SU(1,1) coherent states for the Kepler–Coulomb problem
Shape space figure-8 solution of three body problem with two equal masses
Yu, Guowei
2017-06-01
In a preprint by Montgomery (https://people.ucsc.edu/~rmont/Nbdy.html), the author attempted to prove the existence of a shape space figure-8 solution of the Newtonian three body problem with two equal masses (it looks like a figure 8 in the shape space, which is different from the famous figure-8 solution with three equal masses (Chenciner and Montgomery 2000 Ann. Math. 152 881-901)). Unfortunately there is an error in the proof and the problem is still open. Consider the α-homogeneous Newton-type potential, 1/rα, using action minimization method, we prove the existence of this solution, for α \\in (1, 2) ; for α=1 (the Newtonian potential), an extra condition is required, which unfortunately seems hard to verify at this moment.
Comment on 'analytic solution of the relativistic Coulomb problem for a spinless Salpeter equation'
International Nuclear Information System (INIS)
Lucha, W.; Schoeberl, F.F.
1994-01-01
We demonstrate that the analytic solution for the set of energy eigenvalues of the semi-relativistic Coulomb problem reported by B. and L. Durand is in clear conflict with an upper bound on the ground-state energy level derived by some straightforward variational procedure. (authors)
One particle properties in the 2D Coulomb problem. Luttinger-Ward variational approach
International Nuclear Information System (INIS)
Agnihotri, M.P.
2007-01-01
In this work, we have studied the 2D Coulomb problem. We used the Luttinger-Ward variational principle to determine the self-energy Σ in ring approximation. The use of an ansatz for Σ enables us to perform the frequency sums (integrals as T → 0) analytically. Compared to the usual procedure of iterating the self consistency equation with free Green's function as starting points, the present approach is superior. It works for higher density parameter r s (low density) where the iteration already fails to converge. The motivation of the present work is the quantum Hall system at filling factor 1/2. The Luttinger-Ward procedure is a rather powerful method in particular if combined with an analytical ansatz for Σ. The computation performed here for 2DEG has to be seen as a first step: There, the experiment shows the features of a free Fermion system that is interpreted as a system of Composite Fermions. If one studies the self energy of the Composite Fermions in an conserved approximation that corresponds to the ring approximation, one encounters a self consistency equation. However, an iterative solution of this equation meets with a complication: Instead of the polarization part Π 00 , in the case of the Composite Fermion there appears the longitudinal polarization part Π LL that has an additional factor (2k + q) 2 under the k integral. This integral converges only after the frequency integral is performed. It is highly difficult to reproduce this numerically. Here, the Luttinger-Ward variational approach applied to the 2D Coulomb problem in the present work looks promising. For the 2D Coulomb problem, in the ring approximation for the LW thermodynamic potential, that already leads to a formidable integral equation that has to be studied numerically. (orig.)
One particle properties in the 2D Coulomb problem. Luttinger-Ward variational approach
Energy Technology Data Exchange (ETDEWEB)
Agnihotri, M.P.
2007-04-27
In this work, we have studied the 2D Coulomb problem. We used the Luttinger-Ward variational principle to determine the self-energy {sigma} in ring approximation. The use of an ansatz for {sigma} enables us to perform the frequency sums (integrals as T {yields} 0) analytically. Compared to the usual procedure of iterating the self consistency equation with free Green's function as starting points, the present approach is superior. It works for higher density parameter r{sub s} (low density) where the iteration already fails to converge. The motivation of the present work is the quantum Hall system at filling factor 1/2. The Luttinger-Ward procedure is a rather powerful method in particular if combined with an analytical ansatz for {sigma}. The computation performed here for 2DEG has to be seen as a first step: There, the experiment shows the features of a free Fermion system that is interpreted as a system of Composite Fermions. If one studies the self energy of the Composite Fermions in an conserved approximation that corresponds to the ring approximation, one encounters a self consistency equation. However, an iterative solution of this equation meets with a complication: Instead of the polarization part {pi}{sub 00}, in the case of the Composite Fermion there appears the longitudinal polarization part {pi}{sub LL} that has an additional factor (2k + q){sup 2} under the k integral. This integral converges only after the frequency integral is performed. It is highly difficult to reproduce this numerically. Here, the Luttinger-Ward variational approach applied to the 2D Coulomb problem in the present work looks promising. For the 2D Coulomb problem, in the ring approximation for the LW thermodynamic potential, that already leads to a formidable integral equation that has to be studied numerically. (orig.)
Lu, Wei-Tao; Zhang, Hua; Wang, Shun-Jin
2008-07-01
Symplectic algebraic dynamics algorithm (SADA) for ordinary differential equations is applied to solve numerically the circular restricted three-body problem (CR3BP) in dynamical astronomy for both stable motion and chaotic motion. The result is compared with those of Runge-Kutta algorithm and symplectic algorithm under the fourth order, which shows that SADA has higher accuracy than the others in the long-term calculations of the CR3BP.
Time-frequency analysis of the restricted three-body problem: transport and resonance transitions
International Nuclear Information System (INIS)
Vela-Arevalo, Luz V; Marsden, Jerrold E
2004-01-01
A method of time-frequency analysis based on wavelets is applied to the problem of transport between different regions of the solar system, using the model of the circular restricted three-body problem in both the planar and the spatial versions of the problem. The method is based on the extraction of instantaneous frequencies from the wavelet transform of numerical solutions. Time-varying frequencies provide a good diagnostic tool to discern chaotic trajectories from regular ones, and we can identify resonance islands that greatly affect the dynamics. Good accuracy in the calculation of time-varying frequencies allows us to determine resonance trappings of chaotic trajectories and resonance transitions. We show the relation between resonance transitions and transport in different regions of the phase space
The baryonic spectrum in a constituent quark model including a three-body force
International Nuclear Information System (INIS)
Desplanques, B.; Gignoux, C.; Silvestre-Brac, B.; Gonzalez, P.; Navarro, J.; Noguera, S.
1992-01-01
We analyze, within a non-relativistic quark model, the low energy part of the baryonic spectrum in the octet and decuplet flavour representations. The relevance of a strong Coulomb potential is emphasized in order to explain its general features. The addition of a three-body force allows to solve the 'Roper puzzle', giving a consistent explanation to its relative position in the spectrum. (orig.)
Renormalization-group study of the four-body problem
International Nuclear Information System (INIS)
Schmidt, Richard; Moroz, Sergej
2010-01-01
We perform a renormalization-group analysis of the nonrelativistic four-boson problem by means of a simple model with pointlike three- and four-body interactions. We investigate in particular the region where the scattering length is infinite and all energies are close to the atom threshold. We find that the four-body problem behaves truly universally, independent of any four-body parameter. Our findings confirm the recent conjectures of others that the four-body problem is universal, now also from a renormalization-group perspective. We calculate the corresponding relations between the four- and three-body bound states, as well as the full bound-state spectrum and comment on the influence of effective range corrections.
Directory of Open Access Journals (Sweden)
Takashi Ito
2016-01-01
Full Text Available Terms in the analytic expansion of the doubly averaged disturbing function for the circular restricted three-body problem using the Legendre polynomial are explicitly calculated up to the fourteenth order of semimajor axis ratio (α between perturbed and perturbing bodies in the inner case (α1. The expansion outcome is compared with results from numerical quadrature on an equipotential surface. Comparison with direct numerical integration of equations of motion is also presented. Overall, the high-order analytic expansion of the doubly averaged disturbing function yields a result that agrees well with the numerical quadrature and with the numerical integration. Local extremums of the doubly averaged disturbing function are quantitatively reproduced by the high-order analytic expansion even when α is large. Although the analytic expansion is not applicable in some circumstances such as when orbits of perturbed and perturbing bodies cross or when strong mean motion resonance is at work, our expansion result will be useful for analytically understanding the long-term dynamical behavior of perturbed bodies in circular restricted three-body systems.
Convergence problems of Coulomb and multipole sums in crystals
International Nuclear Information System (INIS)
Kholopov, Evgenii V
2004-01-01
Different ways of calculating Coulomb and dipole sums over crystal lattices are analyzed comparatively. It is shown that the currently alleged disagreement between various approaches originates in ignoring the requirement for the self-consistency of surface conditions, which are of fundamental importance due to the long-range nature of the bulk interactions that these sums describe. This is especially true of surfaces arising when direct sums for infinite translation-invariant structures are truncated. The charge conditions for actual surfaces being self-consistently adjusted to the bulk state are formally the same as those on the truncation surface, consistent with the concept of the thermodynamic limit for the bulk-state absolute equilibrium and with the fact that the surface energy contribution in this case is, naturally, statistically small compared to the bulk contribution. Two-point multipole expansions are briefly discussed, and the problems associated with the boundary of their convergence circle are pointed out. (reviews of topical problems)
Frolov, Alexei M.
2018-03-01
The universal variational expansion for the non-relativistic three-body systems is explicitly constructed. This universal expansion can be used to perform highly accurate numerical computations of the bound state spectra in various three-body systems, including Coulomb three-body systems with arbitrary particle masses and electric charges. Our main interest is related to the adiabatic three-body systems which contain one bound electron and two heavy nuclei of hydrogen isotopes: the protium p, deuterium d and tritium t. We also consider the analogous (model) hydrogen ion ∞H2+ with the two infinitely heavy nuclei.
Coulomb potentials between spherical heavy ions
International Nuclear Information System (INIS)
Iwe, H.
1982-01-01
The Coulomb interaction between spherical nuclei having arbitrary radial nuclear charge distributions is calculated. All these realistic Coulomb potentials are given in terms of analytical expressions and are available for immediate application. So in no case a numerical computation of the Coulomb integral is required. The parameters of the charge distributions are taken from electron scattering analysis. The Coulomb self-energies of the charge distributions used are also calculated analytically in a closed form. For a number of nucleus-nucleus pairs, the Coulomb potentials derived from realistic charge distributions are compared with those normally used in various nucleus-nucleus optical model calculations. In this connection a detailed discussion of the problem how to choose consistently Coulomb parameters for different approximations is given. (orig.)
Global solutions to the electrodynamic two-body problem on a straight line
Bauer, G.; Deckert, D.-A.; Dürr, D.; Hinrichs, G.
2017-06-01
The classical electrodynamic two-body problem has been a long standing open problem in mathematics. For motion constrained to the straight line, the interaction is similar to that of the two-body problem of classical gravitation. The additional complication is the presence of unbounded state-dependent delays in the Coulomb forces due to the finiteness of the speed of light. This circumstance renders the notion of local solutions meaningless, and therefore, straightforward ODE techniques cannot be applied. Here, we study the time-symmetric case, i.e., the Fokker-Schwarzschild-Tetrode (FST) equations, comprising both advanced and retarded delays. We extend the technique developed in Deckert and Hinrichs (J Differ Equ 260:6900-6929, 2016), where existence of FST solutions was proven on the half line, to ensure global existence—a result that had been obtained by Bauer (Ein Existenzsatz für die Wheeler-Feynman-Elektrodynamik, Herbert Utz Verlag, München, 1997). Due to the novel technique, the presented proof is shorter and more transparent but also relies on the idea to employ asymptotic data to characterize solutions.
International Nuclear Information System (INIS)
Szalewicz, K.; Monkhorst, H.J.
1986-04-01
A solution of the Coulomb three-body problem is the beginning point for calculations of sticking fractions in muon catalyzed fusion. The basis set is constructed from the following functions xi/sup r/n/sup s/e/sup - αxi - β n/R/sup -3 /2//H/sub eta/(x)exp(-x 2 /2), where xi and eta are elliptic coordinates of muon, R is the internuclear distance, H/sub eta/ is the nth Hermite polynomial, and x = γ (R-R/sub e/). The nonlinear parameters α, β, γ, and R/sub e/ are to be optimized. 21 refs., 1 tab
International Nuclear Information System (INIS)
Kazantzis, P.G.
1979-01-01
New families of three-dimensional double-symmetric periodic orbits are determined numerically in the Sun-Jupiter case of the restricted three-body problem. These families bifurcate from the 'vertical-critical' orbits (αsub(ν) = -1, csub(ν) = 0) of the 'basic' plane families i. g 1 g 2 h, a, m and I. Further the numerical procedure employed in the determination of these families has been described and interesting results have been pointed out. Also, computer plots of the orbits of these families have been shown in conical projections. (orig.)
Method of resonating groups in the Faddeev-Hahn equation formalism for three-body nuclear problem
Nasirov, M Z
2002-01-01
The Faddeev-Hahn equation formalism for three-body nuclear problem is considered. For solution of the equations the method of resonant groups have applied. The calculations of tritium binding energy and doublet nd-scattering length have been carried out. The results obtained shows that Faddeev-Hahn equation formalism is very simple and effective. (author)
Benson, Christopher R; Maffeo, Christopher; Fatila, Elisabeth M; Liu, Yun; Sheetz, Edward G; Aksimentiev, Aleksei; Singharoy, Abhishek; Flood, Amar H
2018-05-07
The coordinated motion of many individual components underpins the operation of all machines. However, despite generations of experience in engineering, understanding the motion of three or more coupled components remains a challenge, known since the time of Newton as the "three-body problem." Here, we describe, quantify, and simulate a molecular three-body problem of threading two molecular rings onto a linear molecular thread. Specifically, we use voltage-triggered reduction of a tetrazine-based thread to capture two cyanostar macrocycles and form a [3]pseudorotaxane product. As a consequence of the noncovalent coupling between the cyanostar rings, we find the threading occurs by an unexpected and rare inchworm-like motion where one ring follows the other. The mechanism was derived from controls, analysis of cyclic voltammetry (CV) traces, and Brownian dynamics simulations. CVs from two noncovalently interacting rings match that of two covalently linked rings designed to thread via the inchworm pathway, and they deviate considerably from the CV of a macrocycle designed to thread via a stepwise pathway. Time-dependent electrochemistry provides estimates of rate constants for threading. Experimentally derived parameters (energy wells, barriers, diffusion coefficients) helped determine likely pathways of motion with rate-kinetics and Brownian dynamics simulations. Simulations verified intercomponent coupling could be separated into ring-thread interactions for kinetics, and ring-ring interactions for thermodynamics to reduce the three-body problem to a two-body one. Our findings provide a basis for high-throughput design of molecular machinery with multiple components undergoing coupled motion.
Canonical three-body angular basis
International Nuclear Information System (INIS)
Matveenko, A.V.
2001-01-01
Three-body problems are basic for the quantum mechanics of molecular, atomic, or nuclear systems. We demonstrate that their variational solution for rotational states can be greatly simplified. A special choice of coordinates (hyperspherical) and of the kinematics (body-fixed coordinate frame) allows one to choose basis functions in a form that makes the angular coupling trivial. (author)
Study of the 17Ne Coulomb dissociation process and its role for the rp process of nucleosynthesis
Energy Technology Data Exchange (ETDEWEB)
Marganiec, Justyna [TU Darmstadt (Germany); EMMI, GSI Darmstadt (Germany); Wamers, Felix [EMMI, GSI Darmstadt (Germany); TU Darmstadt (Germany); GSI Darmstadt (Germany); FIAS, Frankfurt am Main (Germany); Aumann, Thomas [TU Darmstadt (Germany); GSI Darmstadt (Germany); Egorova, Irina [BLTP JINR Dubna (Russian Federation); Grigorenko, Leonid [FLNR JINR Dubna (Russian Federation); RRC KI, Moscow (Russian Federation); Heil, Michael [GSI Darmstadt (Germany); Perfenova, Yuliya [FLNR JINR Dubna (Russian Federation); INP, Moscow (Russian Federation); Plag, Ralf [GSI Darmstadt (Germany); Goethe-Universitaet, Frankfurt am Main (Germany); Collaboration: R3B-Collaboration
2014-07-01
The study of {sup 17}Ne Coulomb dissociation process gives us a possibility to study the time-reversed reaction {sup 15}O(2p,γ){sup 17}Ne, with the detailed balance theorem. This reaction could serve as a bypass of {sup 15}O waiting point during the rp process, and move the initial CNO material towards heavier nuclei. The two-proton capture can proceed sequentially or directly from the three-body continuum. And the reaction rate can be enhanced by a few orders of magnitude by taking the three-body continuum into account. The Coulomb dissociation method is the one way to experimentally determine the three-body radiative capture cross section, which is needed to verify theoretical calculations, and which was not experimentally determined yet. The experiment has been performed at the LAND/R3B setup at GSI.
Stability and periodicity in the Sitnikov three-body problem when primaries are oblate spheroids
Rahman, M. A.; Garain, D. N.; Hassan, M. R.
2015-05-01
This paper deals with the effect of oblateness of the primaries of equal masses on the series solutions of the Sitnikov problem of three bodies. Effects of oblateness have also been shown on the stability of libration points and Poincare surface of section. Here series solutions have been developed with the help of iteration process of Green's function and by the Lindstedt-Poincare method. Following Murray and Dermott (Solar System Dynamics, Cambridge University Press, Cambridge, 1999) we have checked the stability of the equilibrium points in the Sitnikov problem. Periodicity and quasi-periodicity have been examined by drawing the Poincare surfaces of section using the mathematical software.
Three-body approach to the nucleon-nucleus optical potential
International Nuclear Information System (INIS)
Tandy, P.C.; Redish, E.F.; Bolle, D.
1976-01-01
In the Watson single scattering theory of the optical potential it is customary to approximate the propagation by two-body Green functions in order to simplify calculations. The reaction mechanism being described, however, is decidedly three-body in character. The central difficulty in building three-body models for nucleon-nucleus elastic scattering is to find the proper way of imbedding the superposed three-body reaction mechanism in the many-body problem without introducing serious overcounting effects. One would also like an explicit description of the intermediate state processes responsible for absorption. In this paper a three-body approximation to the optical potential theory is presented which overcomes the overcounting problem and is capable of including the following effects: (1) the proper kinematics of the struck nucleon, (2) its binding potential, (3) the identity of target nucleons, and (4) realistic wave functions and spectroscopic factors. The three-body model for the optical potential can be extended using unitarity methods to yield a unified three-body-like model of elastic scattering, pickup, and single nucleon knockout. (Auth.)
Stability at Potential Maxima: The L-4 and L-5 Points of the Restricted Three-Body Problem.
Greenberg, Richard; Davis, Donald R.
1978-01-01
Describes a dynamical system which is stable at potential maxima. The maxima, called L-4 and L-5, are stable locations of the restricted three-body problem. Energy loss from the system will tend to drive it away from stability. (GA)
A uniform semi-classical approach to the Coulomb fission problem
International Nuclear Information System (INIS)
Levit, S.; Smilansky, U.
1978-01-01
A semi-classical theory based on the path integral formalism is applied to the description of Coulomb fission. Complex classical trajectories are used to compute the classically forbidden transitions from the target's ground state to fission. In a simple model the energy spectrum and angular distributions of the fragments are calculated for the Coulomb fission in the Xe + U collision. Theoretical predictions are made which may be checked experimentally. (author)
The three-point function in split dimensional regularization in the Coulomb gauge
Leibbrandt, G
1998-01-01
We use a gauge-invariant regularization procedure, called ``split dimensional regularization'', to evaluate the quark self-energy $\\Sigma (p)$ and quark-quark-gluon vertex function $\\Lambda_\\mu (p^\\prime,p)$ in the Coulomb gauge, $\\vec{\\bigtriangledown}\\cdot\\vec{A}^a = 0$. The technique of split dimensional regularization was designed to regulate Coulomb-gauge Feynman integrals in non-Abelian theories. The technique which is based on two complex regulating parameters, $\\omega$ and $\\sigma$, is shown to generate a well-defined set of Coulomb-gauge integrals. A major component of this project deals with the evaluation of four-propagator and five-propagator Coulomb integrals, some of which are nonlocal. It is further argued that the standard one-loop BRST identity relating $\\Sigma$ and $\\Lambda_\\mu$, should by rights be replaced by a more general BRST identity which contains two additional contributions from ghost vertex diagrams. Despite the appearance of nonlocal Coulomb integrals, both $\\Sigma$ and $\\Lambda_\\...
Configuration space methods in the three-nucleon problem
International Nuclear Information System (INIS)
Friar, J.L.
1985-01-01
The assumptions underlying the formulation and solution of the Schroedinger equation for three nucleons in configuration space are reviewed. Those qualitative aspects of the two-nucleon problem which play an important role in the trinucleon are discussed. The geometrical aspects of the problem are developed, and the importance of the angular momentum barrier is demonstrated. The Faddeev-Noyes formulation of the Schroedinger equation is motivated, and the boundary conditions for various three-body problems is reviewed. The method of splines is shown to provide a particularly useful numerical modelling technique for solving the Faddeev-Noyes equation. The properties of explicit trinucleon solutions for various two-body force models are discussed, and the evidence for three-body forces is reviewed. The status of calculations of trinucleon observables is discussed, and conclusions are presented. 40 refs., 14 figs
Energy Technology Data Exchange (ETDEWEB)
Igamov, S. B., E-mail: igamov@inp.uz [Uzbek Academy of Sciences, Institute of Nuclear Physics (Uzbekistan)
2017-03-15
On the basis of the distorted-wave method, experimental data on the triple-differential cross section for the Coulomb breakup reaction {sup 208}Pb({sup 6}Li, αd){sup 208}Pb are analyzed by employing a correct expression for the final-state {sup 208}Pb–α–d three-particle Coulomb wave function. It is shown that the effect of final-state three-particle Coulomb dynamics can be used to assess the kinematical condition of clean Coulomb breakup processes. New values of the astrophysical S factor for the direct-radiative-capture reaction d(α, γ){sup 6}Li at ultralow energies in the range of 70 ≤ E{sub dα} ≤ 600 keV were extracted from experimental data. The value of S(0) = 1.60 ± 0.17 MeV nb was obtained.
Optimization of the variational basis in the three body problem
International Nuclear Information System (INIS)
Simenog, I.V.; Pushkash, O.M.; Bestuzheva, A.B.
1995-01-01
The procedure of variational oscillator basis optimization is proposed to the calculation the energy spectra of three body systems. The hierarchy of basis functions is derived and energies of ground and excited states for three gravitating particles is obtained with high accuracy. 12 refs
Three-body continuum states on a Lagrange mesh
International Nuclear Information System (INIS)
Descouvemont, P.; Tursunov, E.; Baye, D.
2006-01-01
Three-body continuum states are investigated with the hyperspherical method on a Lagrange mesh. The R-matrix theory is used to treat the asymptotic behaviour of scattering wave functions. The formalism is developed for neutral as well as for charged systems. We point out some specificities of continuum states in the hyperspherical method. The collision matrix can be determined with a good accuracy by using propagation techniques. The method is applied to the 6 He (=α+n+n) and 6 Be (=α+p+p) systems, as well as to 14 Be (=Be12+n+n). For 6 He, we essentially recover results of the literature. Application to 14 Be suggests the existence of an excited 2 + state below threshold. The calculated B(E2) value should make this state observable with Coulomb excitation experiments
Yangian Y(sl(2)) in Coulomb problem
International Nuclear Information System (INIS)
Zhang Shengli
1998-01-01
In this paper, the Yangian Y(sl(2)) is shown existing in the system that a particle moves in Coulomb field. The generators of Y(sl(2)) are constructed in terms of the angular momentum operators and so-called Yangian Runge-Lenz vector. The selection rule and matrix element of Y(sl(2)) generators are calculated. (orig.)
Coulomb corrections in the low-energy scattering
International Nuclear Information System (INIS)
Mur, V.D.; Popov, V.S.
1985-01-01
Renormalization of the coefficients of the ''effective range expansion'' is considered for the short-range Coulomb problem. The exactly solvable model of the Coulomb plus short range potential is considered. Exact solutions are compared with approximations frequently used in the theory of hadronic atoms
The three-point function in split dimensional regularization in the Coulomb gauge
International Nuclear Information System (INIS)
Leibbrandt, G.
1998-01-01
We use a gauge-invariant regularization procedure, called split dimensional regularization, to evaluate the quark self-energy Σ(p) and quark-quark-gluon vertex function Λ μ (p',p) in the Coulomb gauge, ∇-vector.A - vectora=0. The technique of split dimensional regularization was designed to regulate Coulomb-gauge Feynman integrals in non-Abelian theories. The technique which is based on two complex regulating parameters, ω and σ, is shown to generate a well-defined set of Coulomb-gauge integrals. A major component of this project deals with the evaluation of four-propagator and five-propagator Coulomb integrals, some of which are non-local. It is further argued that the standard one-loop BRST identity relating Σ and Λ μ , should by rights be replaced by a more general BRST identity which contains two additional contributions from ghost vertex diagrams. Despite the appearance of non-local Coulomb integrals, both Σ and Λ μ are local functions which satisfy the appropriate BRST identity. Application of split dimensional regularization to two-loop energy integrals is briefly discussed. (orig.)
Application of the three-body model to the reactions 6Li(3He,t 3He)3He and 6Li(3He,3He3He)3H
International Nuclear Information System (INIS)
Haftel, M.I.; Allas, R.G.; Beach, L.A.; Bondelid, R.O.; Petersen, E.L.; Slaus, I.; Lambert, J.M.; Treado, P.A.
1977-01-01
Experimental and theoretical cross sections are presented for the 6 Li( 3 He, 3 He 3 He) 3 H and 6 Li( 3 He,t 3 He) 3 He reactions for the symmetric angle pairs 20 0 -20 0 , 28.3 0 -28.3 0 , and 35 0 -35 0 . The theoretical cross sections are calculated in a three-body model where the trions (i.e., mass-3 nuclei) are treated as elementary particles with 6 Li being a 3 He- 3 H bound state. The trion-trion interaction is represented by S wave separable potentials with the breakup cross sections calculated with the tree-body Haftel-Ebenhoeh code. the Coulomb interaction is taken into account by fitting the separable potential parameters to the trion-trion scattering data and is included approximately in the breakup code. The experimental cross sections are compared with both the plane-wave impulse approximation and the three-body model predictions. The plane-wave impulse approximation predicts both the shapes and magnitudes poorly (10 to 20 times experiment). Without Coulomb corrections the three-body model gives good agreement with experiment for the shapes of the spectra with the magnitudes generally being about 40% of experiment for 6 Li( 3 He, 3 He 3 He) 3 H and about 80% for 6 Li( 3 He,t 3 He) 3 He. The Coulomb corrections improve the magnitudes predicted by the three-body model but not the shapes. It is observed that for these reactions S wave separable potentials describe the breakup data much better than they do the two-body trion-trion scattering data. This result should encourage further three-body treatment of these and similar reactions
Three-body molecular description of 9Be
International Nuclear Information System (INIS)
Revai, J.; Matveenko, A.V.
1979-01-01
The low lying spectrum of the 9 Be nucleus is calculated in the α+α+n three-body model. The molecular approach to this three-body problem based on the exact evalution of the two-center wave functions for separable n-α potentials is considered in detail. The numerical results are obtained in the generalized Born-Oppenheimer approximation which preserves total angular momentum and parity
Comparison of three empirical force fields for phonon calculations in CdSe quantum dots
Energy Technology Data Exchange (ETDEWEB)
Kelley, Anne Myers [Chemistry and Chemical Biology, University of California, Merced, 5200 North Lake Road, Merced, California 95343 (United States)
2016-06-07
Three empirical interatomic force fields are parametrized using structural, elastic, and phonon dispersion data for bulk CdSe and their predictions are then compared for the structures and phonons of CdSe quantum dots having average diameters of ~2.8 and ~5.2 nm (~410 and ~2630 atoms, respectively). The three force fields include one that contains only two-body interactions (Lennard-Jones plus Coulomb), a Tersoff-type force field that contains both two-body and three-body interactions but no Coulombic terms, and a Stillinger-Weber type force field that contains Coulombic interactions plus two-body and three-body terms. While all three force fields predict nearly identical peak frequencies for the strongly Raman-active “longitudinal optical” phonon in the quantum dots, the predictions for the width of the Raman peak, the peak frequency and width of the infrared absorption peak, and the degree of disorder in the structure are very different. The three force fields also give very different predictions for the variation in phonon frequency with radial position (core versus surface). The Stillinger-Weber plus Coulomb type force field gives the best overall agreement with available experimental data.
Analytic structure of many-body Coulombic wave functions
DEFF Research Database (Denmark)
Fournais, Søren; Hoffmann-Ostenhof, Maria; Hoffmann-Ostenhof, Thomas
2009-01-01
We investigate the analytic structure of solutions of non-relativistic Schrödinger equations describing Coulombic many-particle systems. We prove the following: Let ψ(x) with denote an N-electron wavefunction of such a system with one nucleus fixed at the origin. Then in a neighbourhood of a coal...
Efimov three-body states on top of a Fermi sea
International Nuclear Information System (INIS)
Nygaard, Nicolai Gayle; Zinner, Nikolaj Thomas
2014-01-01
The stabilization of Cooper pairs of bound electrons in the background of a Fermi sea is the origin of superconductivity and the paradigmatic example of the striking influence of many-body physics on few-body properties. In the quantum-mechanical three-body problem the famous Efimov effect yields unexpected scaling relations among a tower of universal states. These seemingly unrelated problems can now be studied in the same setup thanks to the success of ultracold atomic gas experiments. In light of the tremendous effect of a background Fermi sea on two-body properties, a natural question is whether a background can modify or even destroy the Efimov effect. Here we demonstrate how the generic problem of three interacting particles changes when one particle is embedded in a background Fermi sea, and show that Efimov scaling persists. It is found in a scaling that relates the three-body physics to the background density of fermionic particles
Ferrari, Fabio; Lavagna, Michèle
2018-06-01
The design of formations of spacecraft in a three-body environment represents one of the most promising challenges for future space missions. Two or more cooperating spacecraft can greatly answer some very complex mission goals, not achievable by a single spacecraft. The dynamical properties of a low acceleration environment such as the vicinity of libration points associated to a three-body system, can be effectively exploited to design spacecraft configurations able of satisfying tight relative position and velocity requirements. This work studies the evolution of an uncontrolled formation orbiting in the proximity of periodic orbits about collinear libration points under the Circular and Elliptic Restricted Three-Body Problems. A three spacecraft triangularly-shaped formation is assumed as a representative geometry to be investigated. The study identifies initial configurations that provide good performance in terms of formation keeping, and investigates key parameters that control the relative dynamics between the spacecraft within the three-body system. Formation keeping performance is quantified by monitoring shape and size changes of the triangular formation. The analysis has been performed under five degrees of freedom to define the geometry, the orientation and the location of the triangle in the synodic rotating frame.
International Nuclear Information System (INIS)
Hoffmann, B.
1984-07-01
In three chapters different physical situations are described which have commonly the Coulomb interaction as driving force. The first two chapters study the Coulomb interactions in connection with the excitation of inner electron shells and the Coulomb excitation of nuclei in first order. In the third part on effect ofthe Coulomb interaction between electronic shell and nucleus is treated in second order (nuclear polarization), and its effect on the isotopic and isomeric shift is studied. (orig./HSI) [de
International Nuclear Information System (INIS)
Melde, T.; Canton, L.; Svenne, J.P.
2002-01-01
We formulate the three-body problem in one dimension in terms of the (Faddeev-type) integral equation approach. As an application, we develop a spinless, one-dimensional (1-D) model that mimics three-nucleon dynamics in one dimension. Using simple two-body potentials that reproduce the deuteron binding, we obtain that the three-body system binds at about 7.5 MeV. We then consider two types of residual pionic corrections in the dynamical equation; one related to the 2π-exchange three-body diagram, the other to the 1π-exchange three-body diagram. We find that the first contribution can produce an additional binding effect of about 0.9 MeV. The second term produces smaller binding effects, which are, however, dependent on the uncertainty in the off-shell extrapolation of the two-body t-matrix. This presents interesting analogies with what occurs in three dimensions. The paper also discusses the general three-particle quantum scattering problem, for motion restricted to the fall line. (author)
Czech Academy of Sciences Publication Activity Database
Eck, Ch.; Jarušek, Jiří; Sofonea, M.
2010-01-01
Roč. 21, č. 3 (2010), s. 229-251 ISSN 0956-7925 R&D Projects: GA AV ČR IAA100750802 Institutional research plan: CEZ:AV0Z10190503 Keywords : elastic-vosco plastic material * dynamic contact problem * normal damped response * unilateral constraint * Coulomb friction * weak solution * penalitazion * smoothing Subject RIV: BA - General Mathematics Impact factor: 1.480, year: 2010 http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7675484&fileId=S0956792510000045
Ablikim, Utuq; Bomme, Cédric; Xiong, Hui; Savelyev, Evgeny; Obaid, Razib; Kaderiya, Balram; Augustin, Sven; Schnorr, Kirsten; Dumitriu, Ileana; Osipov, Timur; Bilodeau, René; Kilcoyne, David; Kumarappan, Vinod; Rudenko, Artem; Berrah, Nora; Rolles, Daniel
2016-12-02
An experimental route to identify and separate geometric isomers by means of coincident Coulomb explosion imaging is presented, allowing isomer-resolved photoionization studies on isomerically mixed samples. We demonstrate the technique on cis/trans 1,2-dibromoethene (C 2 H 2 Br 2 ). The momentum correlation between the bromine ions in a three-body fragmentation process induced by bromine 3d inner-shell photoionization is used to identify the cis and trans structures of the isomers. The experimentally determined momentum correlations and the isomer-resolved fragment-ion kinetic energies are matched closely by a classical Coulomb explosion model.
Directory of Open Access Journals (Sweden)
A. Narayan
2013-01-01
Full Text Available The oblateness and the photogravitational effects of both the primaries on the location and the stability of the triangular equilibrium points in the elliptical restricted three-body problem have been discussed. The stability of the triangular points under the photogravitational and oblateness effects of both the primaries around the binary systems Achird, Lyeten, Alpha Cen-AB, Kruger 60, and Xi-Bootis, has been studied using simulation techniques by drawing different curves of zero velocity.
International Nuclear Information System (INIS)
Volkov, M. V.; Elander, N.; Yakovlev, S. L.; Yarevsky, E. A.
2013-01-01
The complex-rotation method adapted to solving the multichannel scattering problem in the two-body system where the interaction potential contains the long-range Coulomb components is described. The scattering problem is reformulated as the problem of solving a nonhomogeneous Schrödinger equation in which the nonhomogeneous term involves a Coulomb potential cut off at large distances. The incident wave appearing in the nonhomogeneous term is a solution of the Schrödinger equation with longrange Coulomb interaction. This formulation is free from approximations associated with a direct cutoff of Coulomb interaction at large distances. The efficiency of this formalism is demonstrated by considering the example of solving scattering problems in the α-α and p-p systems.
Pederson, Mark R
2015-04-14
It is tacitly accepted that, for practical basis sets consisting of N functions, solution of the two-electron Coulomb problem in quantum mechanics requires storage of O(N(4)) integrals in the small N limit. For localized functions, in the large N limit, or for planewaves, due to closure, the storage can be reduced to O(N(2)) integrals. Here, it is shown that the storage can be further reduced to O(N(2/3)) for separable basis functions. A practical algorithm, that uses standard one-dimensional Gaussian-quadrature sums, is demonstrated. The resulting algorithm allows for the simultaneous storage, or fast reconstruction, of any two-electron Coulomb integral required for a many-electron calculation on processors with limited memory and disk space. For example, for calculations involving a basis of 9171 planewaves, the memory required to effectively store all Coulomb integrals decreases from 2.8 Gbytes to less than 2.4 Mbytes.
One-Step Direct Return Method For Mohr-Coulomb Plasticity
DEFF Research Database (Denmark)
Clausen, Johan; Damkilde, Lars; Andersen, Lars
2004-01-01
A new return method for the Mohr-Coulomb yield criteria is presented. The idea is to transform the problem into the principal direction and thereby achieve very simple formulas for calculating the elastic return stresses.......A new return method for the Mohr-Coulomb yield criteria is presented. The idea is to transform the problem into the principal direction and thereby achieve very simple formulas for calculating the elastic return stresses....
Coulomb gap triptych in a periodic array of metal nanocrystals.
Chen, Tianran; Skinner, Brian; Shklovskii, B I
2012-09-21
The Coulomb gap in the single-particle density of states (DOS) is a universal consequence of electron-electron interaction in disordered systems with localized electron states. Here we show that in arrays of monodisperse metallic nanocrystals, there is not one but three identical adjacent Coulomb gaps, which together form a structure that we call a "Coulomb gap triptych." We calculate the DOS and the conductivity in two- and three-dimensional arrays using a computer simulation. Unlike in the conventional Coulomb glass models, in nanocrystal arrays the DOS has a fixed width in the limit of large disorder. The Coulomb gap triptych can be studied via tunneling experiments.
3D Oscillator and Coulomb Systems reduced from Kahler spaces
Nersessian, Armen; Yeranyan, Armen
2003-01-01
We define the oscillator and Coulomb systems on four-dimensional spaces with U(2)-invariant Kahler metric and perform their Hamiltonian reduction to the three-dimensional oscillator and Coulomb systems specified by the presence of Dirac monopoles. We find the Kahler spaces with conic singularity, where the oscillator and Coulomb systems on three-dimensional sphere and two-sheet hyperboloid are originated. Then we construct the superintegrable oscillator system on three-dimensional sphere and ...
International Nuclear Information System (INIS)
Haberzettl, H.; Sandhas, W.
1981-01-01
Noclear reactions: Four-body problem. Effective two-body equations with exact (2+2)-subsystem contributions. Relation to field-theoretical model by Fonseca and Shanley. Three-body propagator with exchange effects. (orig.)
Czech Academy of Sciences Publication Activity Database
Beremlijski, P.; Outrata, Jiří; Haslinger, Jaroslav; Pathó, R.
2014-01-01
Roč. 52, č. 5 (2014), s. 3371-3400 ISSN 0363-0129 R&D Projects: GA ČR(CZ) GAP201/12/0671 Grant - others:GA MŠK(CZ) CZ.1.05/1.1.00/02.0070; GA MŠK(CZ) CZ.1.07/2.3.00/20.0070 Institutional support: RVO:67985556 ; RVO:68145535 Keywords : shape optimization * contact problems * Coulomb friction * solution-dependent coefficient of friction * mathematical programs with equilibrium constraints Subject RIV: BA - General Mathematics Impact factor: 1.463, year: 2014 http://library.utia.cas.cz/separaty/2014/MTR/outrata-0434234.pdf
Exact solution of the N-dimensional generalized Dirac-Coulomb equation
International Nuclear Information System (INIS)
Tutik, R.S.
1992-01-01
An exact solution to the bound state problem for the N-dimensional generalized Dirac-Coulomb equation, whose potential contains both the Lorentz-vector and Lorentz-scalar terms of the Coulomb form, is obtained. 24 refs. (author)
Three-body force in the three-nucleon system
International Nuclear Information System (INIS)
Gibson, B.F.
1986-01-01
A brief summary of the symposium is presented. Three-nucleon force models are discussed, including the two-pion exchange potential, NN-ΔN coupled-channels model, and phenomenological parametrization. Relevant experimental data and model calculations are discussed including form factors, binding energies, charge radii, and charge density for 3 H and 3 He. A calculation of the EMC effect for 3 He is also made using Sasakawa's wave function and compared to experimental data obtained at SLAC. The paper ends with discussions of proton-deuteron scattering, investigations at intermediate energies, and QCD efforts to understand the three-body problem
On Coulomb disintegration of relativistic nuclei and hypernuclei
International Nuclear Information System (INIS)
Lyuboshits, V.L.
1989-01-01
The dependence of the total cross-section of excitation and disintegration of a relativistic nucleus in the Coulomb field on the energy and parameters characterizing nuclear dimensions is investigated. The analogy with the problem of atomic ionization at the passage of charged particles through matter is used. The results are applied to the description of the Coulomb dissociation of nuclei with small binding energies. An explicit expression for the effective cross-section of the Coulomb disintegration of the hypernucleus-Λ 3 H into a deuteron and Λ-particle. 12 refs
On analytical solutions to the problem of the Coulomb and confining potentials
International Nuclear Information System (INIS)
Dineykhan, M.; Nazmitdinov, R.G.
1997-01-01
The oscillator representation method is presented and applied to calculate the energy spectrum of the superposition of the Coulomb and the power-law potentials, the Coulomb and the Yukawa potentials. The method provides an efficient way to obtain analytical results for arbitrary set of parameters of the considered potentials. The energies of ground and excited states of a quantum system are in good agreement with the exact results
Coulomb corrections for interferometry analysis of expanding hadron systems
Energy Technology Data Exchange (ETDEWEB)
Sinyukov, Yu.M.; Lednicky, R.; Pluta, J.; Erazmus, B. [Centre National de la Recherche Scientifique, 44 - Nantes (France). Lab. de Physique Subatomique et des Technologies Associees; Akkelin, S.V. [ITP, Kiev (Ukraine)
1997-09-01
The problem of the Coulomb corrections to the two-boson correlation functions for the systems formed in ultra-relativistic heavy ion collisions is considered for large effective system volumes. The modification of the standard zero-distance correction (so called Gamow or Coulomb factor) has been proposed for such a kind of systems. For the {pi}{sup +}{pi}{sup +} and K{sup +}K{sup +} correlation functions the analytical calculations of the Coulomb correction are compared with the exact numerical results. (author). 20 refs.
SUSY shape-invariant Hamiltonians for the generalized dirac-coulomb problem
International Nuclear Information System (INIS)
Rodrigues, R. de Lima; Vaidya, Arvind Narayan
2007-02-01
A spin 1/2 relativistic particle described by a general potential in terms of the sum of the Coulomb potential with a Lorentz scalar potential is investigated via supersymmetry in quantum mechanics. (author)
Ordering in classical Coulombic systems
International Nuclear Information System (INIS)
Schiffer, J. P.
1998-01-01
The author discusses the properties of classical Coulombic matter at low temperatures. It has been well known for some time [1,2] that infinite Coulombic matter will crystallize in body-centered cubic form when the quantity Λ (the dimensionless ratio of the average two-particle Coulomb energy to the kinetic energy per particle) is larger than approximately175. But the systems of such particles that have been produced in the laboratory in ion traps, or ion beams, are finite with surfaces defined by the boundary conditions that have to be satisfied. This results in ion clouds with sharply defined curved surfaces, and interior structures that show up as a set of concentric layers that are parallel to the outer surface. The ordering does not appear to be cubic, but the charges on each shell exhibit a ''hexatic'' pattern of equilateral triangles that is the characteristic of liquid crystals. The curvature of the surfaces prevents the structures on successive shells from interlocking in any simple fashion. This class of structures was first found in simulations [3] and later in experiments [4
Quasi-Three Body Systems: Properties and Scattering
International Nuclear Information System (INIS)
Amusia, M. Ya.
2017-01-01
We investigate systems of three mutually interacting particles with masses m e , m μ , M that obey the following inequality m e ≪ m μ ≪ M. Then the three-body problem reduces to the two-body scattering or structure of m e in the field of the pseudo-nucleus m μ M. We calculate analytically the properties of considered systems, such as the scattering cross-sections, hyperfine splitting, Auger decay of exited states and Lamb shifts, presenting them as expansions in powers of the parameter β=m e /m μ ≪1. (author)
On the special relativistic two-body problem
International Nuclear Information System (INIS)
Afanas'ev, G.N.; Asanov, R.A.
1979-01-01
The Poincare method is applied to the consideration of the two-body problem within the Special Relativity. The formulation of the theory contains two arbitrary functions of the Lorentz invariants. A specific choice of these functions leads to the correct description of three crucial experiments of the General Relativity. The expansion on the inverse powers of the light velocity being performed, the approximate Lorentz covariant two-body equations without retardation effects are obtained
Three-body vertices with two-body techniques
International Nuclear Information System (INIS)
Mitra, A.N.; Sharma, V.K.
1976-01-01
It has long been recognized that vertex functions for few particle systems provide a convenient medium for the analysis of reactions in the language of Feynman diagrams, analogously to elementary particle processes. The development of three-particle theory during the last decade has provided considerably more impetus for the use of the language of three-body vertex functions through the possibility of their 'exact' evaluations with only two-body input. While three-body vertices are probably superfluous for the description of only three-body processes (for which exact amplitudes are already available) their practical usefulness often extends to reactions involving more than three-particle systems (for which 'exact' amplitudes are still a distant goal), as long as such systems can be meaningfully described in terms of not more than three particles playing the active role. This paper investigates a simplified construction of three-body vertices. This must check against their standard definition as overlap integral. Unfortunately this definition involves a non-trivial normalization of three-body wave functions with realistic NN potentials, and has little practical scope for extension beyond A=3. (Auth.)
Directory of Open Access Journals (Sweden)
Jagadish Singh
2012-01-01
Full Text Available This paper investigates the positions and linear stability of an infinitesimal body around the equilibrium points in the framework of the Robe’s circular restricted three-body problem, with assumptions that the hydrostatic equilibrium figure of the first primary is an oblate spheroid and the second primary is an oblate body as well. It is found that equilibrium point exists near the centre of the first primary. Further, there can be one more equilibrium point on the line joining the centers of both primaries. Points on the circle within the first primary are also equilibrium points under certain conditions and the existence of two out-of-plane points is also observed. The linear stability of this configuration is examined and it is found that points near the center of the first primary are conditionally stable, while the circular and out of plane equilibrium points are unstable.
Resonances in three-particle systems
International Nuclear Information System (INIS)
Moeller, K.; Orlov, Y.V.
1989-01-01
Studies of the theory of resonances in three-particle systems are reviewed. Particular attention is paid to a method which uses analytic continuation of the Faddeev integral equations to the unphysical sheets of the Riemann energy surface. The features of the method are studied in the example of the two-body potential problem. In this case, Fourier transformation, normalization, and calculation of the matrix elements in the momentum representation are generalized to include Gamow states. The main subject of study is systems of nucleons. For these systems the results of experimental investigations during the last 20 years are also summarized. Problems of allowance for the Coulomb interaction are briefly discussed. Applications of the theory to other hadronic systems, including mesons and antinucleons, are mentioned
Internal or shape coordinates in the n-body problem
International Nuclear Information System (INIS)
Littlejohn, R.G.; Reinsch, M.
1995-01-01
The construction of global shape coordinates for the n-body problem is considered. Special attention is given to the three- and four-body problems. Quantities, including candidates for coordinates, are organized according to their transformation properties under so-called democracy transformations (orthogonal transformations of Jacobi vectors). Important submanifolds of shape space are identified and their topology studied, including the manifolds upon which shapes are coplanar or collinear, and the manifolds upon which the moment of inertia tensor is degenerate
Perturbative ambiguities in Coulomb gauge QCD
International Nuclear Information System (INIS)
Doust, P.
1987-01-01
The naive Coulomb gauge Feynman rules in non-abelian gauge theory give rise to ambiguous integrals, in addition to the usual ultraviolet divergences. Generalizing the work of Cheng and Tsai, these ambiguities are resolved to all orders in perturbation theory, by defining a gauge that interpolates smoothly between the Feynman gauge and the Coulomb gauge. The extra terms V 1 +V 2 of Christ and Lee are identified with certain two-loop ambiguous terms. However, there still seem to be unsolved problems connected with renormalisation. copyright 1987 Academic Press, Inc
Huang, K.-N.
1977-01-01
A computational procedure for calculating correlated wave functions is proposed for three-particle systems interacting through Coulomb forces. Calculations are carried out for the muonic helium atom. Variational wave functions which explicitly contain interparticle coordinates are presented for the ground and excited states. General Hylleraas-type trial functions are used as the basis for the correlated wave functions. Excited-state energies of the muonic helium atom computed from 1- and 35-term wave functions are listed for four states.
A Hamilton-like vector for the special-relativistic Coulomb problem
International Nuclear Information System (INIS)
Munoz, Gerardo; Pavic, Ivana
2006-01-01
A relativistic point charge moving in a Coulomb potential does not admit a conserved Hamilton vector. Despite this fact, a Hamilton-like vector may be developed that proves useful in the derivation and analysis of the particle's orbit
International Nuclear Information System (INIS)
Kayumov, S.S.; Mukhamedzhanov, A.M.; Yarmukhamedov, R.
1988-01-01
In the four-body model for partial amplitudes of two-neutron transfer induced by heavy ions we derive in the approximation of the mechanism of simultaneous transfer the expression for the senior term for l→∞ taking into account the Coulomb effects. The senior singular term of the amplitude at z = zeta is singled out explicitly (z = cos θ, θ is the scattering angle in the c.m.s. and zeta is the singularity closest to the physical region which corresponds to the mechanism of simultaneous transfer). We calculate differential cross sections for the transfer of two neutrons between heavy ions and estimate the accuracy of taking into account the Coulomb effects in the traditional method of distorted waves
Efimov three-body states on top of a Fermi sea
DEFF Research Database (Denmark)
Nygaard, Nicolai Gayle; Zinner, Nikolaj Thomas
2014-01-01
The stabilization of Cooper pairs of bound electrons in the background of a Fermi sea is the origin of superconductivity and the paradigmatic example of the striking influence of many-body physics on few-body properties. In the quantum-mechanical three-body problem the famous Efimov effect yields...
Guzzo, Massimiliano; Lega, Elena
2018-06-01
The circular restricted three-body problem has five relative equilibria L1 ,L2, . . . ,L5. The invariant stable-unstable manifolds of the center manifolds originating at the partially hyperbolic equilibria L1 ,L2 have been identified as the separatrices for the motions which transit between the regions of the phase-space which are internal or external with respect to the two massive bodies. While the stable and unstable manifolds of the planar problem have been extensively studied both theoretically and numerically, the spatial case has not been as deeply investigated. This paper is devoted to the global computation of these manifolds in the spatial case with a suitable finite time chaos indicator. The definition of the chaos indicator is not trivial, since the mandatory use of the regularizing Kustaanheimo-Stiefel variables may introduce discontinuities in the finite time chaos indicators. From the study of such discontinuities, we define geometric chaos indicators which are globally defined and smooth, and whose ridges sharply approximate the stable and unstable manifolds of the center manifolds of L1 ,L2. We illustrate the method for the Sun-Jupiter mass ratio, and represent the topology of the asymptotic manifolds using sections and three-dimensional representations.
International Nuclear Information System (INIS)
Barford, Thomas; Birse, Michael C
2005-01-01
A distorted-wave version of the renormalization group is applied to scattering by an inverse-square potential and to three-body systems. In attractive three-body systems, the short-distance wavefunction satisfies a Schroedinger equation with an attractive inverse-square potential, as shown by Efimov. The resulting oscillatory behaviour controls the renormalization of the three-body interactions, with the renormalization-group flow tending to a limit cycle as the cut-off is lowered. The approach used here leads to single-valued potentials with discontinuities as the bound states are cut off. The perturbations around the cycle start with a marginal term whose effect is simply to change the phase of the short-distance oscillations, or the self-adjoint extension of the singular Hamiltonian. The full power counting in terms of the energy and two-body scattering length is constructed for short-range three-body forces
Coulomb matrix elements in multi-orbital Hubbard models.
Bünemann, Jörg; Gebhard, Florian
2017-04-26
Coulomb matrix elements are needed in all studies in solid-state theory that are based on Hubbard-type multi-orbital models. Due to symmetries, the matrix elements are not independent. We determine a set of independent Coulomb parameters for a d-shell and an f-shell and all point groups with up to 16 elements (O h , O, T d , T h , D 6h , and D 4h ). Furthermore, we express all other matrix elements as a function of the independent Coulomb parameters. Apart from the solution of the general point-group problem we investigate in detail the spherical approximation and first-order corrections to the spherical approximation.
Representation of the Coulomb Matrix Elements by Means of Appell Hypergeometric Function F 2
Bentalha, Zine el abidine
2018-06-01
Exact analytical representation for the Coulomb matrix elements by means of Appell's double series F 2 is derived. The finite sum obtained for the Appell function F 2 allows us to evaluate explicitly the matrix elements of the two-body Coulomb interaction in the lowest Landau level. An application requiring the matrix elements of Coulomb potential in quantum Hall effect regime is presented.
International Nuclear Information System (INIS)
McGowan, F.K.; Stelson, P.H.
1974-01-01
The theory of Coulomb excitation and a brief review of pertinent treatments of the Coulomb excitation process that are useful for the analysis of experiments are given. Examples demonstrating the scope of nuclear structure information obtainable from gamma spectroscopy are presented. Direct Elambda excitation of 232 Th is discussed in terms of the one phonon octupole vibrational spectrum. B(MI) reduced transition probabilities resulting from Coulomb excitation of odd-A deformed nuclei with heavy ions are presented as a test of the rotational model. The use of gamma ray coincidence and particle-gamma coincidence as tools for investigating Coulomb excitation is discussed. (U.S.)
Coulomb Dissociation of {sup 17}Ne and its role for nuclear astrophysics
Energy Technology Data Exchange (ETDEWEB)
Marganiec, Justyna [ExtreMe Matter Institute EMMI, GSI, Darmstadt (Germany); Aumann, Thomas; Wamers, Felix [Kernreaktion und Nuklear Astrophysik, GSI, Darmstadt (Germany); Institut fuer Kernphysik, TU, Darmstadt (Germany); Heil, Michael [Kernreaktion und Nuklear Astrophysik, GSI, Darmstadt (Germany); Plag, Ralf [Kernreaktion und Nuklear Astrophysik, GSI, Darmstadt (Germany); Goethe-Universitaet, Frankfurt am Main (Germany); Collaboration: R3B-Collaboration
2011-07-01
The study of the Coulomb break up of {sup 17}Ne gives us an access to information about the time-reversed reaction {sup 15}O(2p,{gamma}){sup 17}Ne, which could serve as a bypass of {sup 15}O waiting point during the rp process, and move the initial CNO material towards heavier nuclei. The three-body radiative capture can proceed sequentially (J. Goerres, et al., Phys. Rev. C 51, 392, 1995) or directly from the three-body continuum (L.V. Grigorenko, M.V. Zhukov, Phys. Rev. C 72, 015803, 2005). It has been suggested that the reaction rate can be enhanced by a few orders of magnitude by taking into account the three-body continuum. In order to verify these calculations, the {sup 15}O(2p,{gamma}){sup 17}Ne cross section has been investigated. The experiment has been performed at the LAND/R{sup 3}B setup at GSI, using the fragment separator FRS to select a {sup 17}Ne secondary beam.
A psychiatric dialogue on the mind-body problem.
Kendler, K S
2001-07-01
Of all the human professions, psychiatry is most centrally concerned with the relationship of mind and brain. In many clinical interactions, psychiatrists need to consider both subjective mental experiences and objective aspects of brain function. This article attempts to summarize, in the form of a dialogue between a philosophically informed attending psychiatrist and three residents, the major philosophical positions on the mind-body problem. The positions reviewed include the following: substance dualism, property dualism, type identity, token identity, functionalism, eliminative materialism, and explanatory dualism. This essay seeks to provide a brief user-friendly introduction, from a psychiatric perspective, to current thinking about the mind-body problem.
Hip-hop solutions of the 2N-body problem
Barrabés, Esther; Cors, Josep Maria; Pinyol, Conxita; Soler, Jaume
2006-05-01
Hip-hop solutions of the 2N-body problem with equal masses are shown to exist using an analytic continuation argument. These solutions are close to planar regular 2N-gon relative equilibria with small vertical oscillations. For fixed N, an infinity of these solutions are three-dimensional choreographies, with all the bodies moving along the same closed curve in the inertial frame.
11Li Breakup on 208 at energies around the Coulomb barrier.
Fernández-García, J P; Cubero, M; Rodríguez-Gallardo, M; Acosta, L; Alcorta, M; Alvarez, M A G; Borge, M J G; Buchmann, L; Diget, C A; Falou, H A; Fulton, B R; Fynbo, H O U; Galaviz, D; Gómez-Camacho, J; Kanungo, R; Lay, J A; Madurga, M; Martel, I; Moro, A M; Mukha, I; Nilsson, T; Sánchez-Benítez, A M; Shotter, A; Tengblad, O; Walden, P
2013-04-05
The inclusive breakup for the (11)Li + (208)Pb reaction at energies around the Coulomb barrier has been measured for the first time. A sizable yield of (9)Li following the (11)Li dissociation has been observed, even at energies well below the Coulomb barrier. Using the first-order semiclassical perturbation theory of Coulomb excitation it is shown that the breakup probability data measured at small angles can be used to extract effective breakup energy as well as the slope of B(E1) distribution close to the threshold. Four-body continuum-discretized coupled-channels calculations, including both nuclear and Coulomb couplings between the target and projectile to all orders, reproduce the measured inclusive breakup cross sections and support the presence of a dipole resonance in the (11)Li continuum at low excitation energy.
Exclusion of nuclear forces in heavy-ion Coulomb excitation and Coulomb fission experiments
International Nuclear Information System (INIS)
Neese, R.E.; Guidry, M.W.
1982-01-01
A simple prescription for estimating the energy at which nuclear forces begin to play a role in heavy-ion Coulomb excitation and Coulomb fission experiments is presented. The method differs from most commonly used recipes in accounting for projectile and target nucleus deformation effects. Using a single adjustable parameter the formula reproduces the energy for the onset of Coulomb-nuclear interference effects for a broad range of heavy-ion systems. It is suggested that most Coulomb fission experiments which have been done involve both Coulomb and nuclear excitation processes and should more properly be termed Coulomb-nuclear fission experiments
Critical opalescence in the pure Coulomb system
Energy Technology Data Exchange (ETDEWEB)
Bobrov, V.B., E-mail: vic5907@mail.r [Joint Institute for High Temperatures, Russian Academy of Sciences, Izhorskaia St., 13, Bd. 2. Moscow 125412 (Russian Federation); Trigger, S.A., E-mail: satron@mail.r [Joint Institute for High Temperatures, Russian Academy of Sciences, Izhorskaia St., 13, Bd. 2. Moscow 125412 (Russian Federation); Institut fuer Physik, Humboldt-Universitaet zu Berlin, Newtonstrasse 15, D-12489 Berlin (Germany)
2011-04-18
Highlights: The review of the critical opalescence problem is presented. Light scattering in a two-component electron-nuclear system is studied. The exact relations between the structure factors and compressibility are found. The obtained relations are valid for strong interaction for the Coulomb systems. The experimental verification of these relations is possible for various elements. - Abstract: Based on the dielectric formalism and quantum field theory methods, the phenomenon of critical opalescence is explained for light scattering in pure matter as a two-component electron-nuclear system with Coulomb interaction. A similar phenomenon is shown to occur in the case of neutron scattering in pure substances as well. The obtained results are valid for quantum case and arbitrary strong Coulomb interaction. Thus, the relations between structure factors derived for the electron-nuclear system are the exact result of the quantum statistical mechanics.
The Coulomb gap and low energy statistics for Coulomb glasses
International Nuclear Information System (INIS)
Glatz, Andreas; Vinokur, Valerii M; Bergli, Joakim; Kirkengen, Martin; Galperin, Yuri M
2008-01-01
We study the statistics of local energy minima in the configuration space of two-dimensional lattice Coulomb glasses with site disorder and the behavior of the Coulomb gap depending on the strength of random site energies. At intermediate disorder, i.e., when the typical strength of the disorder is of the same order as the nearest-neighbor Coulomb energy, the high energy tail of the distribution of the local minima is exponential. We furthermore analyze the structure of the local minima and show that most sites of the system have the same occupation numbers in all of these states. The density of states (DOS) shows a transition from the crystalline state at zero disorder (with a hard gap) to an intermediate, probably glassy state with a Coulomb gap. We analyze this Coulomb gap in some detail and show that the DOS deviates slightly from the traditional linear behavior in 2D. For finite systems these intermediate Coulomb gap states disappear for large disorder strengths and only a random localized state in which all electrons are in the minima of the random potential exists. Dedication: This paper is dedicated to Thomas Nattermann, our dearest friend, brilliant colleague, and outstanding teacher
Evaluation of the Coulomb logarithm using cutoff and screened Coulomb interaction potentials
International Nuclear Information System (INIS)
Ordonez, C.A.; Molina, M.I.
1994-01-01
The Coulomb logarithm is a fundamental plasma parameter which is commonly derived within the framework of the binary collision approximation. The conventional formula for the Coulomb logarithm, λ=ln Λ, takes into account a pure Coulomb interaction potential for binary collisions and is not accurate at small values (λ D in place of λ D (the Debye length) in the conventional formula for the Coulomb logarithm
Analytical treatment of Coriolis coupling for three-body systems
Energy Technology Data Exchange (ETDEWEB)
Poirier, Bill
2005-01-31
In a previous article [J. Chem. Phys. 108 (1998) 5216], an efficient method was presented for performing 'exact' quantum calculations for the three-body rovibrational Hamiltonian, within the helicity-conserving approximation. This approach makes use of a certain three-body ''effective potential,'' enabling the same bend angle basis set to be employed for all values of the rotational quantum numbers, J, K and M. In the present work, the method is extended to incorporate Coriolis coupling, for which the relevant matrix elements are derived exactly. These can be used to solve the full three-body rovibrational problem, in the standard Jacobi coordinate vector embedding. Generalization of the method for coupled kinetic energy operators arising from other coordinate systems, embeddings, and/or system sizes, is also discussed.
Monopole operators and Hilbert series of Coulomb branches of 3 d = 4 gauge theories
Cremonesi, Stefano; Hanany, Amihay; Zaffaroni, Alberto
2014-01-01
This paper addresses a long standing problem - to identify the chiral ring and moduli space (i.e. as an algebraic variety) on the Coulomb branch of an = 4 superconformal field theory in 2+1 dimensions. Previous techniques involved a computation of the metric on the moduli space and/or mirror symmetry. These methods are limited to sufficiently small moduli spaces, with enough symmetry, or to Higgs branches of sufficiently small gauge theories. We introduce a simple formula for the Hilbert series of the Coulomb branch, which applies to any good or ugly three-dimensional = 4 gauge theory. The formula counts monopole operators which are dressed by classical operators, the Casimir invariants of the residual gauge group that is left unbroken by the magnetic flux. We apply our formula to several classes of gauge theories. Along the way we make various tests of mirror symmetry, successfully comparing the Hilbert series of the Coulomb branch with the Hilbert series of the Higgs branch of the mirror theory.
International Nuclear Information System (INIS)
1980-01-01
Considerable progress has been made on the long-range problems described in the original proposal document (1 February 1979 to 31 January 1980) and on the shorter-range problems described in the last renewal proposal (1 February 1980 to 31 January 1981). This progress concerns few-body structure problems (e.g., the existence of isobar components in 3 H, predictions of few-body-hypernuclei properties as a test of hyperon-nucleon interactions, investigation of the A = 6 ground states with exact three-body calculations, and the relation of triton D-state properties to the deuteron's D-state percentage) and electromagnetic properties and interactions of few-body nuclei (e.g., Coulomb effects in calculating and measuring asymptotic normalization constants, and γ + 3 He breakup reaction mechanisms at intermediate energies). Descriptions of the progress made indicate where each subject stands at present, and emphasize the significant results obtained. A publication list is attached
Fermi-edge transmission resonance in graphene driven by a single Coulomb impurity.
Karnatak, Paritosh; Goswami, Srijit; Kochat, Vidya; Pal, Atindra Nath; Ghosh, Arindam
2014-07-11
The interaction between the Fermi sea of conduction electrons and a nonadiabatic attractive impurity potential can lead to a power-law divergence in the tunneling probability of charge through the impurity. The resulting effect, known as the Fermi edge singularity (FES), constitutes one of the most fundamental many-body phenomena in quantum solid state physics. Here we report the first observation of FES for Dirac fermions in graphene driven by isolated Coulomb impurities in the conduction channel. In high-mobility graphene devices on hexagonal boron nitride substrates, the FES manifests in abrupt changes in conductance with a large magnitude ≈e(2)/h at resonance, indicating total many-body screening of a local Coulomb impurity with fluctuating charge occupancy. Furthermore, we exploit the extreme sensitivity of graphene to individual Coulomb impurities and demonstrate a new defect-spectroscopy tool to investigate strongly correlated phases in graphene in the quantum Hall regime.
Contact parameters in two dimensions for general three-body systems
DEFF Research Database (Denmark)
F. Bellotti, F.; Frederico, T.; T. Yamashita, M.
2014-01-01
a subsystem is composed of two identical non-interacting particles. We also show that the three-body contact parameter is negligible in the case of one non-interacting subsystem compared to the situation where all subsystem are bound. As example, we present results for mixtures of Lithium with two Cesium......We study the two dimensional three-body problem in the general case of three distinguishable particles interacting through zero-range potentials. The Faddeev decomposition is used to write the momentum-space wave function. We show that the large-momentum asymptotic spectator function has the same...... to obtain two- and three-body contact parameters. We specialize from the general cases to examples of two identical, interacting or non-interacting, particles. We find that the two-body contact parameter is not a universal constant in the general case and show that the universality is recovered when...
Critical opalescence in the pure Coulomb system
International Nuclear Information System (INIS)
Bobrov, V.B.; Trigger, S.A.
2011-01-01
Highlights: → The review of the critical opalescence problem is presented. → Light scattering in a two-component electron-nuclear system is studied. → The exact relations between the structure factors and compressibility are found. → The obtained relations are valid for strong interaction for the Coulomb systems. → The experimental verification of these relations is possible for various elements. - Abstract: Based on the dielectric formalism and quantum field theory methods, the phenomenon of critical opalescence is explained for light scattering in pure matter as a two-component electron-nuclear system with Coulomb interaction. A similar phenomenon is shown to occur in the case of neutron scattering in pure substances as well. The obtained results are valid for quantum case and arbitrary strong Coulomb interaction. Thus, the relations between structure factors derived for the electron-nuclear system are the exact result of the quantum statistical mechanics.
Qazi, Faisal; Fette, Don; Jafri, Syed S; I Padela, Aasim
2018-07-01
Famously posed by seventeenth-century French philosopher René Descartes, the mind-body problem remains unresolved in western philosophy and science, with both disciplines unable to move convincingly beyond the dualistic model. The persistence of dualism calls for a reframing of the problem through interdisciplinary modes of inquiry that include non-western points of view. One such perspective is Islamic theology of the soul, which, while approaching the problem from a distinct point of view, also adopts a position commensurate with (substance) dualism. Using this point of convergence as a conceptual starting point, we argue that bringing into dialogue contemporary neuroscientific, philosophy of mind, and Sunni Islamic theological discourses may provide a fruitful way of reframing the age-old mind-body problem. This paper provides an overview of how these three discourses have approached the issue of the mind-body (-soul) problem. Juxtaposing these three discourses, we hope, may ignite further scholarly dialogue and investigation.
Optically induced structural phase transitions in ion Coulomb crystals
DEFF Research Database (Denmark)
Horak, Peter; Dantan, Aurelien Romain; Drewsen, Michael
2012-01-01
We investigate numerically the structural dynamics of ion Coulomb crystals confined in a three-dimensional harmonic trap when influenced by an additional one-dimensional optically induced periodical potential. We demonstrate that transitions between thermally excited crystal structures, such as b......We investigate numerically the structural dynamics of ion Coulomb crystals confined in a three-dimensional harmonic trap when influenced by an additional one-dimensional optically induced periodical potential. We demonstrate that transitions between thermally excited crystal structures...
11Li Breakup on 208Pb at Energies Around the Coulomb Barrier
DEFF Research Database (Denmark)
Fernández-García, J.P.; Cubero, M.; Rodríguez-Gallardo, M.
2013-01-01
The inclusive breakup for the 11Li+208Pb reaction at energies around the Coulomb barrier has been measured for the first time. A sizable yield of 9Li following the 11Li dissociation has been observed, even at energies well below the Coulomb barrier. Using the first-order semiclassical perturbation...... theory of Coulomb excitation it is shown that the breakup probability data measured at small angles can be used to extract effective breakup energy as well as the slope of B(E1) distribution close to the threshold. Four-body continuum-discretized coupled-channels calculations, including both nuclear...... and Coulomb couplings between the target and projectile to all orders, reproduce the measured inclusive breakup cross sections and support the presence of a dipole resonance in the 11Li continuum at low excitation energy....
Coulomb torque - a general theory for electrostatic forces in many-body systems
International Nuclear Information System (INIS)
Khachatourian, Armik V M; Wistrom, Anders O
2003-01-01
In static experiments that comprise three conducting spheres suspended by torsion wires and held at constant electric potential, a net angular displacement about their centres has been observed. We demonstrate that the observed rotation is consistent with Coulomb's law of electrical forces complemented by Gauss' surface integrals for electrical potential. Analysis demonstrates that electrostatic torque is the result of electrostatic forces acting on an asymmetric distribution of charges residing on the surfaces of the spheres. The asymptotic value for electrostatic torque is proportional to the inverse of the fourth power of separation distance with the rotation direction, up or down taken perpendicular to a plane passing through sphere centres, given explicitly by the equation for torque. The identification of electrostatic torque prompts further analysis of models of matter at all size scales where electrostatic forces are the dominant operative force
Coulomb torque - a general theory for electrostatic forces in many-body systems
Khachaturian, A V M
2003-01-01
In static experiments that comprise three conducting spheres suspended by torsion wires and held at constant electric potential, a net angular displacement about their centres has been observed. We demonstrate that the observed rotation is consistent with Coulomb's law of electrical forces complemented by Gauss' surface integrals for electrical potential. Analysis demonstrates that electrostatic torque is the result of electrostatic forces acting on an asymmetric distribution of charges residing on the surfaces of the spheres. The asymptotic value for electrostatic torque is proportional to the inverse of the fourth power of separation distance with the rotation direction, up or down taken perpendicular to a plane passing through sphere centres, given explicitly by the equation for torque. The identification of electrostatic torque prompts further analysis of models of matter at all size scales where electrostatic forces are the dominant operative force.
Heat Coulomb blockade of one ballistic channel
Sivre, E.; Anthore, A.; Parmentier, F. D.; Cavanna, A.; Gennser, U.; Ouerghi, A.; Jin, Y.; Pierre, F.
2018-02-01
Quantum mechanics and Coulomb interaction dictate the behaviour of small circuits. The thermal implications cover fundamental topics from quantum control of heat to quantum thermodynamics, with prospects of novel thermal machines and an ineluctably growing influence on nanocircuit engineering. Experimentally, the rare observations thus far include the universal thermal conductance quantum and heat interferometry. However, evidence for many-body thermal effects paving the way to markedly different heat and electrical behaviours in quantum circuits remains wanting. Here we report on the observation of the Coulomb blockade of electronic heat flow from a small metallic circuit node, beyond the widespread Wiedemann-Franz law paradigm. We demonstrate this thermal many-body phenomenon for perfect (ballistic) conduction channels to the node, where it amounts to the universal suppression of precisely one quantum of conductance for the transport of heat, but none for electricity. The inter-channel correlations that give rise to such selective heat current reduction emerge from local charge conservation, in the floating node over the full thermal frequency range (laws for thermal transport in nanocircuits.
Screening of Coulomb interaction and many-body perturbation theory in atoms
International Nuclear Information System (INIS)
Dzyuba, V.A.; Flambaum, V.V.; Sil'vestrov, P.G.; Sushkov, O.P.
1988-01-01
Taking into account the electron Coulomb interaction screening considerably improves the convergence of perturbation theory in residual interaction. The developed technique allows to take into account screening diagrams in all orders of perturbation theory. Calculation of the correlation corrections to the thallium energy levels is carried out as an example
Three-body forces for electrons by the S-matrix method
International Nuclear Information System (INIS)
Margaritelli, R.
1989-01-01
A electromagnetic three-body potential between eletrons is derived by the S-matrix method. This potential can be compared up to a certain point with other electromagnetic potentials (obtained by other methods) encountered in the literature. However, since the potential derived here is far more complete than others, this turns direct comparison with the potentials found in the literature somewhat difficult. These calculations allow a better understanding of the S-matrix method as applied to problems which involve the calculations of three-body nuclear forces (these calculations are performed in order to understand the 3 He form factor). Furthermore, these results enable us to decide between two discrepant works which derive the two-pion exchange three-body potential, both by the S-matrix method. (author) [pt
Few-body problem in celestial mechanics
Energy Technology Data Exchange (ETDEWEB)
Dermott, S F [Cornell Univ., Ithaca, NY (USA). Center for Radiophysics and Space Research
1984-03-26
The approaches taken by solar system dynamicists to various outstanding problems has changed considerably in recent years. Some problems for which few-body approaches have been tried in the past are now thought to involve collective phenomena. Observed features in Saturn's rings associated with resonances are examples. On the other hand, the problem of the origin of the Kirkwood gaps in the asteroid belt, for which a number of a many-body approaches (involving collisions or gas friction) have been tried, probably has a few-body solution and may involve chaos.
Stripping reactions in a three-body system. Comparison of DWBA and exact solutions
International Nuclear Information System (INIS)
Brinati, J.R.
1976-01-01
Stripping reactions 'a estados no continuo' are studied in a three particle system. Since the three-body problem has an exact treatment, comparison will be made between the exact solution and the DWBA model solution. This problem is more complex in the continuous case, as shown in the convergence problem of the standard DWBA amplitude radial integral
Geometrical themes inspired by the n-body problem
Herrera, Haydeé; Herrera, Rafael
2018-01-01
Presenting a selection of recent developments in geometrical problems inspired by the N-body problem, these lecture notes offer a variety of approaches to study them, ranging from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references. A. Guillot’s notes aim to describe differential equations in the complex domain, motivated by the evolution of N particles moving on the plane subject to the influence of a magnetic field. Guillot studies such differential equations using different geometric structures on complex curves (in the sense of W. Thurston) in order to find isochronicity conditions. R. Montgomery’s notes deal with a version of the planar Newtonian three-body equation. Namely, he investigates the problem of whether every free homotopy class is realized by a periodic geodesic. The solution involves geometry, dynamical systems, and the McGehee blow-up. A novelty of the approach is the use of energy-balance in order t...
Coulomb Problem for Z > Zcr in Doped Graphene
Kuleshov, V. M.; Mur, V. D.; Fedotov, A. M.; Lozovik, Yu. E.
2017-12-01
The dynamics of charge carriers in doped graphene, i.e., graphene with a gap in the energy spectrum depending on the substrate, in the presence of a Coulomb impurity with charge Z is considered within the effective two-dimensional Dirac equation. The wave functions of carriers with conserved angular momentum J = M + 1/2 are determined for a Coulomb potential modified at small distances. This case, just as any two-dimensional physical system, admits both integer and half-integer quantization of the orbital angular momentum in plane, M = 0, ±1, ±2, …. For J = 0, ±1/2, ±1, critical values of the effective charge Z cr( J, n) are calculated for which a level with angular momentum J and radial quantum numbers n = 0 and n = 1 reaches the upper boundary of the valence band. For Z function of charge Z for the lowest values of orbital angular momentum M, the level with J = 0 being the first to descend to the band edge. For Z > Z cr ( J, n = 0), scattering phases are calculated as a function of hole energy for several values of supercriticality, as well as the positions ɛ0 and widths γ of quasistationary states as a function of supercriticality. The values of ɛ0* and width γ* are pointed out for which quasidiscrete levels may show up as Breit-Wigner resonances in the scattering of holes by a supercritical impurity. Since the phases are real, the partial scattering matrix is unitary, so that the radial Dirac equation is consistent even for Z > Z cr. In this single-particle approximation, there is no spontaneous creation of electron-hole pairs, and the impurity charge cannot be screened by this mechanism.
Coulomb interaction in multiple scattering theory
International Nuclear Information System (INIS)
Ray, L.; Hoffmann, G.W.; Thaler, R.M.
1980-01-01
The treatment of the Coulomb interaction in the multiple scattering theories of Kerman-McManus-Thaler and Watson is examined in detail. By neglecting virtual Coulomb excitations, the lowest order Coulomb term in the Watson optical potential is shown to be a convolution of the point Coulomb interaction with the distributed nuclear charge, while the equivalent Kerman-McManus-Thaler Coulomb potential is obtained from an averaged, single-particle Coulombic T matrix. The Kerman-McManus-Thaler Coulomb potential is expressed as the Watson Coulomb term plus additional Coulomb-nuclear and Coulomb-Coulomb cross terms, and the omission of the extra terms in usual Kerman-McManus-Thaler applications leads to negative infinite total reaction cross section predictions and incorrect pure Coulomb scattering limits. Approximations are presented which eliminate these anomalies. Using the two-potential formula, the full projectile-nucleus T matrix is separated into two terms, one resulting from the distributed nuclear charge and the other being a Coulomb distorted nuclear T matrix. It is shown that the error resulting from the omission of the Kerman-McManus-Thaler Coulomb terms is effectively removed when the pure Coulomb T matrix in Kerman-McManus-Thaler is replaced by the analogous quantity in the Watson approach. Using the various approximations, theoretical angular distributions are obtained for 800 MeV p+ 208 Pb elastic scattering and compared with experimental data
Generalized Coulomb gauge without Gribov ambiguity
Energy Technology Data Exchange (ETDEWEB)
Fachin, S.; Parrinello, C. (New York Univ., NY (United States). Physics Dept.)
1992-05-01
We discuss a global gauge-fixing prescription that is free of the Gribov problem, preserves reflection positivity and contains as a limiting case the (maximal) Coulomb gauge. In such a formalism it is very easy to check that only color singlet states propagate in Euclidean time, for any value of [beta]. (orig.).
Molecular integrals for slater type orbitals using coulomb sturmians
DEFF Research Database (Denmark)
Avery, James Emil; Avery, John Scales
2014-01-01
The use of Slater type orbitals in molecular calculations is hindered by the slowness of integral evaluation. In the present paper, we introduce a method for overcoming this problem by expanding STO's in terms of Coulomb Sturmians, for which the problem of evaluating molecular integrals rapidly has...
Nuclear structure with unitarily transformed two-body plus phenomenological three-body interactions
Energy Technology Data Exchange (ETDEWEB)
Guenther, Anneke
2011-02-02
The importance of three-nucleon forces for a variety of nuclear structure phenomena is apparent in various investigations. This thesis provides a first step towards the inclusion of realistic three-nucleon forces by studying simple phenomenological threebody interactions. The Unitary Correlation Operator Method (UCOM) and the Similarity Renormalization Group (SRG) provide two different approaches to derive soft phase-shift equivalent nucleon-nucleon (NN) interactions via unitary transformations. Although their motivations are quite different the NN interactions obtained with the two methods exhibit some similarities. The application of the UCOM- or SRG-transformed Argonne V18 potential in the Hartree-Fock (HF) approximation and including the second-order energy corrections emerging from many-body perturbation theory (MBPT) reveals that the systematics of experimental ground-state energies can be reproduced by some of the interactions considering a series of closed-shell nuclei across the whole nuclear chart. However, charge radii are systematically underestimated, especially for intermediate and heavy nuclei. This discrepancy to experimental data is expected to result from neglected three-nucleon interactions. As first ansatz for a three-nucleon force, we consider a finite-range three-body interaction of Gaussian shape. Its influence on ground-state energies and charge radii is discussed in detail on the basis of HF plus MBPT calculations and shows a significant improvement in the description of experimental data. As the handling of the Gaussian three-body interaction is time-extensive, we show that it can be replaced by a regularized three-body contact interaction exhibiting a very similar behavior. An extensive study characterizes its properties in detail and confirms the improvements with respect to nuclear properties. To take into account information of an exact numerical solution of the nuclear eigenvalue problem, the No-Core Shell Model is applied to
Energy Technology Data Exchange (ETDEWEB)
Harper, E P; Lehman, D R; Prats, F
1980-11-07
Considerable progress has been made on the long-range problems described in the original proposal document (1 February 1979 to 31 January 1980) and on the shorter-range problems described in the last renewal proposal (1 February 1980 to 31 January 1981). This progress concerns few-body structure problems (e.g., the existence of isobar components in /sup 3/H, predictions of few-body-hypernuclei properties as a test of hyperon-nucleon interactions, investigation of the A = 6 ground states with exact three-body calculations, and the relation of triton D-state properties to the deuteron's D-state percentage) and electromagnetic properties and interactions of few-body nuclei (e.g., Coulomb effects in calculating and measuring asymptotic normalization constants, and ..gamma.. + /sup 3/He breakup reaction mechanisms at intermediate energies). Descriptions of the progress made indicate where each subject stands at present, and emphasize the significant results obtained. A publication list is attached.
Higher-order dynamical effects in Coulomb dissociation
International Nuclear Information System (INIS)
Esbensen, H.
1994-06-01
We study the effect of higher-order processes in Coulomb dissociation of 11 Li by numerically solving the three-dimensional time-dependent Schroedinger equation for the relative motion of a di-neutron and the 9 Li core. Comparisons are made to first-order perturbation theory and to measurements. The calculated Coulomb reacceleration effects improve the agreement with experiment, but some discrepancy remains. The effects are much smaller in the dissociation of 11 Be, and they decrease with increasing beam energy. (orig.)
Three-body segment musculoskeletal model of the upper limb
Directory of Open Access Journals (Sweden)
Valdmanová L.
2013-06-01
Full Text Available The main aim is to create a computational three-body segment model of an upper limb of a human body for determination of muscle forces generated to keep a given loaded upper limb position. The model consists of three segments representing arm, forearm, hand and of all major muscles connected to the segments. Muscle origins and insertions determination corresponds to a real anatomy. Muscle behaviour is defined according to the Hill-type muscle model consisting of contractile and viscoelastic element. The upper limb is presented by a system of three rigid bars connected by rotational joints. The whole limb is fixed to the frame in the shoulder joint. A static balance problem is solved by principle of virtual work. The system of equation describing the musculoskeletal system is overdetermined because more muscles than necessary contribute to get the concrete upper limb position. Hence the mathematical problem is solved by an optimization method searching the least energetically-consuming solution. The upper limb computational model is verified by electromyography of the biceps brachii muscle.
Core polarization and Coulomb displacement energies
International Nuclear Information System (INIS)
Shlomo, S.; Love, W.G.
1982-01-01
The contributions of core polarization terms (other than the Auerbach-Kahana-Weneser (AKW) effect) to Coulomb displacement energies of mirror nuclei near A = 16 and A = 40 are examined within the particle-vibration coupling model. The parameters of the model are determined using updated data on the locations and strengths of multipole core excitations. In the absence of relevant data an energy-weighted sum rule (EWSR) is exploited. Taking into account multipole excitations up to L = 5 and subtracting the contributions which are due to short-range correlations, significant contributions (1-3%) to ΔEsub(c) are found. These corrections arise from particle coupling to low-lying collective states (long-range correlations). The implications of these results on the Coulomb energy problem are discussed. (Auth.)
Three-dimensional imaging of atomic four-body processes
Schulz, M; Fischer, D; Kollmus, H; Madison, D H; Jones, S; Ullrich, J
2003-01-01
To understand the physical processes that occur in nature we need to obtain a solid concept about the 'fundamental' forces acting between pairs of elementary particles. it is also necessary to describe the temporal and spatial evolution of many mutually interacting particles under the influence of these forces. This latter step, known as the few-body problem, remains an important unsolved problem in physics. Experiments involving atomic collisions represent a useful testing ground for studying the few-body problem. For the single ionization of a helium atom by charged particle impact, kinematically complete experiments have been performed since 1969. The theoretical analysis of such experiments was thought to yield a complete picture of the basic features of the collision process, at least for large collision energies. These conclusions are, however, almost exclusively based on studies of restricted electron-emission geometries. We report three- dimensional images of the complete electron emission pattern for...
Przybytek, Michal; Helgaker, Trygve
2013-08-07
We analyze the accuracy of the Coulomb energy calculated using the Gaussian-and-finite-element-Coulomb (GFC) method. In this approach, the electrostatic potential associated with the molecular electronic density is obtained by solving the Poisson equation and then used to calculate matrix elements of the Coulomb operator. The molecular electrostatic potential is expanded in a mixed Gaussian-finite-element (GF) basis set consisting of Gaussian functions of s symmetry centered on the nuclei (with exponents obtained from a full optimization of the atomic potentials generated by the atomic densities from symmetry-averaged restricted open-shell Hartree-Fock theory) and shape functions defined on uniform finite elements. The quality of the GF basis is controlled by means of a small set of parameters; for a given width of the finite elements d, the highest accuracy is achieved at smallest computational cost when tricubic (n = 3) elements are used in combination with two (γ(H) = 2) and eight (γ(1st) = 8) Gaussians on hydrogen and first-row atoms, respectively, with exponents greater than a given threshold (αmin (G)=0.5). The error in the calculated Coulomb energy divided by the number of atoms in the system depends on the system type but is independent of the system size or the orbital basis set, vanishing approximately like d(4) with decreasing d. If the boundary conditions for the Poisson equation are calculated in an approximate way, the GFC method may lose its variational character when the finite elements are too small; with larger elements, it is less sensitive to inaccuracies in the boundary values. As it is possible to obtain accurate boundary conditions in linear time, the overall scaling of the GFC method for large systems is governed by another computational step-namely, the generation of the three-center overlap integrals with three Gaussian orbitals. The most unfavorable (nearly quadratic) scaling is observed for compact, truly three-dimensional systems
Two-craft Coulomb formation study about circular orbits and libration points
Inampudi, Ravi Kishore
This dissertation investigates the dynamics and control of a two-craft Coulomb formation in circular orbits and at libration points; it addresses relative equilibria, stability and optimal reconfigurations of such formations. The relative equilibria of a two-craft tether formation connected by line-of-sight elastic forces moving in circular orbits and at libration points are investigated. In circular Earth orbits and Earth-Moon libration points, the radial, along-track, and orbit normal great circle equilibria conditions are found. An example of modeling the tether force using Coulomb force is discussed. Furthermore, the non-great-circle equilibria conditions for a two-spacecraft tether structure in circular Earth orbit and at collinear libration points are developed. Then the linearized dynamics and stability analysis of a 2-craft Coulomb formation at Earth-Moon libration points are studied. For orbit-radial equilibrium, Coulomb forces control the relative distance between the two satellites. The gravity gradient torques on the formation due to the two planets help stabilize the formation. Similar analysis is performed for along-track and orbit-normal relative equilibrium configurations. Where necessary, the craft use a hybrid thrusting-electrostatic actuation system. The two-craft dynamics at the libration points provide a general framework with circular Earth orbit dynamics forming a special case. In the presence of differential solar drag perturbations, a Lyapunov feedback controller is designed to stabilize a radial equilibrium, two-craft Coulomb formation at collinear libration points. The second part of the thesis investigates optimal reconfigurations of two-craft Coulomb formations in circular Earth orbits by applying nonlinear optimal control techniques. The objective of these reconfigurations is to maneuver the two-craft formation between two charged equilibria configurations. The reconfiguration of spacecraft is posed as an optimization problem using the
Impact of electron-electron Coulomb interaction on the high harmonic generation process in graphene
Avetissian, H. K.; Mkrtchian, G. F.
2018-03-01
Generation of high harmonics in a monolayer graphene initiated by a strong coherent radiation field, taking into account electron-electron Coulomb interaction, is investigated. A microscopic theory describing the nonlinear optical response of graphene is developed. The Coulomb interaction of electrons is treated in the scope of dynamic Hartree-Fock approximation. The closed set of integrodifferential equations for the single-particle density matrix of a graphene quantum structure is solved numerically. The obtained solutions show the significance of many-body Coulomb interaction on the high harmonic generation process in graphene.
Sub-Coulomb heavy ion neutron transfer reactions and neutron orbit sizes
International Nuclear Information System (INIS)
Phillips, W.R.
1976-01-01
Direct transfer reactions below the Coulomb barrier offer the best means of determining neutron densities near the nuclear surface. This paper describes how heavy ion sub-Coulomb transfer can be used to determine the rms radii of neutron orbits in certain nuclei. The theoretical background is outlined and problems associated with the comparison of experiment and theory are discussed. Experiments performed to calibrate sub-Coulomb heavy ion transfer reactions are presented, and some comments are made on the relative roles of light and heavy ion reactions. Preliminary values for the rms radii of neutron orbits and neutron excesses extracted from recent experiments are given, and some remarks are made concerning the implications of these results for the triton wave function and for the Coulomb energy difference anomaly. (author)
Unitary Pole Approximation For 16O S12state And 40ca P32state When Coulomb Interaction Is Included
Directory of Open Access Journals (Sweden)
A. Acharya
2015-08-01
Full Text Available Abstract The form factor of a separable interaction between a pair of particles is an important input in a three body calculation for a transfer reaction. The three body equations of Alt Grassberger and Sandhas have been solved for a system of three particles viz.p n and 16Oand p n and 40Ca when coulomb interaction is included between the particle pairs. The input in this calculation i.e. the two body t-matrices representing the interaction between the pairs of particles is taken to be of a separable form conforming to the bound state of the pair. The form factors of the total interaction between the particle pairs are constructed using the prescription of Ueta and Bund.
Coulomb corrections to scattering length and effective radius
International Nuclear Information System (INIS)
Mur, V.D.; Kudryavtsev, A.E.; Popov, V.S.
1983-01-01
The problem considered is extraction of the ''purely nuclear'' scattering length asub(s) (corresponding to the strong potential Vsub(s) at the Coulomb interaction switched off) from the Coulomb-nuclear scattering length asub(cs), which is an object of experimental measurement. The difference between asub(s) and asub(cs) is especially large if the potential Vsub(s) has a level (real or virtual) with an energy close to zero. For this case formulae are obtained relating the scattering lengths asub(s) and asub(cs), as well as the effective radii rsub(s) and rsub(cs). The results are extended to states with arbitrary angular momenta l. It is shown that the Coulomb correction is especially large for the coefficient with ksup(2l) in the expansion of the effective radius; in this case the correction contains a large logarithm ln(asub(B)/rsub(0)). The Coulomb renormalization of other terms in the effective radius espansion is of order (rsub(0)/asub(B)), where r 0 is the nuclear force radius, asub(B) is the Bohr radius. The obtained formulae are tried on a number of model potentials Vsub(s), used in nuclear physics
The body force in a three-dimensional Lame system identification and regularization
DEFF Research Database (Denmark)
Trong, Dang Duc; Phan, Thanh Nam; Thuc, Phung Trong
2012-01-01
Let a three-dimensional isotropic elastic body be described by the Lamé system with the body force of the form F(x, t) = (t)f (x), where is known. We consider the problem of determining the unknown spatial term f (x) of the body force when the surface stress history is given...
Stability of Dirac Liquids with Strong Coulomb Interaction.
Tupitsyn, Igor S; Prokof'ev, Nikolay V
2017-01-13
We develop and apply the diagrammatic Monte Carlo technique to address the problem of the stability of the Dirac liquid state (in a graphene-type system) against the strong long-range part of the Coulomb interaction. So far, all attempts to deal with this problem in the field-theoretical framework were limited either to perturbative or random phase approximation and functional renormalization group treatments, with diametrically opposite conclusions. Our calculations aim at the approximation-free solution with controlled accuracy by computing vertex corrections from higher-order skeleton diagrams and establishing the renormalization group flow of the effective Coulomb coupling constant. We unambiguously show that with increasing the system size L (up to ln(L)∼40), the coupling constant always flows towards zero; i.e., the two-dimensional Dirac liquid is an asymptotically free T=0 state with divergent Fermi velocity.
Energy Technology Data Exchange (ETDEWEB)
Salinic, Slavisa [University of Kragujevac, Faculty of Mechanical Engineering, Kraljevo (RS)
2010-10-15
In this paper, an analytical solution for the problem of finding profiles of gravity flow discharge chutes required to achieve maximum exit velocity under Coulomb friction is obtained by application of variational calculus. The model of a particle which moves down a rough curve in a uniform gravitational field is used to obtain a solution of the problem for various boundary conditions. The projection sign of the normal reaction force of the rough curve onto the normal to the curve and the restriction requiring that the tangential acceleration be non-negative are introduced as the additional constraints in the form of inequalities. These inequalities are transformed into equalities by introducing new state variables. Although this is fundamentally a constrained variational problem, by further introducing a new functional with an expanded set of unknown functions, it is transformed into an unconstrained problem where broken extremals appear. The obtained equations of the chute profiles contain a certain number of unknown constants which are determined from a corresponding system of nonlinear algebraic equations. The obtained results are compared with the known results from the literature. (orig.)
More than six hundred new families of Newtonian periodic planar collisionless three-body orbits
Li, XiaoMing; Liao, ShiJun
2017-12-01
The famous three-body problem can be traced back to Isaac Newton in the 1680s. In the 300 years since this "three-body problem" was first recognized, only three families of periodic solutions had been found, until 2013 when Šuvakov and Dmitrašinović [Phys. Rev. Lett. 110, 114301 (2013)] made a breakthrough to numerically find 13 new distinct periodic orbits, which belong to 11 new families of Newtonian planar three-body problem with equal mass and zero angular momentum. In this paper, we numerically obtain 695 families of Newtonian periodic planar collisionless orbits of three-body system with equal mass and zero angular momentum in case of initial conditions with isosceles collinear configuration, including the well-known figure-eight family found by Moore in 1993, the 11 families found by Šuvakov and Dmitrašinović in 2013, and more than 600 new families that have never been reported, to the best of our knowledge. With the definition of the average period T = T/L f, where L f is the length of the so-called "free group element", these 695 families suggest that there should exist the quasi Kepler's third law T* ≈ 2:433 ± 0:075 for the considered case, where T ≈ = T | E|3/2 is the scale-invariant average period and E is its total kinetic and potential energy, respectively. The movies of these 695 periodic orbits in the real space and the corresponding close curves on the "shape sphere" can be found via the website: http://numericaltank.sjtu.edu.cn/three-body/three-body.htm.
Electron capture by alpha particles from helium atoms in a Coulomb-Born distorted-wave approximation
International Nuclear Information System (INIS)
Ghanbari-Adivi, E; Ghavaminia, H
2012-01-01
A three-body Coulomb-Born continuum distorted-wave approximation is applied to calculate the differential and total cross sections for single-electron exchange in the collision of fast alpha particles with helium atoms in their ground states. The applied first-order distorted wave theory satisfies correct Coulomb boundary conditions. Both post and prior forms of the transition amplitude are calculated. The nuclear-screening effect of the passive electron on the differential and total cross sections is investigated. The results are compared with those of other theories and with the available experimental data. For differential cross sections, the comparisons show a reasonable agreement with empirical measurements at higher impact energies. The agreement between experimental data and the present calculations for total cross sections with the average of the post and prior forms of the transition amplitude is reasonable at all the specified energies.
Simbuca, using a graphics card to simulate Coulomb interactions in a penning trap
Van Gorp, S; Friedag, P; De Leebeeck, V; Tandecki, M; Weinheimer, C; Breitenfeldt, M; Traykov, E; Severijn, N; Mader, J; Soti, G; Iitaka, T; Herlert, A; Wauters, F; Zakoucky, D; Kozlov, V; Roccia, S
2011-01-01
In almost all cases, N-body simulations are limited by the computation time available. Coulomb interaction calculations scale with O(N(2)) with N the number of particles. Approximation methods exist already to reduce the computation time to O(NlogN) although calculating the interaction still dominates the total simulation time. We present Simbuca, a simulation package for thousands of ions moving in a Penning trap which will be applied for the WITCH experiment. Simbuca uses the output of the Cunbody-1 library, which calculates the gravitational interaction between entities on a graphics card, and adapts it for Coulomb calculations. Furthermore the program incorporates three realistic buffer gas models, the possibility of importing realistic electric and magnetic fieldmaps and different order integrators with adaptive step size and error control. The software is released under the GNU General Public License and free for use. Crown Copyright (C) 2010 Published by Elsevier B.V. All rights reserved.
Oblique water entry of a three dimensional body
Directory of Open Access Journals (Sweden)
Scolan Yves-Marie
2014-12-01
Full Text Available The problem of the oblique water entry of a three dimensional body is considered. Wagner theory is the theoretical framework. Applications are discussed for an elliptic paraboloid entering an initially flat free surface. A dedicated experimental campaign yields a data base for comparisons. In the present analysis, pressure, force and dynamics of the wetted surface expansion are assessed.
Metal nanoparticle film-based room temperature Coulomb transistor.
Willing, Svenja; Lehmann, Hauke; Volkmann, Mirjam; Klinke, Christian
2017-07-01
Single-electron transistors would represent an approach to developing less power-consuming microelectronic devices if room temperature operation and industry-compatible fabrication were possible. We present a concept based on stripes of small, self-assembled, colloidal, metal nanoparticles on a back-gate device architecture, which leads to well-defined and well-controllable transistor characteristics. This Coulomb transistor has three main advantages. By using the scalable Langmuir-Blodgett method, we combine high-quality chemically synthesized metal nanoparticles with standard lithography techniques. The resulting transistors show on/off ratios above 90%, reliable and sinusoidal Coulomb oscillations, and room temperature operation. Furthermore, this concept allows for versatile tuning of the device properties such as Coulomb energy gap and threshold voltage, as well as period, position, and strength of the oscillations.
Three-dimensional problems in the theory of cracks
International Nuclear Information System (INIS)
Panasyuk, V.V.; Andrejkiv, A.E.; Stadnik, M.M.
1979-01-01
Review of the main mechanical conceptions and mathematic methods, used in solving of spatial problems of the theory of cracks is given. At that, cases of effects upon a body of force static and cyclic and geometrically variable temperature fields are considered. The main calculation models of the theory of cracks are characterized in detail. Other models, derived from these ones and used in solving the above problems are also mentioned. Analysis and synthesis of the most general mathematic methods of solving three-dimensional problems of the theory of cracks are made. Besides precise methods, approximate ones are also presented, being efficient enough in engineering practice
The Tucson-Melbourne Three-Body Force in a Translationally-Invariant Harmonic Oscillator Basis
Marsden, David; Navratil, Petr; Barrett, Bruce
2000-09-01
A translationally-invariant three-body basis set has been employed in shell model calculations on ^3H and ^3He including the Tucson-Melbourne form of the real nuclear three-body force. The basis consists of harmonic oscillators in Jacobi coordinates, explicitly avoiding the centre of mass drift problem in the calculations. The derivation of the three-body matrix elements and the results of large basis effective interaction shell model calculations will be presented. J. L. Friar, B. F. Gibson, G. L. Payne and S. A. Coon; Few Body Systems 5, 13 (1988) P. Navratil, G.P. Kamuntavicius and B.R. Barrett; Phys. Rev. C. 61, 044001 (2000)
Noll, Ellis; Koehlinger, Mervin; Kowalski, Ludwik; Swackhamer, Gregg
1998-01-01
Describes the use of a computer-linked camera to demonstrate Coulomb's law. Suggests a way of reducing the difficulties in presenting Coulomb's law by teaching the inverse square law of gravity and the inverse square law of electricity in the same unit. (AIM)
Efficient evaluation of the Coulomb force in the Gaussian and finite-element Coulomb method.
Kurashige, Yuki; Nakajima, Takahito; Sato, Takeshi; Hirao, Kimihiko
2010-06-28
We propose an efficient method for evaluating the Coulomb force in the Gaussian and finite-element Coulomb (GFC) method, which is a linear-scaling approach for evaluating the Coulomb matrix and energy in large molecular systems. The efficient evaluation of the analytical gradient in the GFC is not straightforward as well as the evaluation of the energy because the SCF procedure with the Coulomb matrix does not give a variational solution for the Coulomb energy. Thus, an efficient approximate method is alternatively proposed, in which the Coulomb potential is expanded in the Gaussian and finite-element auxiliary functions as done in the GFC. To minimize the error in the gradient not just in the energy, the derived functions of the original auxiliary functions of the GFC are used additionally for the evaluation of the Coulomb gradient. In fact, the use of the derived functions significantly improves the accuracy of this approach. Although these additional auxiliary functions enlarge the size of the discretized Poisson equation and thereby increase the computational cost, it maintains the near linear scaling as the GFC and does not affects the overall efficiency of the GFC approach.
Fodor, Jerry A.
1981-01-01
Describes several different philosophies of mind with each philosophy's explanation of the mind-body problem. Philosophies discussed include dualism, materialism, functionalism, radical behaviorism, logical behaviorism and central-state identity. (DS)
Coulomb effects in relativistic laser-assisted Mott scattering
International Nuclear Information System (INIS)
Ngoko Djiokap, J.M.; Kwato Njock, M.G.; Tetchou Nganso, H.M.
2004-09-01
We reconsider the influence of the Coulomb interaction on the process of relativistic Mott scattering in a powerful electromagnetic plane wave for which the ponderomotive energy is of the order of the magnitude of the electron's rest mass. Coulomb effects of the bare nucleus on the laser-dressed electron are treated more completely than in the previous work of Li et al. [J. Phys. B: At. Mol. Opt. Phys. 37 (2004) 653]. To this end we use Coulomb-Dirac-Volkov functions to describe the initial and the final states of the electron. First-order Born differential cross sections of induced and inverse bremsstrahlung are obtained for circularly and linearly polarized laser light. Numerical calculations are carried out from both polarizations, for various nucleus charge values, three angular configurations and an incident energy in the MeV range. It is found that for parameters used in the present work, incorporating Coulomb effects of the target nucleus either in the initial state or in the final state yields cross sections which are quite similar whatever the scattering geometry and polarization considered. When Coulomb distortions are included in both states, the cross sections are strongly modified with the increase of Z, as compared to the outcome of the prior form of the T-matrix treatment. (author)
Electron stereodynamics in coulomb explosion of molecules by slow highly charged ions
International Nuclear Information System (INIS)
Ichimura, Atsushi; Ohyama-Yamaguchi, Tomoko
2008-01-01
The three-center Coulombic over-the-barrier model is developed for Coulomb explosion of a homonuclear diatomic molecule in collisions with a slow (∼10 eV/amu) highly charged ion. A conventional two-step picture of multiple electron transfer followed by Coulomb explosion is far from appropriate because the molecule sets out to dissociate before the incident ion approaches the closest distance. We treat the formation of a quasi-molecule and its decay into the three moving atomic ions. Charge-asymmetric population between fragment ions observed in a triple-coincidence measurement is suggested to reflect the bond elongation during a collision. Collisions of Kr 8+ + N 2 are analyzed. (author)
International Nuclear Information System (INIS)
Kapshay, V.N.; Skachkov, N.B.
1979-01-01
A composite system of two relativistic particles is studied on the basis of the Kadyshevsky quasipotential equation, in which the ''Coulomb'' potential is taken in the form of a propagator of the massless-scalar-particle exchange. The obtained exact solutions to this equation are shown to be a geometrical generalization of nonrelativistic Coulomb wave functions in the sense of change of the Euclidean geometry of momentum space to the Lobachevsky geometry
Metal nanoparticle film–based room temperature Coulomb transistor
Willing, Svenja; Lehmann, Hauke; Volkmann, Mirjam; Klinke, Christian
2017-01-01
Single-electron transistors would represent an approach to developing less power–consuming microelectronic devices if room temperature operation and industry-compatible fabrication were possible. We present a concept based on stripes of small, self-assembled, colloidal, metal nanoparticles on a back-gate device architecture, which leads to well-defined and well-controllable transistor characteristics. This Coulomb transistor has three main advantages. By using the scalable Langmuir-Blodgett method, we combine high-quality chemically synthesized metal nanoparticles with standard lithography techniques. The resulting transistors show on/off ratios above 90%, reliable and sinusoidal Coulomb oscillations, and room temperature operation. Furthermore, this concept allows for versatile tuning of the device properties such as Coulomb energy gap and threshold voltage, as well as period, position, and strength of the oscillations. PMID:28740864
Three-body forces: a status report
International Nuclear Information System (INIS)
Coon, S.A.
1976-01-01
Real three-body forces due to meson exchange are distinguished from effective three-body interactions of a nuclear Hamiltonian. The long-range part of the real three-body force is proportional to the off-mass-shell sup(PI)N scattering amplitude. Its contribution to the binding energy of nuclear matter is quite dependent upon the treatment of correlations (due to the two-body potential) in the three-body wave function. A recent improvemrnt in the amplitude implies a very small contribution. But, a recent improvement in the treatment of correlations implies a large contribution. Work towards including both these improvements in a single calculation is in progress. (author)
A frictional contact problem for an electro-viscoelastic body
Directory of Open Access Journals (Sweden)
Mircea Sofonea
2007-12-01
Full Text Available A mathematical model which describes the quasistatic frictional contact between a piezoelectric body and a deformable conductive foundation is studied. A nonlinear electro-viscoelastic constitutive law is used to model the piezoelectric material. Contact is described with the normal compliance condition, a version of Coulomb's law of dry friction, and a regularized electrical conductivity condition. A variational formulation of the model, in the form of a coupled system for the displacements and the electric potential, is derived. The existence of a unique weak solution of the model is established under a smallness assumption on the surface conductance. The proof is based on arguments of evolutionary variational inequalities and fixed points of operators.
Gauge orbits and the Coulomb potential
International Nuclear Information System (INIS)
Greensite, J.
2009-01-01
If the color Coulomb potential is confining, then the Coulomb field energy of an isolated color charge is infinite on an infinite lattice, even if the usual UV divergence is lattice regulated. A simple criterion for Coulomb confinement is that the expectation value of timelike link variables vanishes in the Coulomb gauge, but it is unclear how this criterion is related to the spectrum of the corresponding Faddeev-Popov operator, which can be used to formulate a quite different criterion for Coulomb confinement. The purpose of this article is to connect the two seemingly different Coulomb confinement criteria, and explain the geometrical basis of the connection.
Numerical solutions of the N-body problem
International Nuclear Information System (INIS)
Marciniak, A.
1985-01-01
Devoted to the study of numerical methods for solving the general N-body problem and related problems, this volume starts with an overview of the conventional numerical methods for solving the initial value problem. The major part of the book contains original work and features a presentation of special numerical methods conserving the constants of motion in the general N-body problem and methods conserving the Jacobi constant in the problem of motion of N bodies in a rotating frame, as well as an analysis of the applications of both (conventional and special) kinds of methods for solving these problems. For all the methods considered, the author presents algorithms which are easily programmable in any computer language. Moreover, the author compares various methods and presents adequate numerical results. The appendix contains PL/I procedures for all the special methods conserving the constants of motion. 91 refs.; 35 figs.; 41 tabs
Expansions for Coulomb wave functions
Boersma, J.
1969-01-01
In this paper we derive a number of expansions for Whittaker functions, regular and irregular Coulomb wave functions. The main result consists of a new expansion for the irregular Coulomb wave functions of orders zero and one in terms of regular Coulomb wave functions. The latter expansions are
International Nuclear Information System (INIS)
Liu Jianye; Guo Wenjun; Li Xiguo; Xing Yongzhong
2004-01-01
The authors investigate the isospin effect of Coulomb interaction on the momentum dissipation or nuclear stopping in the intermediate energy heavy ion collisions by using the isospin-dependent quantum molecular dynamics model. The calculated results show that the Coulomb interaction induces obviously the reductions of the momentum dissipation. The authors also find that the variation amplitude of momentum dissipation induced by the Coulomb interaction depends sensitively on the form and strength of symmetry potential. However, the isospin effect of Coulomb interaction on the momentum dissipation is less than that induced by the in-medium nucleon-nucleon cross section. In this case, Coulomb interaction does not changes obviously the isospin effect of momentum dissipation induced by the in-medium two-body collision. In particular, the Coulomb interaction is preferable for standing up the isospin effect of in-medium nucleon-nucleon cross section on the momentum dissipation and reducing the isospin effect of symmetry potential on it, which is important for obtaining the feature about the sensitive dependence of momentum dissipation on the in-medium nucleon-nucleon cross section and weakly on the symmetry potential. (author)
Numerical solver of the time-dependent Schroedinger equation with Coulomb singularities
International Nuclear Information System (INIS)
Gordon, Ariel; Jirauschek, Christian; Kaertner, Franz X.
2006-01-01
This paper addresses a very fundamental and important problem in the numerical analysis of atomic and molecular systems: How to discretize Hamiltonians with divergent potential terms, such as Coulomb singularities. At the point of a Coulomb singularity, the wave function cannot be described by a Taylor series expansion, which results in problems when standard discretization schemes are used. We propose using the known asymptotic form of the wave function near the singularity instead of the (nonexistent) Taylor series. This principle, namely discretization by asymptotic behavior correspondence (ABC), is employed in this paper for obtaining grid-discretizations for the Coulomb potential in Cartesian, cylindrical and spherical coordinate systems. We show that computations with the ABC discretization are faster and more precise than with a naive discretization by orders of magnitude. The ABC discretization is well suited for the standard numerical time propagators, such as the Crank-Nicholson, Peaceman-Rachford, and leapfrog schemes. We use the latter, since it is faster and has the same order of accuracy. The leapfrog scheme is generalized to allow absorbing potentials at the grid boundaries
Existence of solutions for the dynamic frictional contact problem of isotropic viscoelastic bodies
Czech Academy of Sciences Publication Activity Database
Eck, C.; Jarušek, Jiří
2003-01-01
Roč. 53, č. 2 (2003), s. 157-181 ISSN 0362-546X R&D Projects: GA AV ČR IAA1075005; GA AV ČR IAA1075707 Institutional research plan: CEZ:AV0Z1019905; CEZ:AV0Z1019905 Keywords : dynamic contact problem * parabolic equation * Coulomb law of friction Subject RIV: BA - General Mathematics Impact factor: 0.354, year: 2003
Many-body problem in one-dimension
International Nuclear Information System (INIS)
Emery, V.J.
1979-11-01
This work attempts to give a qualitative feeling for the more important physical ideas involved with the study of many-body systems in one dimension, and considers a particular strong-coupling model. This model provides an excellent description of the chains of mercury ions in Hg/sub 3-delta/AsF 6 ; some of the predictions of the theory can be checked by x-ray and neutron diffraction. Much of the physics of nearly one-dimensional materials is concerned with understanding the possible types of phase transition that may take place, and establishing the conditions in which one or another will be predominant. The most significant feature of purely one-dimensional systems is the dominant effect of fluctuations. The paper is organized as follows: introduction; qualitative aspects of one-dimensional systems (general survey, mathematical model, qualitative discussion of strong coupling - strong attractive U, strong repulsive U, large V); strong coupling between parallel spins (independent spin systems, coupling between opposite spins); mercury chains; electrons with arbitrary coupling; boson representations of operators; and classical Coulomb gas
Spectral sum for the color-Coulomb potential in SU(3) Coulomb gauge lattice Yang-Mills theory
International Nuclear Information System (INIS)
Nakagawa, Y.; Nakamura, A.; Saito, T.; Toki, H.
2010-01-01
We discuss the essential role of the low-lying eigenmodes of the Faddeev-Popov (FP) ghost operator on the confining color-Coulomb potential using SU(3) quenched lattice simulations in the Coulomb gauge. The color-Coulomb potential is expressed as a spectral sum of the FP ghost operator and has been explored by partially summing the FP eigenmodes. We take into account the Gribov copy effects that have a great impact on the FP eigenvalues and the color-Coulomb potential. We observe that the lowest eigenvalue vanishes in the thermodynamic limit much faster than that in the Landau gauge. The color-Coulomb potential at large distances is governed by the near-zero FP eigenmodes; in particular, the lowest one accounts for a substantial portion of the color-Coulomb string tension comparable to the Wilson string tension.
Institutional Solutions to the ``Two-Body Problem"
Knezek, P.
2005-05-01
The Committee on the Status of Women (CSWA), in conjunction with the Employment Committee (EC), will hold a special session that will focus on institutional approaches to solving the ``two-body problem". In step with the national employment trend, for the majority of astronomers with partners, those partners work outside the home. This is particularly true for female astronomers, who generally are married to professionals (and often to other astronomers). Academic and professional institutions that employ the majority of astronomers are now beginning to recognize the importance of addressing what has come to be known as the ``two-body" problem in order to attract and retain the best scientists. A few of those institutions are making pioneering efforts to create pro-active approaches to the issue of dual-career couples. The special session will feature two or three speakers involved with the administration at institutions with pro-active policies. This special session will be coupled with the normal afternoon CSWA session, which will focus on the other side of the issue - how dual-career couples have successfully approached the issue at institutions that do NOT have proactive policies.
Coulomb corrections for interferometry analysis of expanding hadron systems
Energy Technology Data Exchange (ETDEWEB)
Sinyukov, Yu.M. [Centre National de la Recherche Scientifique, 44 - Nantes (France). Lab. de Physique Subatomique et des Technologies Associees]|[Institute for Theoretical Physics of National Acad. Sci., Kiev (Ukraine); Lednicky, R. [Centre National de la Recherche Scientifique, 44 - Nantes (France). Lab. de Physique Subatomique et des Technologies Associees]|[Institute of Physics, Prague (Czech Republic); Akkelin, S.V. [AN Ukrainskoj SSR, Kiev (Ukraine). Inst. Teoreticheskoj Fiziki; Pluta, J. [Centre National de la Recherche Scientifique, 44 - Nantes (France). Lab. de Physique Subatomique et des Technologies Associees]|[Warsaw Univ. (Poland). Inst. of Physics; Erazmus, B. [Centre National de la Recherche Scientifique, 44 - Nantes (France). Lab. de Physique Subatomique et des Technologies Associees
1998-10-01
The problem of the Coulomb corrections to the two-boson correlation functions for the systems formed in ultra-relativistic heavy ion collisions is considered for large effective volumes predicted in the realistic evolution scenarios taking into account the collective flows. A simple modification of the standard zero-distance correction (so called Gamow or Coulomb factor) has been proposed for such a kind of systems. For {pi}{sup +}{pi}{sup +} and K{sup +}K{sup +} correlation functions this approximate analytical approach is compared with the exact numerical results and a good agreement is found for typical conditions at SPS, RHIC and even LHC energies. (author) 21 refs.
Coulomb Stress Accumulation along the San Andreas Fault System
Smith, Bridget; Sandwell, David
2003-01-01
Stress accumulation rates along the primary segments of the San Andreas Fault system are computed using a three-dimensional (3-D) elastic half-space model with realistic fault geometry. The model is developed in the Fourier domain by solving for the response of an elastic half-space due to a point vector body force and analytically integrating the force from a locking depth to infinite depth. This approach is then applied to the San Andreas Fault system using published slip rates along 18 major fault strands of the fault zone. GPS-derived horizontal velocity measurements spanning the entire 1700 x 200 km region are then used to solve for apparent locking depth along each primary fault segment. This simple model fits remarkably well (2.43 mm/yr RMS misfit), although some discrepancies occur in the Eastern California Shear Zone. The model also predicts vertical uplift and subsidence rates that are in agreement with independent geologic and geodetic estimates. In addition, shear and normal stresses along the major fault strands are used to compute Coulomb stress accumulation rate. As a result, we find earthquake recurrence intervals along the San Andreas Fault system to be inversely proportional to Coulomb stress accumulation rate, in agreement with typical coseismic stress drops of 1 - 10 MPa. This 3-D deformation model can ultimately be extended to include both time-dependent forcing and viscoelastic response.
A Coulomb-Like Off-Shell T-Matrix with the Correct Coulomb Phase Shift
International Nuclear Information System (INIS)
Oryu, Shinsho; Watanabe, Takashi; Hiratsuka, Yasuhisa; Togawa, Yoshio
2017-01-01
We confirm the reliability of the well-known Coulomb renormalization method (CRM). It is found that the CRM is only available for a very-long-range screened Coulomb potential (SCP). However, such an SCP calculation in momentum space is considerably difficult because of the cancellation of significant digits. In contrast to the CRM, we propose a new method by using an on-shell equivalent SCP and the rest term. The two-potential theory with r-space is introduced, which defines fully the off-shell Coulomb amplitude. (author)
Single-photon Coulomb explosion of methanol using broad bandwidth ultrafast EUV pulses.
Luzon, Itamar; Jagtap, Krishna; Livshits, Ester; Lioubashevski, Oleg; Baer, Roi; Strasser, Daniel
2017-05-31
Single-photon Coulomb explosion of methanol is instigated using the broad bandwidth pulse achieved through high-order harmonics generation. Using 3D coincidence fragment imaging of one molecule at a time, the kinetic energy release (KER) and angular distributions of the products are measured in different Coulomb explosion (CE) channels. Two-body CE channels breaking either the C-O or the C-H bonds are described as well as a proton migration channel forming H 2 O + , which is shown to exhibit higher KER. The results are compared to intense-field Coulomb explosion measurements in the literature. The interpretation of broad bandwidth single-photon CE data is discussed and supported by ab initio calculations of the predominant C-O bond breaking CE channel. We discuss the importance of these findings for achieving time resolved imaging of ultrafast dynamics.
Hyperspherical functions and quantum-mechanical three-body problem with application to carbon 12
International Nuclear Information System (INIS)
Letz, H.
1975-01-01
In this work a system of three identical particles (bosons) interacting by a particular two-body force is discussed. Using the complete set of the hyperspherical functions (K-harmonics), analytical expressions for eigenvalues and wave functions of the stationary states are found. The numerical evaluation gives a level sequence for a definite pair of potential parameters similar to that of the nucleus carbon 12
Introduction to Hamiltonian dynamical systems and the N-body problem
Meyer, Kenneth R
2017-01-01
This third edition text provides expanded material on the restricted three body problem and celestial mechanics. With each chapter containing new content, readers are provided with new material on reduction, orbifolds, and the regularization of the Kepler problem, all of which are provided with applications. The previous editions grew out of graduate level courses in mathematics, engineering, and physics given at several different universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. This text provides a mathematical structure of celestial mechanics ideal for beginners, and will be useful to graduate students and researchers alike. Reviews of the second edition: "The primary subject here is the basic theory of Hamiltonian differential equations studied from the perspective of differential dynamical systems. The N-body problem is used as the primary exa...
Pseudo-Coulomb potential in singlet superconductivity
International Nuclear Information System (INIS)
Daemen, L.L.; Overhauser, A.W.
1988-01-01
Reduction of the screened Coulomb potential parameter μ to μ/sup */ = μ/[1+μ ln(E/sub F//(h/2π)ω/sub D/)] is related to the pair correlation function at r = 0. This correlation function is calculated for both the simple Cooper-pair problem and standard Bardeen-Cooper-Schrieffer (BCS) theory by use of a two-square-well model (with λ and μ describing the attraction and repulsion). Results are compared with values obtained for a one-square-well model (having the suitable net attraction, e.g., λ-μ/sup */ in the BCS case). For the BCS case, the ''true'' pair correlation at r = 0 is reduced by a factor (μ/sup *//μ) 2 relative to the fictitious (one-square-well) value (even though Δ is the same for both models). The reduction factor is typically ≅(1/25. It follows that any short-range attractive contribution to superconducting pairing will suffer a reduction similar to that for the Coulomb repulsion
Coulomb energy, vortices, and confinement
International Nuclear Information System (INIS)
Greensite, Jeff; Olejnik, Stefan
2003-01-01
We estimate the Coulomb energy of static quarks from a Monte Carlo calculation of the correlator of timelike link variables in the Coulomb gauge. We find, in agreement with Cucchieri and Zwanziger, that this energy grows linearly with distance at large quark separations. The corresponding string tension, however, is several times greater than the accepted asymptotic string tension, indicating that a state containing only static sources, with no constituent gluons, is not the lowest energy flux tube state. The Coulomb energy is also measured on thermalized lattices with center vortices removed by the de Forcrand-D'Elia procedure. We find that when vortices are removed, the Coulomb string tension vanishes
Chen, Zhenning; Shao, Xinxing; He, Xiaoyuan; Wu, Jialin; Xu, Xiangyang; Zhang, Jinlin
2017-09-01
Noninvasive, three-dimensional (3-D), full-field surface deformation measurements of the human body are important for biomedical investigations. We proposed a 3-D noninvasive, full-field body sensor based on stereo digital image correlation (stereo-DIC) for surface deformation monitoring of the human body in vivo. First, by applying an improved water-transfer printing (WTP) technique to transfer optimized speckle patterns onto the skin, the body sensor was conveniently and harmlessly fabricated directly onto the human body. Then, stereo-DIC was used to achieve 3-D noncontact and noninvasive surface deformation measurements. The accuracy and efficiency of the proposed body sensor were verified and discussed by considering different complexions. Moreover, the fabrication of speckle patterns on human skin, which has always been considered a challenging problem, was shown to be feasible, effective, and harmless as a result of the improved WTP technique. An application of the proposed stereo-DIC-based body sensor was demonstrated by measuring the pulse wave velocity of human carotid artery.
Coulomb disintegration as an information source for relevant processes in nuclear astrophysics
International Nuclear Information System (INIS)
Bertulani, C.A.
1989-01-01
The possibility of obtaining the photodisintegration cross section using the equivalent-photon number method first deduced and employed for the Coulomb disintegration processes has been suggested. This is very interesting because there exist radioactive capture processes, related to the photodisintegration through time reversal, that are relevant in astrophysics. In this paper, the recent results of the Karlsruhe and the Texas A and M groups on the Coulomb disintegration of 6 Li and 7 Li and the problems of the method are discussed. The ideas developed in a previous paper (Nucl. Phys. A458 (1986) 188) are confirmed qualitatively. To understand the process quantitatively it is necessary to use a quantum treatment that would imply the introduction of Coulomb excitation effects of higher orders. The Coulomb disintegration of exotic secondary beams is also studied. It is particularly interesting the question about what kind of nuclear structure information, as binding energies of momentum distributions, may be obtained. (Author) [es
Yang-Mills theory in Coulomb gauge; Yang-Mills-theorie in Coulombeichung
Energy Technology Data Exchange (ETDEWEB)
Feuchter, C.
2006-07-01
In this thesis we study the Yang-Mills vacuum structure by using the functional Schroedinger picture in Coulomb gauge. In particular we discuss the scenario of colour confinement, which was originally formulated by Gribov. After a short introduction, we recall some basic aspects of Yang-Mills theories, its canonical quantization in the Weyl gauge and the functional Schroedinger picture. We then consider the minimal Coulomb gauge and the Gribov problem of the gauge theory. The gauge fixing of the Coulomb gauge is done by using the Faddeev-Popov method, which enables the resolution of the Gauss law - the constraint on physical states. In the third chapter, we variationally solve the stationary Yang-Mills Schroedinger equation in Coulomb gauge for the vacuum state. Therefor we use a vacuum wave functional, which is strongly peaked at the Gribov horizon. The vacuum energy functional is calculated and minimized resulting in a set of coupled Schwinger-Dyson equations for the gluon energy, the ghost and Coulomb form factors and the curvature in gauge orbit space. Using the angular approximation these integral equations have been solved analytically in both the infrared and the ultraviolet regime. The asymptotic analytic solutions in the infrared and ultraviolet regime are reasonably well reproduced by the full numerical solutions of the coupled Schwinger-Dyson equations. In the fourth chapter, we investigate the dependence of the Yang-Mills wave functional in Coulomb gauge on the Faddeev-Popov determinant. (orig.)
Effective linear two-body method for many-body problems in atomic and nuclear physics
International Nuclear Information System (INIS)
Kim, Y.E.; Zubarev, A.L.
2000-01-01
We present an equivalent linear two-body method for the many body problem, which is based on an approximate reduction of the many-body Schroedinger equation by the use of a variational principle. The method is applied to several problems in atomic and nuclear physics. (author)
Universality in low energy three-body systems
International Nuclear Information System (INIS)
Amorim, A.E.A.; Tomio, L; Frederico, T.
1997-01-01
The renormalizability of the quantum theory of non-relativistic three-body system with zero range interaction, warranties that all the low-energy three-body properties are well defined and the low-energy two-body and only one three-body physical information are known. Considering this observation, we have shown that the conditions for the occurrence of Efimov states can be easily reached with any model of short range potential where the three-body ground state and the corresponding binding energy of the subsystems are kept fixed. This approach was applied to the recently discovered halo nuclei. (author)
Coulomb correction calculations of pp Bremsstrahlung
International Nuclear Information System (INIS)
Katsogiannis, A.; Amos, K.; Jetter, M.; von Geramb, H.V.
1994-01-01
The effects of the Coulomb interaction upon the photon cross section and analyzing power from pp Bremsstrahlung have been studied in detail. Off-shell properties of the Coulomb T matrices have been considered but the associated, Coulomb modified, hadronic T matrices are important elements in any analyses of low energy, forward proton scattering data. At the lowest energy considered (5 MeV), the full calculations gave cross sections that were half the size of those found without Coulomb effects or with a simple model approximation to them. With increasing energy, the cross sections varied to those characteristic of magnetic interaction dominance and the specific differences due to Coulomb effects diminished. 47 refs., 7 figs
Spherical harmonic expansion of short-range screened Coulomb interactions
Energy Technology Data Exchange (ETDEWEB)
Angyan, Janos G [Laboratoire de Cristallographie et de Modelisation des Materiaux Mineraux et Biologiques, UMR 7036, CNRS-Universite Henri Poincare, BP 239, F-54506 Vandoeuvre-les-Nancy (France); Gerber, Iann [Laboratoire de Cristallographie et de Modelisation des Materiaux Mineraux et Biologiques, UMR 7036, CNRS-Universite Henri Poincare, BP 239, F-54506 Vandoeuvre-les-Nancy (France); Marsman, Martijn [Institut fuer Materialphysik and Center for Computational Materials Science, Universitaet Wien, Sensengasse 8, A-1090, Vienna (Austria)
2006-07-07
Spherical harmonic expansions of the screened Coulomb interaction kernel involving the complementary error function are required in various problems in atomic, molecular and solid state physics, like for the evaluation of Ewald-type lattice sums or for range-separated hybrid density functionals. A general analytical expression is derived for the kernel, which is non-separable in the radial variables. With the help of series expansions a separable approximate form is proposed, which is in close analogy with the conventional multipole expansion of the Coulomb kernel in spherical harmonics. The convergence behaviour of these expansions is studied and illustrated by the electrostatic potential of an elementary charge distribution formed by products of Slater-type atomic orbitals.
Prospects for coherently driven nuclear radiation by Coulomb excitation
International Nuclear Information System (INIS)
Karamyan, S.A.; Carroll, J.J.
2006-01-01
Possible experiments are discussed in which the Coulomb excitation of nuclear isomers would be followed by sequential energy release. The possibility of the coherent Coulomb excitation of nuclei ensconced in a crystal by channeled relativistic heavy projectiles is considered. The phase shift between neighbor-nuclei excitations can be identical to the photon phase shift for emission in forward direction. Thus, the elementary string of atoms can radiate coherently with emission of characteristic nuclear γ rays and the intensity of the radiation could be increased due to the summation of amplitudes. The Moessbauer conditions should be important for this new type of collective radiation that could be promising in the context of the γ-lasing problem
Generalized second-order Coulomb phase shift functions
International Nuclear Information System (INIS)
Rosendorff, S.
1982-01-01
Some specific properties and the evaluation of the generalized second-order Coulomb phase shift functions (two-dimensional integrals of four spherical cylinder functions) are discussed. The dependence on the three momenta k 1 ,k-bar,k 2 , corresponding to the final, intermediate, and initial states is illustrated
COULN, a program for evaluating negative energy Coulomb functions
International Nuclear Information System (INIS)
Noble, C.J.; Thompson, I.J.
1984-01-01
Program COULN calculates exponentially decaying Whittaker functions, Wsub(K,μ)(z) corresponding to negative energy Coulomb functions. The method employed is most appropriate for parameter ranges which commonly occur in atomic and molecular asymptotic scattering problems using a close-coupling approximation in the presence of closed channels. (orig.)
Four-body effects in the 6He+58Ni scattering
International Nuclear Information System (INIS)
Morcelle, V.; Pires, K.C.C.; Rodríguez-Gallardo, M.; Lichtenthäler, R.; Lépine-Szily, A.; Guimarães, V.; Faria, P.N. de; Mendes Junior, D.R.; Moro, A.M.; Gasques, L.R.; Leistenschneider, E.; Pampa Condori, R.; Scarduelli, V.; Morais, M.C.
2014-01-01
We present angular distributions of the 6 He+ 58 Ni scattering measured at three bombarding energies above the Coulomb barrier: E lab =12.2 MeV,16.5 MeV,and 21.7 MeV. The angular distributions have been analysed in terms of three- and four-body Continuum-Discretized Coupled-Channels calculations considering the effect of the 6 He breakup. A behaviour in the cross section at large angles has been observed which was reproduced only by the four-body Continuum-Discretized Coupled-Channels calculation.
Calogero, Francesco
2001-01-01
This book focuses on exactly treatable classical (i.e. non-quantal non-relativistic) many-body problems, as described by Newton's equation of motion for mutually interacting point particles. Most of the material is based on the author's research and is published here for the first time in book form. One of the main novelties is the treatment of problems in two- and three-dimensional space. Many related techniques are presented, e.g. the theory of generalized Lagrangian-type interpolation in higher-dimensional spaces. This book is written for students as well as for researchers; it works out detailed examples before going on to treat more general cases. Many results are presented via exercises, with clear hints pointing to their solutions.
Properties of three-body decay functions derived with time-like jet calculus beyond leading order
International Nuclear Information System (INIS)
Sugiura, Tetsuya
2002-01-01
Three-body decay functions in time-like parton branching are calculated using the jet calculus to the next-to-leading logarithmic (NLL) order in perturbative quantum chromodynamics (QCD). The phase space contributions from each of the ladder diagrams and interference diagrams are presented. We correct part of the results for the three-body decay functions calculated previously by two groups. Employing our new results, the properties of the three-body decay functions in the regions of soft partons are examined numerically. Furthermore, we examine the contribution of the three-body decay functions modified by the restriction resulting from the kinematical boundary of the phase space for two-body decay in the parton shower model. This restriction leads to some problems for the parton shower model. For this reason, we propose a new restriction introduced by the kinematical boundary of the phase space for two-body decay. (author)
Three-body unitarity with isobars revisited
Energy Technology Data Exchange (ETDEWEB)
Mai, M.; Hu, B. [The George Washington University, Washington, DC (United States); Doering, M. [The George Washington University, Washington, DC (United States); Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Pilloni, A. [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Szczepaniak, A. [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Indiana University, Center for Exploration of Energy and Matter, Bloomington, IN (United States); Indiana University, Physics Department, Bloomington, IN (United States)
2017-09-15
The particle exchange model of hadron interactions can be used to describe three-body scattering under the isobar assumption. In this study we start from the 3 → 3 scattering amplitude for spinless particles, which contains an isobar-spectator scattering amplitude. Using a Bethe-Salpeter Ansatz for the latter, we derive a relativistic three-dimensional scattering equation that manifestly fulfills three-body unitarity and two-body unitarity for the sub-amplitudes. This property holds for energies above breakup and also in the presence of resonances in the sub-amplitudes. (orig.)
International Nuclear Information System (INIS)
Rekab, S.; Zenine, N.
2006-01-01
We consider the three dimensional non relativistic eigenvalue problem in the case of a Coulomb potential plus linear and quadratic radial terms. In the framework of the Rayleigh-Schrodinger Perturbation Theory, using a specific choice of the unperturbed Hamiltonian, we obtain approximate analytic expressions for the eigenvalues of orbital excitations. The implications and the range of validity of the obtained analytic expression are discussed
International Nuclear Information System (INIS)
Haberzettl, H.; Sandhas, W.
1981-01-01
Effective two-body equations for the four-body problem are derived within the general N-body theory of Alt, Grassberger, and Sandhas. In contrast to usual treatments, the final expressions do not require separable (2+2) subamplitudes but incorporate these exactly. All four-body amplitudes can be calculated from the solution of a single integral equation for the reaction (3+1)→(3+1). With single-term separable approximations for the two-particle and the (3+1) subsystem amplitudes the driving terms of the final equations are seen to reduce to those of the field-theoretical model by Fonseca and Shanley. Since our results are based on an exact and complete N-body theory, the investigation of subsystem reaction mechanisms is facilitated. As a consequence, we are led to a three-particle propagator which has the right pole behavior and includes exchange effects
Relativistic three-body model of pion-deuton elasic scattering
International Nuclear Information System (INIS)
Giraud, Noel.
1978-01-01
The Aaron-Amado-Young equations for the relativistic three-body problem are derived following the Blauckenbecker - Sugar method. The angular momentum reduction is carried out using suitable relative momenta. The pion-deuteron elastic scattering is calculated using the equations in which relativistic kinematics are retained only for the pion. After a general study of the observables in the energy range 25 to 256 MeV, detailed calculations are performed at 142 MeV [fr
Chen, Zhenning; Shao, Xinxing; He, Xiaoyuan; Wu, Jialin; Xu, Xiangyang; Zhang, Jinlin
2017-09-01
Noninvasive, three-dimensional (3-D), full-field surface deformation measurements of the human body are important for biomedical investigations. We proposed a 3-D noninvasive, full-field body sensor based on stereo digital image correlation (stereo-DIC) for surface deformation monitoring of the human body in vivo. First, by applying an improved water-transfer printing (WTP) technique to transfer optimized speckle patterns onto the skin, the body sensor was conveniently and harmlessly fabricated directly onto the human body. Then, stereo-DIC was used to achieve 3-D noncontact and noninvasive surface deformation measurements. The accuracy and efficiency of the proposed body sensor were verified and discussed by considering different complexions. Moreover, the fabrication of speckle patterns on human skin, which has always been considered a challenging problem, was shown to be feasible, effective, and harmless as a result of the improved WTP technique. An application of the proposed stereo-DIC-based body sensor was demonstrated by measuring the pulse wave velocity of human carotid artery. (2017) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE).
Super-Coulombic atom-atom interactions in hyperbolic media
Cortes, Cristian L.; Jacob, Zubin
2017-01-01
Dipole-dipole interactions, which govern phenomena such as cooperative Lamb shifts, superradiant decay rates, Van der Waals forces and resonance energy transfer rates, are conventionally limited to the Coulombic near-field. Here we reveal a class of real-photon and virtual-photon long-range quantum electrodynamic interactions that have a singularity in media with hyperbolic dispersion. The singularity in the dipole-dipole coupling, referred to as a super-Coulombic interaction, is a result of an effective interaction distance that goes to zero in the ideal limit irrespective of the physical distance. We investigate the entire landscape of atom-atom interactions in hyperbolic media confirming the giant long-range enhancement. We also propose multiple experimental platforms to verify our predicted effect with phonon-polaritonic hexagonal boron nitride, plasmonic super-lattices and hyperbolic meta-surfaces as well. Our work paves the way for the control of cold atoms above hyperbolic meta-surfaces and the study of many-body physics with hyperbolic media.
The two-body problem of a pseudo-rigid body and a rigid sphere
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall; Vereshchagin, M.; Gózdziewski, K.
2012-01-01
n this paper we consider the two-body problem of a spherical pseudo-rigid body and a rigid sphere. Due to the rotational and "re-labelling" symmetries, the system is shown to possess conservation of angular momentum and circulation. We follow a reduction procedure similar to that undertaken...... in the study of the two-body problem of a rigid body and a sphere so that the computed reduced non-canonical Hamiltonian takes a similar form. We then consider relative equilibria and show that the notions of locally central and planar equilibria coincide. Finally, we show that Riemann's theorem on pseudo......-rigid bodies has an extension to this system for planar relative equilibria....
Three-body forces in p-shell nuclei
International Nuclear Information System (INIS)
Hees, A.G.M. van; Booten, J.G.L.; Glaudemans, P.W.M.
1990-01-01
Within the (0 + 1)ℎω shell-model space for p-shell nuclei we found that a schematic three-body interaction in addition to a translationally invariant two-body interaction leads to a strongly improved description of energy levels. The present three-body interaction is related to the Δ-isobar intermediate-state model of the two-pion exchange three-nucleon interaction. (orig.)
Coulomb-free and Coulomb-distorted recolliding quantum orbits in photoelectron holography
Maxwell, A. S.; Figueira de Morisson Faria, C.
2018-06-01
We perform a detailed analysis of the different types of orbits in the Coulomb quantum orbit strong-field approximation (CQSFA), ranging from direct to those undergoing hard collisions. We show that some of them exhibit clear counterparts in the standard formulations of the strong-field approximation for direct and rescattered above-threshold ionization, and show that the standard orbit classification commonly used in Coulomb-corrected models is over-simplified. We identify several types of rescattered orbits, such as those responsible for the low-energy structures reported in the literature, and determine the momentum regions in which they occur. We also find formerly overlooked interference patterns caused by backscattered Coulomb-corrected orbits and assess their effect on photoelectron angular distributions. These orbits improve the agreement of photoelectron angular distributions computed with the CQSFA with the outcome of ab initio methods for high energy phtotoelectrons perpendicular to the field polarization axis.
Coulomb ionization of inner shells by heavy charged particles
International Nuclear Information System (INIS)
Lapicki, G.
1975-01-01
The theory of inner-shell Coulomb ionization by heavy charged particles, of atomic number small compared to the target atomic number, is developed through the extension of work by Brandt and his coworkers for K shells to L shells. In slow collisions relative to the characteristic times of the inner shell electrons, the quantum-mechanical predictions in the plane-wave Born approximation (PWBA) can exceed experimental cross sections by orders of magnitude. The effects of the perturbation of the atom by and the Coulomb deflection of the particle during collisions are included in the theory. The perturbed atomic states amount to a binding of the inner-shell electrons to the moving particle in slow collisions, and to a polarization of the inner shells by the particle passing at large impact parameters during nonadiabatic collisions. These effects, not contained in the PWBA, are treated in the framework of the perturbed stationary state (PSS) theory for slow collisions and in terms of the harmonic oscillator model of Ashley, Brandt, and Ritchie for stopping powers in fast collisions. The effect of the Coulomb deflection of the particle in the field of the target nucleus on the cross sections is incorporated in the semiclassical approximation of Bang and Hansteen. Except for the lightest target atoms, the contribution of electron capture by the particles to inner-shell ionizations is shown to be negligible. The theory as developed earlier for the K shell, and here for L shells, agrees well with the vast body of experimental data on inner-shell Coulomb ionization by heavy charged particles
Microscopic theory of the Coulomb based exchange coupling in magnetic tunnel junctions.
Udalov, O G; Beloborodov, I S
2017-05-04
We study interlayer exchange coupling based on the many-body Coulomb interaction between conduction electrons in magnetic tunnel junction. This mechanism complements the known interaction between magnetic layers based on virtual electron hopping (or spin currents). We find that these two mechanisms have different behavior on system parameters. The Coulomb based coupling may exceed the hopping based exchange. We show that the Coulomb based exchange interaction, in contrast to the hopping based coupling, depends strongly on the dielectric constant of the insulating layer. The dependence of the interlayer exchange interaction on the dielectric properties of the insulating layer in magnetic tunnel junction is similar to magneto-electric effect where electric and magnetic degrees of freedom are coupled. We calculate the interlayer coupling as a function of temperature and electric field for magnetic tunnel junction with ferroelectric layer and show that the exchange interaction between magnetic leads has a sharp decrease in the vicinity of the ferroelectric phase transition and varies strongly with external electric field.
Coulomb blockade induced by magnetic field
International Nuclear Information System (INIS)
Kusmartsev, F.V.
1992-01-01
In this paper, the authors found that a Coulomb blockade can be induced by magnetic field. The authors illustrated this effect on the example of a ring consisting of two and many Josephson junctions. For the ring with two junctions we present an exact solution. The transition into Coulomb blockade state on a ring transforms into a linear array of Josephson junctions, although in latter case the effect of magnetic field disappears. In the state of Coulomb blockade the magnetization may be both diamagnetic and paramagnetic. The Coulomb blockade may also be removed by external magnetic field
Studies of the nuclear three-body system with three dimensional Faddeev calculations
Liu, Hang
A three-body system consists of either a bound state of three particles with definite binding energy or a beam of single particles scattered from a target, where two of the particles are bound. Of the particles are nucleons, the interactions between them are strong and short ranged. A theoretical framework for studying the dynamics of a nuclear three-body system is the Faddeev scheme. In this work the equation for three-body scattering and the bound state are formulated in momentum space, and directly solved in terms of vector variables. For three identical bosons the Faddeev equation for scattering is a three- dimensional inhomogeneous integral equation in five variables, and is solved by Padé summation. The equation for the bound state is a homogeneous one in three variables, and is solved by a Lanczos' type method. The corresponding algorithms are presented, and their numerical feasibility is demonstrated. Elastic as well as inelastic scattering processes in the intermediate energy regime up to 1 GeV incident energy are studied for the first within a Faddeev scheme. The two-body force employed is of Malfliet-Tjon type. Specific emphasis is placed on studying the convergence of the multiple scattering series given by the Faddeev equations. For the bound state, a three-body force of Fujita- Miyazawa type is incorporated in addition to the two-body force. The effects of this three-body force on the bound state properties are investigated.
The scattering matrix element of the three body reactive collision
International Nuclear Information System (INIS)
Morsy, M.W.; Hilal, A.A.; El-Sabagh, M.A.
1980-08-01
The optical model approximation has been applied to a previously derived set of coupled equations representing the dynamics of the three-body reactive scattering. The Schroedinger equation obtained describing the scattering problem has then been solved by inserting the effective mass approximation. The asymptotic requirements for both the entrance and exit channels, respectively, have been supplied to give the scattering matrix element of the reactive collision. (author)
Morse index for figure-eight choreographies of the planar equal mass three-body problem
Fukuda, Hiroshi; Fujiwara, Toshiaki; Ozaki, Hiroshi
2018-04-01
We report on numerical calculations of the Morse index for figure-eight choreographic solutions to a system of three identical bodies in a plane interacting through the homogeneous potential, -1/r a , or through the Lennard-Jones-type (LJ) potential, 1/r12 - 1/r6 , where r is a distance between the bodies. The Morse index is a number of independent variational functions giving negative second variation S (2) of action functional S. We calculated three kinds of Morse indices, N, N c and N e, in the domain of the periodic, the choreographic and the figure-eight choreographic function, respectively. For the homogeneous system, we obtain N = 4 for 0 ≤slant a index for the solution tending to the figure-eight solution of the a = 6 homogeneous system for the period T \\to ∞ . We obtain N, N c and N e as monotonically increasing functions of T from T \\to ∞ , which start with N=N_c=N_e=0 , jump at the smallest T by 1, and reach N = 12, N_c=4 , and N_e=1 for T \\to ∞ in the other branch.
Smith, C. W.
1992-01-01
The adaptation of the frozen stress photoelastic method to the determination of the distribution of stress intensity factors in three dimensional problems is briefly reviewed. The method is then applied to several engineering problems of practical significance.
Fokker-type dynamics with three-body correlations
International Nuclear Information System (INIS)
Salas, A.; Sanchez-Ron, J.M.
1981-01-01
Dynamical systems of N point particles without internal degrees of freedom are studied. Their equations of motion are derived from a Fokker-type variational principle with n-body correlations (n = 2,3,...,N), with special emphasis on the case n = 3. The distinction between n-body correlation and n-body effective force is analyzed in detail, with the help of an example. Maximal sets of independent three-body Poincare-invariant scalars are given. An example of three-body correlation formally similar to the usual two-body long-range scalar correlation is given and discussed. (author)
The relativistic atomic many-body problem
International Nuclear Information System (INIS)
Brown, G.E.
1987-01-01
Problems connected with the infinite negative energy sea of electrons in the atomic many-body problem are discussed. It is shown that as long as one works in mean-field approximations, wave functions do not need to suffer from continuum dissociation. Various effects from virtual pairs in the wave functions are discussed. (orig.)
Elastic scattering study of three 4n nuclei systems above the Coulomb barrier
International Nuclear Information System (INIS)
Ashok Kumar; Sarita Kumar; Sunita Kumar
2000-01-01
A comprehensive study of elastic scattering of 4n nuclei, namely 16 O + 40 Ca, 24 Mg + 24 Mg and 32 S + 28 Si is carried out at various incident energies near and above the Coulomb barrier using a semi microscopic approach. In the present work real part of the nucleus-nucleus interaction is microscopically calculated using equivalence relation between RGM and GCM
Central configurations of the collinear three-body problem and singular surfaces in the mass space
Energy Technology Data Exchange (ETDEWEB)
Xie, Zhifu, E-mail: zxie@vsu.edu [Department of Mathematics and Computer Science, Virginia State University, Petersburg, VA 23806 (United States)
2011-09-12
This Letter is to provide a new approach to study the phenomena of degeneracy of the number of the collinear central configurations under geometric equivalence. A direct and simple explicit parametric expression of the singular surface H{sub 3} is constructed in the mass space (m{sub 1},m{sub 2},m{sub 3}) element of (R{sup +}){sup 3}. The construction of H{sub 3} is from an inverse respective, that is, by specifying positions for the bodies and then determining the masses that are possible to yield a central configuration. It reveals the relationship between the phenomena of degeneracy and the inverse problem of central configurations. We prove that the number of central configurations is decreased to 3!/2-1=2, m{sub 1}, m{sub 2}, and m{sub 3} are mutually distinct if m element of H{sub 3}. Moreover, we know not only the number of central configurations but also what the nonequivalent central configurations are. -- Highlights: → Provide a new method to study the degeneracy of number of CC. → Results advanced the understanding of number of central configurations. → Singular mass surface H{sub 3} is given by a direct and simple parametric expression. → The proof only requires some basic knowledge of linear algebra. → The method can be applied to some other collinear n-body problem.
Two-body and three-body correlations in Os-shell nuclei
International Nuclear Information System (INIS)
Halderson, D.W.
1974-01-01
It is well known that conventional Brueckner calculations with modern nucleon-nucleon potentials have failed to reproduce experimental saturation properties of finite nuclei. The intent was to determine whether the discrepancies are due to the methods of calculation or the nucleon-nucleon potentials. Brueckner procedures which include only two-body correlations were applied to Os-shell nuclei. Calculations were performed with and without the Hartree-Fock condition, with and without partial occupation probabilities, and with various propagators and Pauli correction techniques. Then the entire class of three-body correlations was calculated by matrix solution of the Bethe-Faddeev equations. The convergence necessary to validate this technique was achieved by constructing a set of basic functions which contain no center of mass excitations and yet are still properly antisymmetrized. The two-body calculations yielded typical Brueckner results. The nuclei were underbound or the radii were too small. However, the three-body calculations yielded reasonable radii and moderate overbinding for the Reid soft core and Hamada-Johnston potentials. Therefore, the Bethe-Faddeev formalism has been shown to be a reasonable approach to calculation of the three-body correlations in finite nuclei; and the results of []these calculations demonstrate that the underbinding and collapsed radii of two-body calculations were largely due to the uncalculated correlations. (auth)
International Nuclear Information System (INIS)
Greensite, J.; Olejnik, S.
2003-01-01
We study the phase structure of SU(2) gauge theories at zero and high temperature, with and without scalar matter fields, in terms of the symmetric/broken realization of the remnant gauge symmetry which exists after fixing to Coulomb gauge. The symmetric realization is associated with a linearly rising color Coulomb potential (which we compute numerically), and is a necessary but not sufficient condition for confinement.
K-harmonic solution for three bound unequal particles
International Nuclear Information System (INIS)
Coelho, H.T.; Consoni, L.; Vallieres, M.
1978-01-01
The three bound unequal particles problem using K-harmonics is analysed concerning how the nature of interactions and asymmetries of the system will affect convergence of the solutions. Coulomb interaction which gives closed expressions for the matrix elements of the potential in the method is discussed [pt
BEC-BCS-laser crossover in Coulomb-correlated electron-hole-photon systems
International Nuclear Information System (INIS)
Yamaguchi, M; Kamide, K; Ogawa, T; Yamamoto, Y
2012-01-01
Many-body features caused by Coulomb correlations are of great importance for understanding phenomena pertaining to polariton systems in semiconductor microcavities, i.e. electron-hole-photon systems. Remarkable many-body effects are shown to exist in both thermal-equilibrium phases and non-equilibrium lasing states. We then show a unified framework for connecting the thermal-equilibrium and the non-equilibrium steady states based on a non-equilibrium Green's function approach. Bose-Einstein condensate (BEC)-Bardeen-Cooper-Schrieffer (BCS)-laser crossovers are investigated by using this approach. (paper)
Coulomb Blockade Plasmonic Switch.
Xiang, Dao; Wu, Jian; Gordon, Reuven
2017-04-12
Tunnel resistance can be modulated with bias via the Coulomb blockade effect, which gives a highly nonlinear response current. Here we investigate the optical response of a metal-insulator-nanoparticle-insulator-metal structure and show switching of a plasmonic gap from insulator to conductor via Coulomb blockade. By introducing a sufficiently large charging energy in the tunnelling gap, the Coulomb blockade allows for a conductor (tunneling) to insulator (capacitor) transition. The tunnelling electrons can be delocalized over the nanocapacitor again when a high energy penalty is added with bias. We demonstrate that this has a huge impact on the plasmonic resonance of a 0.51 nm tunneling gap with ∼70% change in normalized optical loss. Because this structure has a tiny capacitance, there is potential to harness the effect for high-speed switching.
The computationalist reformulation of the mind-body problem.
Marchal, Bruno
2013-09-01
Computationalism, or digital mechanism, or simply mechanism, is a hypothesis in the cognitive science according to which we can be emulated by a computer without changing our private subjective feeling. We provide a weaker form of that hypothesis, weaker than the one commonly referred to in the (vast) literature and show how to recast the mind-body problem in that setting. We show that such a mechanist hypothesis does not solve the mind-body problem per se, but does help to reduce partially the mind-body problem into another problem which admits a formulation in pure arithmetic. We will explain that once we adopt the computationalist hypothesis, which is a form of mechanist assumption, we have to derive from it how our belief in the physical laws can emerge from *only* arithmetic and classical computer science. In that sense we reduce the mind-body problem to a body problem appearance in computer science, or in arithmetic. The general shape of the possible solution of that subproblem, if it exists, is shown to be closer to "Platonist or neoplatonist theology" than to the "Aristotelian theology". In Plato's theology, the physical or observable reality is only the shadow of a vaster hidden nonphysical and nonobservable, perhaps mathematical, reality. The main point is that the derivation is constructive, and it provides the technical means to derive physics from arithmetic, and this will make the computationalist hypothesis empirically testable, and thus scientific in the Popperian analysis of science. In case computationalism is wrong, the derivation leads to a procedure for measuring "our local degree of noncomputationalism". Copyright © 2013 Elsevier Ltd. All rights reserved.
Coulomb dissociation studies for astrophysical thermonuclear reactions
Energy Technology Data Exchange (ETDEWEB)
Motobayashi, T [Dept. of Physics, Rikkyo Univ., Toshima, Tokyo (Japan)
1998-06-01
The Coulomb dissociation method was applied to several radiative capture processes of astrophysical interest. The method has an advantage of high experimental efficiency, which allow measurements with radioactive nuclear beams. The reactions {sup 13}N(p,{gamma}){sup 14}O and {sup 7}Be(p,{gamma}){sup 8}B are mainly discussed. They are the key reaction in the hot CNO cycle in massive stars and the one closely related to the solar neutrino problem, respectively. (orig.)
Abstract Cauchy problems three approaches
Melnikova, Irina V
2001-01-01
Although the theory of well-posed Cauchy problems is reasonably understood, ill-posed problems-involved in a numerous mathematical models in physics, engineering, and finance- can be approached in a variety of ways. Historically, there have been three major strategies for dealing with such problems: semigroup, abstract distribution, and regularization methods. Semigroup and distribution methods restore well-posedness, in a modern weak sense. Regularization methods provide approximate solutions to ill-posed problems. Although these approaches were extensively developed over the last decades by many researchers, nowhere could one find a comprehensive treatment of all three approaches.Abstract Cauchy Problems: Three Approaches provides an innovative, self-contained account of these methods and, furthermore, demonstrates and studies some of the profound connections between them. The authors discuss the application of different methods not only to the Cauchy problem that is not well-posed in the classical sense, b...
Equilibrium Solutions of the Logarithmic Hamiltonian Leapfrog for the N-body Problem
Minesaki, Yukitaka
2018-04-01
We prove that a second-order logarithmic Hamiltonian leapfrog for the classical general N-body problem (CGNBP) designed by Mikkola and Tanikawa and some higher-order logarithmic Hamiltonian methods based on symmetric multicompositions of the logarithmic algorithm exactly reproduce the orbits of elliptic relative equilibrium solutions in the original CGNBP. These methods are explicit symplectic methods. Before this proof, only some implicit discrete-time CGNBPs proposed by Minesaki had been analytically shown to trace the orbits of elliptic relative equilibrium solutions. The proof is therefore the first existence proof for explicit symplectic methods. Such logarithmic Hamiltonian methods with a variable time step can also precisely retain periodic orbits in the classical general three-body problem, which generic numerical methods with a constant time step cannot do.
Geometric characterization for the least Lagrangian action of n-body problems
Institute of Scientific and Technical Information of China (English)
ZHANG; Shiqing
2001-01-01
［1］Manev, G., La gravitation et l'énergie au zéro, Comptes Rendus, 924, 78: 259.［2］Diacu, F. N., Near-collision dynamics for particle systems with quasihomogeneous potentials, J. of Diff. Equ., 996, 28: 58.［3］Ambrosetti, A., Coti Zelati, V., Periodic Solutions of Singular Lagrangian Systems, Basel: Birkhuser, 993.［4］Arnold, V., Kozlov, V., Neishtadt, A., Dynamical Systems (iii): Mathematical Aspects of Classical and Celestial Mechanics, Berlin: Springer-Verlag, 988.［5］Chenciner, A., Desolneux, N., Minima de l'intégrale d'action et équilibres relatifs de n corps, C R Acad. Sci. Paris, serie I, 998, 326: 209.［6］Coti Zelati, V., The periodic solutions of n-body type problems, Ann IHP Anal nonlinéaire, 990, 7: 477.［7］Euler, L., De motu rectilineo trium corprum se mutuo attrahentium, Novi. Comm. Acad. Sci. Imp. Petropll, 767: 45.［8］Gordon, W., A minimizing property of Keplerian orbits, Amer. J. Math., 977, 99: 96.［9］Lagrange, J., Essai sur le problé me des trois corps, 772, Ouvres, 783, 3: 229.［10］Long, Y., Zhang, S. Q., Geometric characterization for variational minimization solutions of the 3-body problem, Chinese Science Bulletin, 999, 44(8): 653.［11］Long, Y., Zhang, S. Q., Geometric characterization for variational minimization solutions of the 3-body problem with fixed energy, J. of Diff. Equ., 2000, 60: 422.［12］Meyer, K., Hall, G., Introduction to Hamiltonian systems and the n-body problems, Berlin: Springer-Verlag,992.［13］Serra, E., Terracini, S., Collisionless periodic solutions to some three-body problems, Arch. Rational Mech. Anal., 992, 20: 305.［14］Siegle, C., Moser, J., Lectures on Celestial Mechanics, Berlin: Springer-Verlag, 97.［15］Wintner, A., Analytical Foundations of Celestial Mechanics, Princeton: Princeton University Press, 94.［16］Hardy, G., Littlewood, J., Pólya, G., Inequalities, 2nd ed., Cambridge: Combridge University Press, 952.
International Nuclear Information System (INIS)
Tornow, W.; Howell, C.R.; Walter, R.L.; Slaus, I.
1992-01-01
Comparison of data for neutron-deuteron and proton-deuteron analyzing power A y for elastic scattering has become crucial for investigating charge-symmetry breaking in the 3 P nucleon-nucleon interactions. We extended this comparison down to 5 MeV and find that the relative difference between n-d and p-d scattering at the A y maximum near 120 degree increases with decreasing energy. By applying a straightforward Coulomb ''correction'' to the p-d data, we account for most of the difference, suggesting that the Coulomb force, rather than charge-symmetry breaking, is responsible for most of the observed difference
Anomalous low-temperature Coulomb drag in graphene-GaAs heterostructures.
Gamucci, A; Spirito, D; Carrega, M; Karmakar, B; Lombardo, A; Bruna, M; Pfeiffer, L N; West, K W; Ferrari, A C; Polini, M; Pellegrini, V
2014-12-19
Vertical heterostructures combining different layered materials offer novel opportunities for applications and fundamental studies. Here we report a new class of heterostructures comprising a single-layer (or bilayer) graphene in close proximity to a quantum well created in GaAs and supporting a high-mobility two-dimensional electron gas. In our devices, graphene is naturally hole-doped, thereby allowing for the investigation of electron-hole interactions. We focus on the Coulomb drag transport measurements, which are sensitive to many-body effects, and find that the Coulomb drag resistivity significantly increases for temperatures law, therefore displaying a notable departure from the ordinary quadratic temperature dependence expected in a weakly correlated Fermi-liquid. This anomalous behaviour is consistent with the onset of strong interlayer correlations. Our heterostructures represent a new platform for the creation of coherent circuits and topologically protected quantum bits.
Short history of nuclear many-body problem
International Nuclear Information System (INIS)
Köhler, H.S.
2014-01-01
This is a very short presentation regarding developments in the theory of nuclear many-body problems, as seen and experienced by the author during the past 60 years with particular emphasis on the contributions of Gerry Brown and his research-group. Much of his work was based on Brueckner's formulation of the nuclear many-body problem. It is reviewed briefly together with the Moszkowski–Scott separation method that was an important part of his early work. The core polarisation and his work related to effective interactions in general are also addressed
Classical- and quantum mechanical Coulomb scattering
International Nuclear Information System (INIS)
Gratzl, W.
1987-01-01
Because in textbooks the quantum mechanical Coulomb scattering is either ignored or treated unsatisfactory, the present work attempts to present a physically plausible, mathematically correct but elementary treatment in a way that it can be used in textbooks and lectures on quantum mechanics. Coulomb scattering is derived as a limiting case of a screened Coulomb potential (finite range) within a time dependent quantum scattering theory. The difference in the asymptotic conditions for potentials of finite versus infinite range leads back to the classical Coulomb scattering. In the classical framework many concepts of the quantum theory can be introduced and are useful in an intuitive understanding of the quantum theory. The differences between classical and quantum scattering theory are likewise useful for didactic purposes. (qui)
Fermi Surface of Sr_{2}RuO_{4}: Spin-Orbit and Anisotropic Coulomb Interaction Effects.
Zhang, Guoren; Gorelov, Evgeny; Sarvestani, Esmaeel; Pavarini, Eva
2016-03-11
The topology of the Fermi surface of Sr_{2}RuO_{4} is well described by local-density approximation calculations with spin-orbit interaction, but the relative size of its different sheets is not. By accounting for many-body effects via dynamical mean-field theory, we show that the standard isotropic Coulomb interaction alone worsens or does not correct this discrepancy. In order to reproduce experiments, it is essential to account for the Coulomb anisotropy. The latter is small but has strong effects; it competes with the Coulomb-enhanced spin-orbit coupling and the isotropic Coulomb term in determining the Fermi surface shape. Its effects are likely sizable in other correlated multiorbital systems. In addition, we find that the low-energy self-energy matrix-responsible for the reshaping of the Fermi surface-sizably differs from the static Hartree-Fock limit. Finally, we find a strong spin-orbital entanglement; this supports the view that the conventional description of Cooper pairs via factorized spin and orbital part might not apply to Sr_{2}RuO_{4}.
A unitarized meson model including color Coulomb interaction
International Nuclear Information System (INIS)
Metzger, Kees.
1990-01-01
Ch. 1 gives a general introduction into the problem field of the thesis. It discusses in how far the internal structure of mesons is understood theoretically and which models exist. It discusses from a phenomenological point of view the problem of confinement indicates how quark models of mesons may provide insight in this phenomenon. In ch. 2 the formal theory of scattering in a system with confinement is given. It is shown how a coupled channel (CC) description and the work of other authors fit into this general framework. Explicit examples and arguments are given to support the CC treatment of such a system. In ch. 3 the full coupled-channel model as is employed in this thesis is presented. On the basis of arguments from the former chapters and the observed regularities in the experimental data, the choices underlying the model are supported. In this model confinement is described with a mass-dependent harmonic-oscillator potential and the presence of open (meson-meson) channels plays an essential role. In ch. 4 the unitarized model is applied to light scalar meson resonances. In this regime the contribution of the open channels is considerable. It is demonstrated that the model parameters as used for the description of the pseudo-scalar and vector mesons, unchanged can be used for the description of these mesons. Ch. 5 treats the color-Coulomb interaction. There the effect of the Coulomb interaction is studied in simple models without decay. The results of incorporating the color-Coulomb interaction into the full CC model are given in ch.6. Ch. 7 discusses the results of the previous chapters and the present status of the model. (author). 182 refs.; 16 figs.; 33 tabs
Interplay between short-range correlated disorder and Coulomb interaction in nodal-line semimetals
Wang, Yuxuan; Nandkishore, Rahul M.
2017-09-01
In nodal-line semimetals, Coulomb interactions and short-range correlated disorder are both marginal perturbations to the clean noninteracting Hamiltonian. We analyze their interplay using a weak-coupling renormalization group approach. In the clean case, the Coulomb interaction has been found to be marginally irrelevant, leading to Fermi liquid behavior. We extend the analysis to incorporate the effects of disorder. The nodal line structure gives rise to kinematical constraints similar to that for a two-dimensional Fermi surface, which plays a crucial role in the one-loop renormalization of the disorder couplings. For a twofold degenerate nodal loop (Weyl loop), we show that disorder flows to strong coupling along a unique fixed trajectory in the space of symmetry inequivalent disorder couplings. Along this fixed trajectory, all symmetry inequivalent disorder strengths become equal. For a fourfold degenerate nodal loop (Dirac loop), disorder also flows to strong coupling, however, the strengths of symmetry inequivalent disorder couplings remain different. We show that feedback from disorder reverses the sign of the beta function for the Coulomb interaction, causing the Coulomb interaction to flow to strong coupling as well. However, the Coulomb interaction flows to strong coupling asymptotically more slowly than disorder. Extrapolating our results to strong coupling, we conjecture that at low energies nodal line semimetals should be described by a noninteracting nonlinear sigma model. We discuss the relation of our results with possible many-body localization at zero temperatures in such materials.
Nucleon many-body problem using quantum-mechanical few-body technique
International Nuclear Information System (INIS)
Horiuchi, Wataru
2016-01-01
A nucleus is treated as a quantum-mechanical many-body system consisting of protons and neutrons that interact with each other by nuclear force. This paper explains the variational calculation using the correlated basis function as a powerful technique for obtaining the precise solution of Schroedinger equation of many-body, and tries to understand the nucleon many-body system from the viewpoint of a few-body through the application cases of various nuclear systems. It describes the important correlation that characterizes the nucleon many-body system such as the mean field, cluster, and tensor of bound state, and shows that non-bound state is also describable. Since such precise theory is mantic, it is essential for explaining the nature of unknown unstable nuclei, and for determining the nuclear reaction rate under the environment of the stars difficult for experiment. The method is general and flexible, and can be applied to various quantum-mechanical many-body problems. For example, the multi-body calculation of atoms and molecules, hypernuclei, and hadron spectroscopy can be carried out only by changing the potential and particles. (A.O.)
Coulomb and nuclear excitations of narrow resonances in 17Ne
Directory of Open Access Journals (Sweden)
J. Marganiec
2016-08-01
Full Text Available New experimental data for dissociation of relativistic 17Ne projectiles incident on targets of lead, carbon, and polyethylene targets at GSI are presented. Special attention is paid to the excitation and decay of narrow resonant states in 17Ne. Distributions of internal energy in the O15+p+p three-body system have been determined together with angular and partial-energy correlations between the decay products in different energy regions. The analysis was done using existing experimental data on 17Ne and its mirror nucleus 17N. The isobaric multiplet mass equation is used for assignment of observed resonances and their spins and parities. A combination of data from the heavy and light targets yielded cross sections and transition probabilities for the Coulomb excitations of the narrow resonant states. The resulting transition probabilities provide information relevant for a better understanding of the 17Ne structure.
Space charge-limited emission studies using Coulomb's Law
Carr, Christopher G.
2004-01-01
Approved for Public Release; Distribution is Unlimited Child and Langmuir introduced a solution to space charge limited emission in an infinite area planar diode. The solution follows from starting with Poisson's equation, and requires solving a non-linear differential equation. This approach can also be applied to cylindrical and spherical geometries, but only for one-dimensional cases. By approaching the problem from Coulomb's law and applying the effect of an assumed charge distribution...
Coulomb interaction in the supermultiplet basis
International Nuclear Information System (INIS)
Ruzha, Ya.Kh.; Guseva, T.V.; Tamberg, Yu.Ya.; Vanagas, V.V.
1989-01-01
An approximate expression for the matrix elements of the Coulomb interaction operator in the supermultiplet basis has been derived with the account for the orbitally-nonsymmetric terms. From the general expression a simplified formula for the Coulomb interaction energy has been proposed. On the basis of the expression obtained the contribution of the Coulomb interaction to the framework of a strongly restricted dynamic model in the light (4≤A≤40) and heavy (158≤A≤196) nuclei region has been studied. 19 refs.; 4 tabs
Energy transfer between two vacuum-gapped metal plates: Coulomb fluctuations and electron tunneling
Zhang, Zu-Quan; Lü, Jing-Tao; Wang, Jian-Sheng
2018-05-01
Recent experimental measurements for near-field radiative heat transfer between two bodies have been able to approach the gap distance within 2 nm , where the contributions of Coulomb fluctuation and electron tunneling are comparable. Using the nonequilibrium Green's function method in the G0W0 approximation, based on a tight-binding model, we obtain for the energy current a Caroli formula from the Meir-Wingreen formula in the local equilibrium approximation. Also, the Caroli formula is consistent with the evanescent part of the heat transfer from the theory of fluctuational electrodynamics. We go beyond the local equilibrium approximation to study the energy transfer in the crossover region from electron tunneling to Coulomb fluctuation based on a numerical calculation.
Beyond mean-ﬁeld approach to heavy-ion reactions around the Coulomb barrier
Directory of Open Access Journals (Sweden)
Ayik Sakir
2011-10-01
Full Text Available Dissipation and ﬂuctuations of one-body observables in heavy-ion reactions around the Coulomb barrier are investigated with a microscopic stochastic mean-ﬁeld approach. By projecting the stochastic meanﬁeld dynamics on a suitable collective path, transport coeﬃcients associated with the relative distance between colliding nuclei and a fragment mass are extracted. Although microscopic mean-ﬁeld approach is know to underestimate the variance of fragment mass distribution, the description of the variance is much improved by the stochastic mean-ﬁeld method. While ﬂuctuations are consistent with the empirical (semiclassical analysis of the experimental data, concerning mean values of macroscopic variables the semiclassical description breaks down below the Coulomb barrier.
Coulomb plus strong interaction bound states - momentum space numerical solutions
International Nuclear Information System (INIS)
Heddle, D.P.; Tabakin, F.
1985-01-01
The levels and widths of hadronic atoms are calculated in momentum space using an inverse algorithm for the eigenvalue problem. The Coulomb singularity is handled by the Lande substraction method. Relativistic, nonlocal, complex hadron-nucleus interactions are incorporated as well as vacuum polarization and finite size effects. Coordinate space wavefunctions are obtained by employing a Fourier Bessel transformation. (orig.)
Three body dynamics and its applications to exoplanets
Musielak, Zdzislaw
2017-01-01
This brief book provides an overview of the gravitational orbital evolution of few-body systems, in particular those consisting of three bodies. The authors present the historical context that begins with the origin of the problem as defined by Newton, which was followed up by Euler, Lagrange, Laplace, and many others. Additionally, they consider the modern works from the 20th and 21st centuries that describe the development of powerful analytical methods by Poincare and others. The development of numerical tools, including modern symplectic methods, are presented as they pertain to the identification of short-term chaos and long term integrations of the orbits of many astronomical architectures such as stellar triples, planets in binaries, and single stars that host multiple exoplanets. The book includes some of the latest discoveries from the Kepler and now K2 missions, as well as applications to exoplanets discovered via the radial velocity method. Specifically, the authors give a unique perspective in rel...
SYMMETRY PROPERTIES OF THE COULOMB POTENTIAL WITH A LINEAR DEPENDENCE ON ENERGY
Directory of Open Access Journals (Sweden)
Radu Budaca
2017-12-01
Full Text Available The D-dimensional Schr ̈odinger equation for a Coulomb potential with a coupling constant depending linearly on energy is analytically solved. The energy spectrum in the asymptotic regime of the slope parameter is found to be fully determined up to a scale only by its quantum numbers. The raising and lowering operators for this limiting model are determined from the recurrence properties of the associated solutions. It is shown that they satisfy the commutation relations of an SU(1,1 algebra and act on wave-functions which are normalized differently from the case of the usual bound state problem for an energy independent Coulomb potential.
The Fermi surface of Sr{sub 2}RuO{sub 4}: spin-orbit and anisotropic Coulomb interaction effects
Energy Technology Data Exchange (ETDEWEB)
Zhang, Guoren; Gorelov, Evgeny; Sarvestani, Esmaeel; Pavarini, Eva [Institute for Advanced Simulation, Forschungszentrum Juelich, D-52425 Juelich (Germany)
2016-07-01
The topology of the Fermi surface of Sr{sub 2}RuO{sub 4} is well described by local density approximation calculations with spin-orbit interaction, but the relative size of its different sheets is not. By accounting for many-body effects via dynamical mean-field theory, we show that the standard isotropic Coulomb interaction worsen or does not correct this discrepancy. In order to reproduce experiments, it is essential to include the Coulomb anisotropy. The latter is small but has strong effects; it competes with the Coulomb-enhanced spin-orbit coupling and with the isotropic Coulomb term. This mechanism is likely to be at work in other multi-orbital systems. Finally, we find a strong spin-orbital entanglement. This supports the view that the conventional description of Cooper pairs via factorized spin and orbital part might not apply to Sr{sub 2}RuO{sub 4}.
Trinucleon asymptotic normalization constants including Coulomb effects
International Nuclear Information System (INIS)
Friar, J.L.; Gibson, B.F.; Lehman, D.R.; Payne, G.L.
1982-01-01
Exact theoretical expressions for calculating the trinucleon S- and D-wave asymptotic normalization constants, with and without Coulomb effects, are presented. Coordinate-space Faddeev-type equations are used to generate the trinucleon wave functions, and integral relations for the asymptotic norms are derived within this framework. The definition of the asymptotic norms in the presence of the Coulomb interaction is emphasized. Numerical calculations are carried out for the s-wave NN interaction models of Malfliet and Tjon and the tensor force model of Reid. Comparison with previously published results is made. The first estimate of Coulomb effects for the D-wave asymptotic norm is given. All theoretical values are carefully compared with experiment and suggestions are made for improving the experimental situation. We find that Coulomb effects increase the 3 He S-wave asymptotic norm by less than 1% relative to that of 3 H, that Coulomb effects decrease the 3 He D-wave asymptotic norm by approximately 8% relative to that of 3 H, and that the distorted-wave Born approximation D-state parameter, D 2 , is only 1% smaller in magnitude for 3 He than for 3 H due to compensating Coulomb effects
Coulomb-Driven Relativistic Electron Beam Compression.
Lu, Chao; Jiang, Tao; Liu, Shengguang; Wang, Rui; Zhao, Lingrong; Zhu, Pengfei; Xiang, Dao; Zhang, Jie
2018-01-26
Coulomb interaction between charged particles is a well-known phenomenon in many areas of research. In general, the Coulomb repulsion force broadens the pulse width of an electron bunch and limits the temporal resolution of many scientific facilities such as ultrafast electron diffraction and x-ray free-electron lasers. Here we demonstrate a scheme that actually makes use of the Coulomb force to compress a relativistic electron beam. Furthermore, we show that the Coulomb-driven bunch compression process does not introduce additional timing jitter, which is in sharp contrast to the conventional radio-frequency buncher technique. Our work not only leads to enhanced temporal resolution in electron-beam-based ultrafast instruments that may provide new opportunities in probing material systems far from equilibrium, but also opens a promising direction for advanced beam manipulation through self-field interactions.
Coulomb-Driven Relativistic Electron Beam Compression
Lu, Chao; Jiang, Tao; Liu, Shengguang; Wang, Rui; Zhao, Lingrong; Zhu, Pengfei; Xiang, Dao; Zhang, Jie
2018-01-01
Coulomb interaction between charged particles is a well-known phenomenon in many areas of research. In general, the Coulomb repulsion force broadens the pulse width of an electron bunch and limits the temporal resolution of many scientific facilities such as ultrafast electron diffraction and x-ray free-electron lasers. Here we demonstrate a scheme that actually makes use of the Coulomb force to compress a relativistic electron beam. Furthermore, we show that the Coulomb-driven bunch compression process does not introduce additional timing jitter, which is in sharp contrast to the conventional radio-frequency buncher technique. Our work not only leads to enhanced temporal resolution in electron-beam-based ultrafast instruments that may provide new opportunities in probing material systems far from equilibrium, but also opens a promising direction for advanced beam manipulation through self-field interactions.
Coulomb drag in the mesoscopic regime
DEFF Research Database (Denmark)
Mortensen, N. Asger; Flensberg, Karsten; Jauho, Antti-Pekka
2002-01-01
We present a theory for Coulomb drug between two mesoscopic systems which expresses the drag in terms of scattering matrices and wave functions. The formalism can be applied to both ballistic and disordered systems and the consequences can be studied either by numerical simulations or analytic...... means such as perturbation theory or random matrix theory. The physics of Coulomb drag in the mesoscopic regime is very different from Coulomb drag between extended electron systems. In the mesoscopic regime we in general find fluctuations of the drag comparable to the mean value. Examples are vanishing...
Coulomb drag in the mesoscopic regime
DEFF Research Database (Denmark)
Mortensen, N.A.; Flensberg, Karsten; Jauho, Antti-Pekka
2002-01-01
We present a theory for Coulomb drag between two mesoscopic systems which expresses the drag in terms of scattering matrices and wave functions. The formalism can be applied to both ballistic and disordered systems and the consequences can be studied either by numerical simulations or analytic...... means such as perturbation theory or random matrix theory. The physics of Coulomb drag in the mesoscopic regime is very different from Coulomb drag between extended electron systems. In the mesoscopic regime we in general find fluctuations of the drag comparable to the mean value. Examples are vanishing...
International Nuclear Information System (INIS)
Yarevsky, E.; Yakovlev, S. L.; Volkov, M. V.; Elander, N.
2014-01-01
We generalize here the splitting approach to the long range (Coulomb) interaction for the three body scattering problem. With this approach, the exterior complex rotation technique can be applied for systems with asymptotic Coulomb interaction. We illustrate the method with calculations of the electron scattering on the hydrogen atom and positive helium ion in the frame of the Temkin–Poet model. (author)
Yarevsky, E.; Yakovlev, S. L.; Elander, N.; Volkov, M. V.
2014-08-01
We generalize here the splitting approach to the long range (Coulomb) interaction for the three body scattering problem. With this approach, the exterior complex rotation technique can be applied for systems with asymptotic Coulomb interaction. We illustrate the method with calculations of the electron scattering on the hydrogen atom and positive helium ion in the frame of the Temkin-Poet model.
Scattering Length Scaling Laws for Ultracold Three-Body Collisions
International Nuclear Information System (INIS)
D'Incao, J.P.; Esry, B.D.
2005-01-01
We present a simple and unifying picture that provides the energy and scattering length dependence for all inelastic three-body collision rates in the ultracold regime for three-body systems with short-range two-body interactions. Here, we present the scaling laws for vibrational relaxation, three-body recombination, and collision-induced dissociation for systems that support s-wave two-body collisions. These systems include three identical bosons, two identical bosons, and two identical fermions. Our approach reproduces all previous results, predicts several others, and gives the general form of the scaling laws in all cases
International Nuclear Information System (INIS)
Igamov, S.B.; Yarmukhamedov, R.
1999-10-01
A method of calculation of the triple-differential cross section of the 208 Pb( 6 Li, αd) 208 Pb Coulomb breakup at astrophysically relevant energies E of the relative motion of the breakup fragments, taking into account the three-body (α - d - 208 Pb) Coulomb effects and the contributions from the E1- and E2- multipoles, including their interference, has been proposed. The new results for the astrophysical S-factor of the direct radiative capture d(α, γ) 6 Li reaction at E ≤ 250 keV have been obtained. It is shown that the experimental triple-differential cross section of the 208 Pb( 6 Li, αd) 208 Pb Coulomb breakup can also be used to give information about the value of the modulus squared of the nuclear vertex constant for the virtual 6 Li → α + d. (author)
Semi-Smooth Newton Method for Solving 2D Contact Problems with Tresca and Coulomb Friction
Directory of Open Access Journals (Sweden)
Kristina Motyckova
2013-01-01
Full Text Available The contribution deals with contact problems for two elastic bodies with friction. After the description of the problem we present its discretization based on linear or bilinear finite elements. The semi--smooth Newton method is used to find the solution, from which we derive active sets algorithms. Finally, we arrive at the globally convergent dual implementation of the algorithms in terms of the Langrange multipliers for the Tresca problem. Numerical experiments conclude the paper.
Dynamics of Three-Body Correlations in Quenched Unitary Bose Gases
Colussi, V. E.; Corson, J. P.; D'Incao, J. P.
2018-03-01
We investigate dynamical three-body correlations in the Bose gas during the earliest stages of evolution after a quench to the unitary regime. The development of few-body correlations is theoretically observed by determining the two- and three-body contacts. We find that the growth of three-body correlations is gradual compared to two-body correlations. The three-body contact oscillates coherently, and we identify this as a signature of Efimov trimers. We show that the growth of three-body correlations depends nontrivially on parameters derived from both the density and Efimov physics. These results demonstrate the violation of scaling invariance of unitary bosonic systems via the appearance of log-periodic modulation of three-body correlations.
Coulomb branches with complex singularities
Argyres, Philip C.; Martone, Mario
2018-06-01
We construct 4d superconformal field theories (SCFTs) whose Coulomb branches have singular complex structures. This implies, in particular, that their Coulomb branch coordinate rings are not freely generated. Our construction also gives examples of distinct SCFTs which have identical moduli space (Coulomb, Higgs, and mixed branch) geometries. These SCFTs thus provide an interesting arena in which to test the relationship between moduli space geometries and conformal field theory data. We construct these SCFTs by gauging certain discrete global symmetries of N = 4 superYang-Mills (sYM) theories. In the simplest cases, these discrete symmetries are outer automorphisms of the sYM gauge group, and so these theories have lagrangian descriptions as N = 4 sYM theories with disconnected gauge groups.
Asymptotic freedom in the axial and Coulomb gauges
International Nuclear Information System (INIS)
Frenkel, J.; Taylor, J.C.
1976-01-01
The sources of the negative contribution to the charge renormalization factor gsup(B)/g-1 in Yang-Mills theories are investigated in the axial and Coulomb gauges. In the axial gauge, a Kaellen dispersion relation exists but the spectral function is not positive definite because of the prescription that is used to integrate the singular polarization vectors. In the Coulomb gauge, the negative contributions are (to the lowest order) isolated in the Coulomb self-energy corrections to the Coulomb field. (Auth.)
Phases and amplitudes for a modified repulsive Coulomb field
International Nuclear Information System (INIS)
Chidichimo, M.C.; Davison, T.S.
1990-01-01
The asymptotic form of the radial wave function for positive-energy states is calculated for the case of a repulsive Coulomb field. The cases of a pure Coulomb potential and a modified Coulomb potential are considered. Second-order analytic solutions for the amplitudes and phases are obtained when the modifications to the pure Coulombic potential take the form αr -2 +βr -3 +γr -4 , using the Jeffreys or WKB method. For the case of a pure Coulomb field, numerical results obtained from this method were compared with ''exact'' numerical results that were obtained using the analytic properties of the Coulomb wave functions. Tables are presented to show the conditions under which the method is accurate
Intersite Coulomb interaction and Heisenberg exchange
Eder, R; van den Brink, J.; Sawatzky, G.A
1996-01-01
Based on exact diagonalization results for small clusters we discuss the effect of intersite Coulomb repulsion in Mott-Hubbard or charge transfers insulators. Whereas the exchange constant J for direct exchange is enhanced by intersite Coulomb interaction, that for superexchange is suppressed. The
Coulomb effects in particle distributions inclusive
International Nuclear Information System (INIS)
Erazmus, B.; Martin, L.; Pluta, J.; Stavinky, A.
1997-01-01
Single pion distributions from central 158 A.GeV/c Pb + Pb collisions measured by the NA44 experiment show the effect of Coulomb interaction with the net charge produced during the reaction. Coulomb effects are analyzed with the help of the microscopic model RQMD and a model including the Coulomb interaction. Different sets of kinematical characteristics of the net charge have been used to reproduce the experimental data and a strong sensitivity to the charge value has been found. This study has evidenced the non-negligible influence of a Coulomb charge, present in the region of the central rapidity in heavy ion collisions on the inclusive distributions of the produced particles. A more thorough analysis of the data obtained from the experiment NA44 is now under way to take into account the hyperon decay that can modify the fraction of different particles, particularly at low transverse momenta
Coulomb string tension, asymptotic string tension, and the gluon chain
Greensite, Jeff; Szczepaniak, Adam P.
2014-01-01
We compute, via numerical simulations, the non-perturbative Coulomb potential of pure SU(3) gauge theory in Coulomb gauge. We find that that the Coulomb potential scales nicely in accordance with asymptotic freedom, that the Coulomb potential is linear in the infrared, and that the Coulomb string tension is about four times larger than the asymptotic string tension. We explain how it is possible that the asymptotic string tension can be lower than the Coulomb string tension by a factor of four.
Structure and Spectrum of Dust Coulomb Clusters
International Nuclear Information System (INIS)
Cheung, F.M.H.; Ford, C.; Barkby, S.; Samarian, A.A.; Vladimirov, S.V.
2005-01-01
In our study, the dynamics of Coulomb cluster systems were simulated for different number of particles. The spectra of energy states of dust Coulomb clusters corresponding to various packing sequences were obtained. The broadening of the spectrum due to inter-ring twist was discovered. It was found that the inter-ring twist will lead to a change in the energy spectrum of Coulomb cluster. This change was accompanied by a distortion of stable shells such that particles are able to compensate for any additional Coulomb energy (owing to the inter-ring twist) by further reducing their radial distance as much as possible. The overall effect is a change in the shape of the outer-shell from circular to elliptical
Coulomb excitation of {sup 8}Li
Energy Technology Data Exchange (ETDEWEB)
Assuncao, Marlete; Britos, Tatiane Nassar [Universidade Federal de Sao Paulo (UNIFESP), SP (Brazil). Dept. de Ciencias Exatas e da Terra; Descouvemont, Pierre [Universite Libre de Bruxelles (ULB), Brussels (Belgium). Physique Nucleaire Theorique et Physique Mathematique; Lepine-Szily, Alinka; Lichtenthaler Filho, Rubens; Barioni, Adriana; Silva, Diego Medeiros da; Pereira, Dirceu; Mendes Junior, Djalma Rosa; Pires, Kelly Cristina Cezaretto; Gasques, Leandro Romero; Morais, Maria Carmen; Added, Nemitala; Neto Faria, Pedro; Rec, Rafael [Universidade de Sao Paulo (IF/USP), SP (Brazil). Inst. de Fisica. Dept. de Fisica Nuclear
2012-07-01
Full text: This work shows the Coulomb Excitation of {sup 8}Li on targets that have effectively behavior of Rutherford in angles and energies of interest for determining the value of the B(E2) electromagnetic transition. Theoretical aspects involved in this type of measure, known as COULEX [1], and some results in the literature [2-3] will be presented. Some problems with the targets and measurement system while performing an experiment on Coulomb Excitation of {sup 8}Li will be discussed: the energy resolution, background, possible contributions of the primary beam and also the excited states of the target near the region of elastic and inelastic peaks. They will be illustrated by measurements of the Coulomb Excitation of {sup 8}Li on targets of {sup 197}Au and {sup 208}Pb using the system RIBRAS(Brazilian Radioactive Ion Beam). In this case, the {sup 8}Li beam(T{sub 1/2} = 838 ms)is produced by {sup 9}Be({sup 7}Li;{sup 8} Li){sup 8}Be reaction from RIBRAS system which is installed at Instituto de Fisica of the Universidade de Sao Paulo. The primary {sup 7L}i beam is provided by Pelletron Accelerator. [1] K. Alder and A. Winther, Electromagnetic Excitation, North-Holland, New York, 1975; [2] P. Descouvemont and D. Baye, Phys. Letts. B 292, 235-238, 1992; [3] J. A. Brown, F. D. Becchetti, J. W. Jaenecke, K, Ashktorab, and D. A. Roberts, J. J. Kolata, R. J. Smith, and K. Lamkin, R. E. Warner, Phys. Rev. Letts., 66, 19, 1991; [4] R. J. Smith, J. J Kolata, K. Lamkin and A. Morsard, F. D. Becchetti, J. A. Brown, W. Z. Liu, J. W. Jaenecke, and D. A. Roberts, R. E. Warner, Phys. Rev. C, 43, 5, 1991. (author)
Generalized separable expansion method of the two-body and the three-body scattering amplitudes
International Nuclear Information System (INIS)
Oryu, S.; Ishihara, T.
1976-01-01
A systematic method is proposed for obtaining new N-rank separable amplitudes of the two-body and the three-body equations. First of all, the authors start from the Amado equation which is modified from the three-body Faddeev equation by using the two-body Yamaguchi potential for the nucleon-nucleon interaction. It is well known that the Amado equation can be integrated on the real axis because the kernel has a logarithmic cut on the real axis. However, a separable three-body form factor which is regular on the real axis except for the cut has been found. (Auth.)
The Gravitational Million-Body Problem: A Multidisciplinary Approach to Star Cluster Dynamics
International Nuclear Information System (INIS)
Tremaine, Scott
2003-01-01
, Dynamical Evolution of Globular Clusters, or that the standard reference on the observational properties of stellar systems is Binney and Merrifield's Galactic Astronomy. A minor irritation is that many concepts are discussed several times before they are defined, and the index provides no pointer to the primary discussion; thus, for example, there are ten index entries for 'phase mixing' and no indication that the fourth of these refers to the actual definition. The book is intended as a graduate textbook but more likely it will be used mainly in other contexts: by theoretical researchers, as an indispensable reference on the dynamics of gravitational N-body systems; by observational astronomers, as a readable summary of the theory of star cluster evolution; and by physicists seeking a well-written and accessible introduction to a simple problem that remains fascinating and incompletely understood after three centuries. (book review)
Tur\\'an type inequalities for regular Coulomb wave functions
Baricz, Árpád
2015-01-01
Tur\\'an, Mitrinovi\\'c-Adamovi\\'c and Wilker type inequalities are deduced for regular Coulomb wave functions. The proofs are based on a Mittag-Leffler expansion for the regular Coulomb wave function, which may be of independent interest. Moreover, some complete monotonicity results concerning the Coulomb zeta functions and some interlacing properties of the zeros of Coulomb wave functions are given.
Extended random-phase approximation with three-body ground-state correlations
International Nuclear Information System (INIS)
Tohyama, M.; Schuck, P.
2008-01-01
An extended random-phase approximation (ERPA) which contains the effects of ground-state correlations up to a three-body level is applied to an extended Lipkin model which contains an additional particle-scattering term. Three-body correlations in the ground state are necessary to preserve the hermiticity of the Hamiltonian matrix of ERPA. Two approximate forms of ERPA which neglect the three-body correlations are also applied to investigate the importance of three-body correlations. It is found that the ground-state energy is little affected by the inclusion of the three-body correlations. On the contrary, three-body correlations for the excited states can become quite important. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Minesaki, Yukitaka [Tokushima Bunri University, Nishihama, Yamashiro-cho, Tokushima 770-8514 (Japan)
2015-01-01
We propose the discrete-time restricted four-body problem (d-R4BP), which approximates the orbits of the restricted four-body problem (R4BP). The d-R4BP is given as a special case of the discrete-time chain regularization of the general N-body problem published in Minesaki. Moreover, we analytically prove that the d-R4BP yields the correct orbits corresponding to the elliptic relative equilibrium solutions of the R4BP when the three primaries form an equilateral triangle at any time. Such orbits include the orbit of a relative equilibrium solution already discovered by Baltagiannis and Papadakis. Until the proof in this work, there has been no discrete analog that preserves the orbits of elliptic relative equilibrium solutions in the R4BP. For a long time interval, the d-R4BP can precisely compute some stable periodic orbits in the Sun–Jupiter–Trojan asteroid–spacecraft system that cannot necessarily be reproduced by other generic integrators.
Experiments on Coulomb ionization by charged particles
International Nuclear Information System (INIS)
Andersen, J.U.; Laegsgaard, E.; Lund, M.
1978-01-01
Inner-shell ionization by light projectiles, i.e., in very asymmetric collisions, is often denoted 'Coulomb ionization' because it is caused by the Coulomb interaction between the electron and the projectile. Although with little justification, the term is also used to distinquish such processes, in which the projectile Coulomb field is a small perturbation, from ionization in more violent, nearly symmetric ion-atom collisions. A discussion of Coulomb ionization of atomic K shells is given, with emphasis on experimental methods and results. The discussion is not intended as a review of the field but rather as a progress report on the anthor's work on the subject. A more detailed account was recently presented at the ICPEAC meeting in Paris. (Auth.)
A simple coordinate space approach to three-body problems ...
Indian Academy of Sciences (India)
problems – Examples: Halo nucleus and double-λ hypernucleus ... Department of Physics, Jadavpur University, Kolkata 700 032, India. £Banaras Hindu ..... thanks the Department of Atomic Energy, India for financial support. References.
RESONANT POST-NEWTONIAN ECCENTRICITY EXCITATION IN HIERARCHICAL THREE-BODY SYSTEMS
Energy Technology Data Exchange (ETDEWEB)
Naoz, Smadar; Kocsis, Bence; Loeb, Abraham [Institute for Theory and Computation, Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Yunes, Nicolas, E-mail: snaoz@cfa.harvard.edu [Department of Physics, Montana State University, Bozeman, MT 59718 (United States)
2013-08-20
We study the secular, hierarchical three-body problem to first-order in a post-Newtonian expansion of general relativity (GR). We expand the first-order post-Newtonian Hamiltonian to leading-order in the ratio of the semi-major axis of the two orbits. In addition to the well-known terms that correspond to the GR precession of the inner and outer orbits, we find a new secular post-Newtonian interaction term that can affect the long-term evolution of the triple. We explore the parameter space for highly inclined and eccentric systems, where the Kozai-Lidov mechanism can produce large-amplitude oscillations in the eccentricities. The standard lore, i.e., that GR effects suppress eccentricity, is only consistent with the parts of phase space where the GR timescales are several orders of magnitude shorter than the secular Newtonian one. In other parts of phase space, however, post-Newtonian corrections combined with the three-body ones can excite eccentricities. In particular, for systems where the GR timescale is comparable to the secular Newtonian timescales, the three-body interactions give rise to a resonant-like eccentricity excitation. Furthermore, for triples with a comparable-mass inner binary, where the eccentric Kozai-Lidov mechanism is suppressed, post-Newtonian corrections can further increase the eccentricity and lead to orbital flips even when the timescale of the former is much longer than the timescale of the secular Kozai-Lidov quadrupole perturbations.
Gravitational waves from periodic three-body systems.
Dmitrašinović, V; Suvakov, Milovan; Hudomal, Ana
2014-09-05
Three bodies moving in a periodic orbit under the influence of Newtonian gravity ought to emit gravitational waves. We have calculated the gravitational radiation quadrupolar waveforms and the corresponding luminosities for the 13+11 recently discovered three-body periodic orbits in Newtonian gravity. These waves clearly allow one to distinguish between their sources: all 13+11 orbits have different waveforms and their luminosities (evaluated at the same orbit energy and body mass) vary by up to 13 orders of magnitude in the mean, and up to 20 orders of magnitude for the peak values.
International Nuclear Information System (INIS)
Wolf, D.; Keblinski, P.; Phillpot, S.R.; Eggebrecht, J.
1999-01-01
Based on a recent result showing that the net Coulomb potential in condensed ionic systems is rather short ranged, an exact and physically transparent method permitting the evaluation of the Coulomb potential by direct summation over the r -1 Coulomb pair potential is presented. The key observation is that the problems encountered in determining the Coulomb energy by pairwise, spherically truncated r -1 summation are a direct consequence of the fact that the system summed over is practically never neutral. A simple method is developed that achieves charge neutralization wherever the r -1 pair potential is truncated. This enables the extraction of the Coulomb energy, forces, and stresses from a spherically truncated, usually charged environment in a manner that is independent of the grouping of the pair terms. The close connection of our approach with the Ewald method is demonstrated and exploited, providing an efficient method for the simulation of even highly disordered ionic systems by direct, pairwise r -1 summation with spherical truncation at rather short range, i.e., a method which fully exploits the short-ranged nature of the interactions in ionic systems. The method is validated by simulations of crystals, liquids, and interfacial systems, such as free surfaces and grain boundaries. copyright 1999 American Institute of Physics
Coulomb Blockade of Tunnel-Coupled Quantum Dots
National Research Council Canada - National Science Library
Golden, John
1997-01-01
.... Though classical charging models can explain the Coulomb blockade of an isolated dot, they must be modified to explain the Coulomb blockade of dots coupled through the quantum mechanical tunneling of electrons...
International Nuclear Information System (INIS)
Tyukhtyaev, Yu.N.
1982-01-01
The problem of taking into account the Coulomb interaction of the ladder type in the analysis of bound states in quantum electrodynamics is discussed in the framework of the quasipotential approach. The main qiasipotential equation and the quasipotential are expressed in the terms of the two-time positive frequency Coulomb Green functions. The corresponding perturbation theory is developed which makes it possible to calculate the shifts of the energy levels in hydrogen-like atoms up to α 6 lnα terms
Coulomb double helical structure
Kamimura, Tetsuo; Ishihara, Osamu
2012-01-01
Structures of Coulomb clusters formed by dust particles in a plasma are studied by numerical simulation. Our study reveals the presence of various types of self-organized structures of a cluster confined in a prolate spheroidal electrostatic potential. The stable configurations depend on a prolateness parameter for the confining potential as well as on the number of dust particles in a cluster. One-dimensional string, two-dimensional zigzag structure and three-dimensional double helical structure are found as a result of the transition controlled by the prolateness parameter. The formation of stable double helical structures resulted from the transition associated with the instability of angular perturbations on double strings. Analytical perturbation study supports the findings of numerical simulations.
Radiative capture versus Coulomb dissociation
International Nuclear Information System (INIS)
Esbensen, H.; Physics
2006-01-01
Measurements of the Coulomb dissociation of 8 B have been used to infer the rate of the inverse radiative proton capture on 7 Be. The analysis is usually based on the assumptions that the two processes are related by detailed balance and described by E1 transitions. However, there are corrections to this relation. The Coulomb form factors for the two processes, for example, are not identical. There are also E2 transitions and higher-order effects in the Coulomb dissociation, and the nuclear induced breakup cannot always be ignored. While adding first-order E2 transitions enhances the decay energy spectrum, the other mechanisms cause a suppression at low relative energies. The net result may accidentally be close to the conventional first-order E1 calculation, but there are differences which cannot be ignored if accuracies of 10% or better are needed
Radiative Capture versus Coulomb Dissociation
International Nuclear Information System (INIS)
Esbensen, Henning
2006-01-01
Measurements of the Coulomb dissociation of 8B have been used to infer the rate of the inverse radiative proton capture on 7Be. The analysis is usually based on the assumptions that the two processes are related by detailed balance and described by E1 transitions. However, there are corrections to this relation. The Coulomb form factors for the two processes, for example, are not identical. There are also E2 transitions and higher-order effects in the Coulomb dissociation, and the nuclear induced breakup cannot always be ignored. While adding first-order E2 transitions enhances the decay energy spectrum, the other mechanisms cause a suppression at low relative energies. The net result may accidentally be close to the conventional first-order E1 calculation, but there are differences which cannot be ignored if accuracies of 10% or better are needed
Three-body forces and the trinucleons
International Nuclear Information System (INIS)
Friar, J.L.
1987-01-01
Three-body forces are discussed in the context of classical, atomic, solid-state and nuclear physics. The basic theoretical ingredients used in the construction of such forces are reviewed. Experimental evidence for three-nucleon forces and an overview of the three-nucleon bound states are presented. 53 refs., 9 figs
Quantum N-body problem with a minimal length
International Nuclear Information System (INIS)
Buisseret, Fabien
2010-01-01
The quantum N-body problem is studied in the context of nonrelativistic quantum mechanics with a one-dimensional deformed Heisenberg algebra of the form [x,p]=i(1+βp 2 ), leading to the existence of a minimal observable length √(β). For a generic pairwise interaction potential, analytical formulas are obtained that allow estimation of the ground-state energy of the N-body system by finding the ground-state energy of a corresponding two-body problem. It is first shown that in the harmonic oscillator case, the β-dependent term grows faster with increasing N than the β-independent term. Then, it is argued that such a behavior should also be observed with generic potentials and for D-dimensional systems. Consequently, quantum N-body bound states might be interesting places to look at nontrivial manifestations of a minimal length, since the more particles that are present, the more the system deviates from standard quantum-mechanical predictions.
Three-body unitarity in the finite volume
Energy Technology Data Exchange (ETDEWEB)
Mai, M. [The George Washington University, Washington, DC (United States); Doering, M. [The George Washington University, Washington, DC (United States); Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
2017-12-15
The physical interpretation of lattice QCD simulations, performed in a small volume, requires an extrapolation to the infinite volume. A method is proposed to perform such an extrapolation for three interacting particles at energies above threshold. For this, a recently formulated relativistic 3 → 3 amplitude based on the isobar formulation is adapted to the finite volume. The guiding principle is two- and three-body unitarity that imposes the imaginary parts of the amplitude in the infinite volume. In turn, these imaginary parts dictate the leading power-law finite-volume effects. It is demonstrated that finite-volume poles arising from the singular interaction, from the external two-body sub-amplitudes, and from the disconnected topology cancel exactly leaving only the genuine three-body eigenvalues. The corresponding quantization condition is derived for the case of three identical scalar-isoscalar particles and its numerical implementation is demonstrated. (orig.)
The mathematical description of resonances in many-body systems
International Nuclear Information System (INIS)
Orth, A.
1985-01-01
We introduce a characterization for quantum-mechanical resonance and use it in order to detect for certain distinct physical states an especially slow decay behaviour. We apply these results to a model of the quantum-mechanical many-body problem and obtain so a mathematical description of the Auger effect (self-ionization of atoms). The class of the interaction potentials admitted for our theory is compared with other theories on resonances extremely large. We establish differentiability conditions and conditions on the fading behaviour in the infinite. Especially the Coulomb potential and the Yukawa potential belong to our class but also non-spherical-symmetric and non-analytic potentials with a Coulomb-like singularity in the origin, two- to threefold differentiable which tend to zero at the infinite. In the introduction we discuss extensively also by means of some examples the problematics of the quantum-mechanical resonance. (orig.) [de
Three-Body Nuclear Forces from a Matrix Model
Hashimoto, Koji
2010-01-01
We compute three-body nuclear forces at short distances by using the nuclear matrix model of holographic QCD proposed in our previous paper with P. Yi. We find that the three-body forces at short distances are repulsive for (a) aligned three neutrons with averaged spins, and (b) aligned proton-proton-neutron / proton-neutron-neutron. These indicate that in dense states of neutrons such as cores of neutron stars, or in Helium-3 / tritium nucleus, the repulsive forces are larger than the ones estimated from two-body forces only.
Optical Trapping of Ion Coulomb Crystals
Schmidt, Julian; Lambrecht, Alexander; Weckesser, Pascal; Debatin, Markus; Karpa, Leon; Schaetz, Tobias
2018-04-01
The electronic and motional degrees of freedom of trapped ions can be controlled and coherently coupled on the level of individual quanta. Assembling complex quantum systems ion by ion while keeping this unique level of control remains a challenging task. For many applications, linear chains of ions in conventional traps are ideally suited to address this problem. However, driven motion due to the magnetic or radio-frequency electric trapping fields sometimes limits the performance in one dimension and severely affects the extension to higher-dimensional systems. Here, we report on the trapping of multiple barium ions in a single-beam optical dipole trap without radio-frequency or additional magnetic fields. We study the persistence of order in ensembles of up to six ions within the optical trap, measure their temperature, and conclude that the ions form a linear chain, commonly called a one-dimensional Coulomb crystal. As a proof-of-concept demonstration, we access the collective motion and perform spectrometry of the normal modes in the optical trap. Our system provides a platform that is free of driven motion and combines advantages of optical trapping, such as state-dependent confinement and nanoscale potentials, with the desirable properties of crystals of trapped ions, such as long-range interactions featuring collective motion. Starting with small numbers of ions, it has been proposed that these properties would allow the experimental study of many-body physics and the onset of structural quantum phase transitions between one- and two-dimensional crystals.
Three-dimensional formulation of the relativistic two-body problem in terms of rapidities
International Nuclear Information System (INIS)
Amirkhanov, I.V.; Grusha, G.V.; Mir-Kasimov, R.M.
1976-01-01
The scheme, based on the three-dimensional relativistic equation of the quasi-potential type is developed. As a basic variable rapidity, canonically conjugated to the relativistic relative distance is adopted. The free Green function has a simple pole in the complex rapidity plane, ensuring the fulfillment of the elastic unitarity for real potentials. In the local potential case the corresponding partial wave equation in configurational r-representation is a differential second-order equation. The problem of boundary conditions, which is a non-trivial one in the relativistic r-space, is studied. The exact solutions of the equation in simple cases have been found
Hadjimichael, E
1986-01-01
This volume consists of two review articles. E Hadjimichael's contribution, 'The Nuclear Three-Body Systems', concentrates on recent experimental and theoretical progress achieved in the field. Together with a pedagogical survey of the theoretical framework extensive discussion on the 3N system in the continuum and reactions of electromagnetic probes with 3N systems are provided. 'Four-Nucleon Transfer Reactions' by W Oelert reviews many aspects of a-particle transfer studies. A careful and balanced presentation of both theory and experiment is given. Reasonable agreement between the two is ob
International Nuclear Information System (INIS)
Zhao Hongsheng; Li Baojiu; Bienayme, Olivier
2010-01-01
We derive a simple analytical expression for the two-body force in a subclass of modified Newtonian dynamics (MOND) theories and make testable predictions in the modification to the two-body orbital period, shape, precession rate, escape speed, etc. We demonstrate the applications of the modified Kepler's law in the timing of satellite orbits around the Milky Way, and checking the feasibility of MOND in the orbit of the large Magellanic cloud, the M31 galaxy, and the merging bullet clusters. MOND appears to be consistent with satellite orbits although with a tight margin. Our results on two-bodies are also generalized to restricted three-body, many-body problems, rings, and shells.
Three-Body Potentials in α-Particle Model of Light Nuclei
International Nuclear Information System (INIS)
Ishikawa, Souichi
2017-01-01
In three-body model calculations of atomic nuclei, e.g., the "1"2C nucleus as α-α-α system and the "9Be nucleus as α-α-n system, the Hamiltonians of the systems consisting of two- and three-body potentials are important inputs. However, our knowledge of three-body potentials is quite restricted. In this paper, I will examine a relation between α-α-α and α-α-n three-body potentials that is obtained in a simple cluster model picture, which gives a phenomenological constraint condition on the three-body potential models to be used. (author)
Role amplification of the coulomb interaction in nuclear reactions
Energy Technology Data Exchange (ETDEWEB)
Kumar, Ashok; Soni, S K; Pancholi, S K; Gupta, S L [AN SSSR, Moscow. Radiotekhnicheskij Inst.
1976-10-01
The genarally adopted estimate of coulomb interaction in nuclear reactions based on the comparison of relative energies of real particles participating in the reaction with the coulomb barrier has been shown to provide wrong presentation of the role of coulomb interaction in the reaction mechanism. The relative energy of particles participating in virtual processes forming the reaction mechanism and its relation to the coulomb barrier turn out to be tens of per cent less than for the particles in an inlet channel. This is the main reason of increasing the role of coulomb interaction in the reaction mechanism. This increase is particularly significant for nuclei with large charges, in particular, in heavy ion reaction.
Atomic Color Superfluid via Three-Body Loss
International Nuclear Information System (INIS)
Kantian, A.; Diehl, S.; Zoller, P.; Daley, A. J.; Dalmonte, M.; Hofstetter, W.
2009-01-01
Large three-body loss rates in a three-component Fermi gas confined in an optical lattice can dynamically prevent atoms from tunneling so as to occupy a lattice site with three atoms. This effective constraint not only suppresses the occurrence of actual loss events, but stabilizes BCS-pairing phases by suppressing the formation of trions. We study the effect of the constraint on the many-body physics using bosonization and density matrix renormalization group techniques, and also investigate the full dissipative dynamics including loss for the example of 6 Li.
Selfconsistent theory of Coulomb mixing in nuclei
International Nuclear Information System (INIS)
Pyatov, N.I.
1978-01-01
The theory of isobaric states is considered according to the Coulomb mixing in nuclei. For a given form of the isovestor potential the separable residual interactions are constructed by means of the isotopic invariance principle. The strength parameter of the force is found from a selfconsistency condition. The charge dependent force is represented by the Coulomb effective potential. The theory of the isobaric states is developed using the random phase approximation. The Coulomb mixing effects in the ground and isobaric 0 + states of even-mass nuclei are investigated
The eikonal phase of supersymmetric Coulomb partners
Lassaut, M; Lombard, R J
1998-01-01
We investigate the eikonal phase and its systematic corrections for the two supersymmetric Coulomb partners V sub 1 and V sub 2 derived by Amado. Apart from a constant shift of -pi for V sub 1 and -2 pi for V sub 2 , the eikonal phase decay to the eikonal phase of the Coulomb potential as 1/kb. For the potential V sub 2 , which is phase equivalent to the Coulomb potential, this result is only valid at b approx =0 and asymptotically; in the intermediate range, it constitutes a lower limit. (author)
[Three cases of an intracranial wooden foreign body].
Fujimoto, S; Onuma, T; Amagasa, M; Okudaira, Y
1987-07-01
Three cases of intracranial wooden foreign body are reported discussing the diagnostic and therapeutic problems. First case is a 50-year-old man. After drinking, he drove a bike and fell to the ground. On admission the wooden foreign body could not been detected in appearance. CT scan showed low density area similar to air in bilateral anterior horn of lateral ventricle. The patient was treated for traumatic pneumocephalus at first. Later, it proved that he was stabbed with a foreign body penetrating into the contralateral frontal lobe through the left nasal cavity. It was extracted by endonasal approach by otolaryngologist, fortunately without trouble. The foreign body was a branch of tree. The second case is an 18-year-old man. He was driving a car, and suffered injury. He was stabbed with a wooden stake penetrating into his left eye. Immediately, bifrontal craniotomy was performed and the stake was withdrawn carefully. Moreover bone fragments were removed. The third case is a 61-year-old man. When he cut the timber by chain saw, a piece of wood hit and stabbed his right eye directly. Immediately right front temporal craniotomy was performed. The piece of wood was withdrawn from the right eye, and pieces of glass, wood and bone fragments were evacuated. It is difficult to confirm intracranial foreign body accurately by means of only plain skull film and usual CT scans. It is necessary to utilize various function of CT scanner. For example, it is useful to know CT values or select measure mode with window width and level or make reconstruction image to sagittal or coronal section, and so on.(ABSTRACT TRUNCATED AT 250 WORDS)
Mandal, Ipsita; Nandkishore, Rahul M.
2018-03-01
Coulomb interactions famously drive three-dimensional quadratic band crossing semimetals into a non-Fermi liquid phase of matter. In a previous work [Nandkishore and Parameswaran, Phys. Rev. B 95, 205106 (2017), 10.1103/PhysRevB.95.205106], the effect of disorder on this non-Fermi liquid phase was investigated, assuming that the band structure was isotropic, assuming that the conduction and valence bands had the same band mass, and assuming that the disorder preserved exact time-reversal symmetry and statistical isotropy. It was shown that the non-Fermi liquid fixed point is unstable to disorder and that a runaway flow to strong disorder occurs. In this paper, we extend that analysis by relaxing the assumption of time-reversal symmetry and allowing the electron and hole masses to differ (but continuing to assume isotropy of the low energy band structure). We first incorporate time-reversal symmetry breaking disorder and demonstrate that there do not appear any new fixed points. Moreover, while the system continues to flow to strong disorder, time-reversal-symmetry-breaking disorder grows asymptotically more slowly than time-reversal-symmetry-preserving disorder, which we therefore expect should dominate the strong-coupling phase. We then allow for unequal electron and hole masses. We show that whereas asymmetry in the two masses is irrelevant in the clean system, it is relevant in the presence of disorder, such that the `effective masses' of the conduction and valence bands should become sharply distinct in the low-energy limit. We calculate the RG flow equations for the disordered interacting system with unequal band masses and demonstrate that the problem exhibits a runaway flow to strong disorder. Along the runaway flow, time-reversal-symmetry-preserving disorder grows asymptotically more rapidly than both time-reversal-symmetry-breaking disorder and the Coulomb interaction.
SELF-CONSISTENT LANGEVIN SIMULATION OF COULOMB COLLISIONS IN CHARGED-PARTICLE BEAMS
International Nuclear Information System (INIS)
QIANG, J.; RYNE, R.; HABIB, S.
2000-01-01
In many plasma physics and charged-particle beam dynamics problems, Coulomb collisions are modeled by a Fokker-Planck equation. In order to incorporate these collisions, we present a three-dimensional parallel Langevin simulation method using a Particle-In-Cell (PIC) approach implemented on high-performance parallel computers. We perform, for the first time, a fully self-consistent simulation, in which the FR-iction and diffusion coefficients are computed FR-om first principles. We employ a two-dimensional domain decomposition approach within a message passing programming paradigm along with dynamic load balancing. Object oriented programming is used to encapsulate details of the communication syntax as well as to enhance reusability and extensibility. Performance tests on the SGI Origin 2000 and the Cray T3E-900 have demonstrated good scalability. Work is in progress to apply our technique to intrabeam scattering in accelerators
An existence proof of a symmetric periodic orbit in the octahedral six-body problem
Cavalcanti, Anete Soares
2016-01-01
We present a proof of the existence of a periodic orbit for the Newtonian six-body problem with equal masses. This orbit has three double collisions each period and no multiple collisions. Our proof is based on the minimization of the Lagrangian action functional on a well chosen class of symmetric loops.
The Hill's three-body problem: a new deduction of motion equations
International Nuclear Information System (INIS)
Fuente Marcos, C. de la.
1995-01-01
Although the Hill's problem has been considered traditionally as a particular case of the restricted problem, it is not but rather a different problem with the same degree of generality. In this paper it is presented a new derivation of the motion equations obtained originally by Hill in 1878 as well as a brief discussion about its possible applications. (Author) 13 refs
Fay, Temple H.
2012-01-01
Viscous damping is commonly discussed in beginning differential equations and physics texts but dry friction or Coulomb friction is not despite dry friction being encountered in many physical applications. One reason for avoiding this topic is that the equations involve a jump discontinuity in the damping term. In this article, we adopt an energy…
Properties of magnetized Coulomb crystals of ions with polarizable electron background
Kozhberov, A. A.
2018-06-01
We have studied phonon and thermodynamic properties of a body-centered cubic (bcc) Coulomb crystal of ions with weakly polarized electron background in a uniform magnetic field B. At B = 0, the difference between phonon moments calculated using the Thomas-Fermi (TF) and random phase approximations is always less than 1% and for description of phonon properties of a crystal, TF formalism was used. This formalism was successfully applied to investigate thermodynamic properties of magnetized Coulomb crystals. It was shown that the influence of the polarization of the electron background is significant only at κ TF a > 0.1 and T ≪ T p ( 1 + h2 ) - 1 / 2 , where κTF is the Thomas-Fermi wavenumber, a is the ion sphere radius, T p ≡ ℏ ω p is the ion plasma temperature, h ≡ ω B / ω p , ωB is the ion cyclotron frequency, and ωp is the ion plasma frequency.
Bound and resonant states in Coulomb-like potentials
International Nuclear Information System (INIS)
Papp, Z.
1985-12-01
The potential separable expansion method was generalized for calculating bound and resonant states in Coulomb-like potentials. The complete set of Coulomb-Sturmian functions was taken as the basis to expand the short-range potential. On this basis the matrix elements of the Coulomb-Green functions were given in closed form as functions of the (complex) energy. The feasibility of the method is demonstrated by a numerical example. (author)
Covariant equations for the three-body bound state
International Nuclear Information System (INIS)
Stadler, A.; Gross, F.; Frank, M.
1997-01-01
The covariant spectator (or Gross) equations for the bound state of three identical spin 1/2 particles, in which two of the three interacting particles are always on shell, are developed and reduced to a form suitable for numerical solution. The equations are first written in operator form and compared to the Bethe-Salpeter equation, then expanded into plane wave momentum states, and finally expanded into partial waves using the three-body helicity formalism first introduced by Wick. In order to solve the equations, the two-body scattering amplitudes must be boosted from the overall three-body rest frame to their individual two-body rest frames, and all effects which arise from these boosts, including Wigner rotations and p-spin decomposition of the shell-particle, are treated exactly. In their final form, the equations reduce to a coupled set of Faddeev-like double integral equations with additional channels arising from the negative p-spin states of the off-shell particle
The Coulomb potential in quantum mechanics and related topics
International Nuclear Information System (INIS)
Haeringen, H. van.
1978-01-01
This dissertation consists of an analytic study of the Coulomb interaction in nonrelativistic quantum mechanics and some related topics. The author investigates in a number of self-contained articles various interesting and important properties of the Coulomb potential. Some of these properties are shared by other potentials which also play a role in quantum mechanics. For such related interactions a comparative study is made. The principal difficulties in the description of proton-deuteron scattering and break-up reactions, due to the Coulomb interaction, are studied by working out a simple model. The bound states are studied for the Coulomb plus Yamaguchi potential, for the symmetric shifted Coulomb potential, and for local potentials with an inverse-distance-squared asymptotic behaviour. (Auth.)
On rate-state and Coulomb failure models
Gomberg, J.; Beeler, N.; Blanpied, M.
2000-01-01
We examine the predictions of Coulomb failure stress and rate-state frictional models. We study the change in failure time (clock advance) Δt due to stress step perturbations (i.e., coseismic static stress increases) added to "background" stressing at a constant rate (i.e., tectonic loading) at time t0. The predictability of Δt implies a predictable change in seismicity rate r(t)/r0, testable using earthquake catalogs, where r0 is the constant rate resulting from tectonic stressing. Models of r(t)/r0, consistent with general properties of aftershock sequences, must predict an Omori law seismicity decay rate, a sequence duration that is less than a few percent of the mainshock cycle time and a return directly to the background rate. A Coulomb model requires that a fault remains locked during loading, that failure occur instantaneously, and that Δt is independent of t0. These characteristics imply an instantaneous infinite seismicity rate increase of zero duration. Numerical calculations of r(t)/r0 for different state evolution laws show that aftershocks occur on faults extremely close to failure at the mainshock origin time, that these faults must be "Coulomb-like," and that the slip evolution law can be precluded. Real aftershock population characteristics also may constrain rate-state constitutive parameters; a may be lower than laboratory values, the stiffness may be high, and/or normal stress may be lower than lithostatic. We also compare Coulomb and rate-state models theoretically. Rate-state model fault behavior becomes more Coulomb-like as constitutive parameter a decreases relative to parameter b. This is because the slip initially decelerates, representing an initial healing of fault contacts. The deceleration is more pronounced for smaller a, more closely simulating a locked fault. Even when the rate-state Δt has Coulomb characteristics, its magnitude may differ by some constant dependent on b. In this case, a rate-state model behaves like a modified
Observation of the Borromean Three-Body Förster Resonances for Three Interacting Rb Rydberg Atoms.
Tretyakov, D B; Beterov, I I; Yakshina, E A; Entin, V M; Ryabtsev, I I; Cheinet, P; Pillet, P
2017-10-27
Three-body Förster resonances at long-range interactions of Rydberg atoms were first predicted and observed in Cs Rydberg atoms by Faoro et al. [Nat. Commun. 6, 8173 (2015)NCAOBW2041-172310.1038/ncomms9173]. In these resonances, one of the atoms carries away an energy excess preventing the two-body resonance, leading thus to a Borromean type of Förster energy transfer. But they were in fact observed as the average signal for the large number of atoms N≫1. In this Letter, we report on the first experimental observation of the three-body Förster resonances 3×nP_{3/2}(|M|)→nS_{1/2}+(n+1)S_{1/2}+nP_{3/2}(|M^{*}|) in a few Rb Rydberg atoms with n=36, 37. We have found here clear evidence that there is no signature of the three-body Förster resonance for exactly two interacting Rydberg atoms, while it is present for N=3-5 atoms. This demonstrates the assumption that three-body resonances can generalize to any Rydberg atom. As such resonance represents an effective three-body operator, it can be used to directly control the three-body interactions in quantum simulations and quantum information processing with Rydberg atoms.
Ice limit of Coulomb gauge Yang-Mills theory
International Nuclear Information System (INIS)
Heinzl, T.; Ilderton, A.; Langfeld, K.; Lavelle, M.; McMullan, D.
2008-01-01
In this paper we describe gauge invariant multiquark states generalizing the path integral framework developed by Parrinello, Jona-Lasinio, and Zwanziger to amend the Faddeev-Popov approach. This allows us to produce states such that, in a limit which we call the ice limit, fermions are dressed with glue exclusively from the fundamental modular region associated with Coulomb gauge. The limit can be taken analytically without difficulties, avoiding the Gribov problem. This is illustrated by an unambiguous construction of gauge invariant mesonic states for which we simulate the static quark-antiquark potential.
The changing features of the body-mind problem.
Agassi, Joseph
2007-01-01
The body-mind problem invites scientific study, since mental events are repeated and repeatable and invite testable explanations. They seemed troublesome because of the classical theory of substance that failed to solve its own central problems. These are soluble with the aid of the theory of the laws of nature, particularly in its emergentist version [Bunge, M., 1980. The Body-mind Problem, Pergamon, Oxford] that invites refutable explanations [Popper, K.R., 1959. The Logic of Scientific Discovery, Hutchinson, London]. The view of mental properties as emergent is a modification of the two chief classical views, materialism and dualism. As this view invites testable explanations of events of the inner world, it is better than the quasi-behaviorist view of self-awareness as computer-style self-monitoring [Minsky, M., Laske, O., 1992. A conversation with Marvin Minsky. AI Magazine 13 (3), 31-45].
Intergrain Coupling in Dusty-Plasma Coulomb Crystals
International Nuclear Information System (INIS)
Mohideen, U.; Smith, M.A.; Rahman, H.U.; Rosenberg, M.; Mendis, D.A.
1998-01-01
We have studied the lattice structure of dusty-plasma Coulomb crystals formed in rectangular conductive grooves as a function of plasma temperature and density. The crystal appears to be made of mutually repulsive columns of grains confined by the walls of the groove. The columns are oriented along the direction of the electrode sheath electric field. A simple phenomenological model wherein the intergrain spacing results from an attractive electric-field-induced dipole-dipole force balanced by a repulsive monopole Coulomb force is consistent with observed features of the Coulomb crystal. copyright 1998 The American Physical Society
On contribution of three-body forces to Nd interaction at intermediate energies
International Nuclear Information System (INIS)
Uzikov, Yu.N.
2001-01-01
Available data on large-angle nucleon-deuteron elastic scattering Nd → dN below the pion threshold give a signal for three-body forces. There is a problem of separation of possible subtle aspects of these forces from off-shell effects in two-nucleon potentials. By considering the main mechanisms of the process Nd → dN, we show qualitatively that in the quasi-binary reaction N + d → (NN) + N with the final spin singlet NN-pair in the S-state the relative contribution of the 3N forces differs substantially from the elastic channel. It gives a new testing ground for the problem in question
Coulomb states in atoms and solids
International Nuclear Information System (INIS)
Ortalano, D.M.
1988-05-01
In this dissertation, an empirical quantum defect approach to describe the valence excitons of the rare gas solids is developed. These Coulomb states are of s-symmetry and form a hydrogen-like series which converges to the bottom of the lowest conduction band. A non-zero quantum defect is found for all of the excitons of neon, argon and xenon. For these systems, then, there exists, in addition to the screened Coulombic component, a non-Coulombic component to the total exciton binding energy. The Wannier formalism is, therefore, inappropriate for the excitons of Ne, Ar and Xe. From the sign of the quantum defect, the non-Coulombic potential is repulsive for Ne and Ar, attractive for Xe, and nearly zero for Kr. This is opposite to that for the Rydberg states of the corresponding rare gas atoms, where the non-Coulombic potential between the electron and the cation is attractive for all of the atoms. The excitons then, are not simply perturbed Rydberg states of the corresponding rare gas atoms (i.e., the excitons do not possess atomic parentage). Interatomic term value/band gap energy correlations and reduced term value/reduced band gap correlations were performed. These correlations were exploited to provide further evidence against both the Wannier formalism and the atomic parentage view point. From these correlations, it was also discovered that the non-Coulombic potential varies smoothly across the valence isoelectronic series of solids, and that it becomes more attractive (or less repulsive) in going from neon to xenon. In order to address the atomic parentage controversy, it was necessary to compare the excitons to the low-n Rydberg states of the rare gas atoms. A review of the quantum defect description of the atomic Rydberg states is, therefore, presented. Also, Rydberg term value/ionization energy correlations are discussed and compared with the analogous exciton correlations. 7 refs., 10 figs., 5 tabs
Techniques for heavy-ion coupled-channels calculations. I. Long-range Coulomb coupling
International Nuclear Information System (INIS)
Rhoades-Brown, M.; Macfarlane, M.H.; Pieper, S.C.
1980-01-01
Direct-reaction calculations for heavy ions require special computational techniques that take advantage of the physical peculiarities of heavy-ion systems. This paper is the first of a series on quantum-mechanical coupled-channels calculations for heavy ions. It deals with the problems posed by the long range of the Coulomb coupling interaction. Our approach is to use the Alder-Pauli factorization whereby the channel wave functions are expressed as products of Coulomb functions and modulating amplitudes. The equations for the modulating amplitudes are used to integrate inwards from infinity to a nuclear matching radius ( approx. = 20 fm). To adequate accuracy, the equations for the amplitudes can be reduced to first order and solved in first Born approximation. The use of the Born approximation leads to rapid recursion relations for the solutions of the Alder-Pauli equations and hence to a great reduction in computational labor. The resulting coupled-channels Coulomb functions can then be matched in the usual way to solutions of the coupled radial equations in the interior region of r space. Numerical studies demonstrate the reliability of the various techniques introduced
International Nuclear Information System (INIS)
Kopytin, I.V.; Karelin, K.N.; Nekipelov, A.A.
2004-01-01
The probability of the endothermic β - decay of nuclei that is stimulated by an electromagnetic field of Planck frequency spectrum (photobeta decay) is calculated, the effect of the Coulomb field on a relativistic electron and a virtual relativistic positron being exactly taken into account in this calculation. It is shown that the inclusion of Coulomb effects is of paramount importance and that the results of the calculations may differ by an order of magnitude from those that were obtained previously in the plane-wave approximation, depending on the energy range being considered. A model for the synthesis of bypassed elements in the interior of massive stars is proposed on the basis of the mechanism of the photobeta decay of stable elements that originate from s and r processes
The quantum n-body problem in dimension d ⩾ n – 1: ground state
Miller, Willard, Jr.; Turbiner, Alexander V.; Escobar-Ruiz, M. A.
2018-05-01
We employ generalized Euler coordinates for the n body system in dimensional space, which consists of the centre-of-mass vector, relative (mutual) mass-independent distances r ij and angles as remaining coordinates. We prove that the kinetic energy of the quantum n-body problem for can be written as the sum of three terms: (i) kinetic energy of centre-of-mass, (ii) the second order differential operator which depends on relative distances alone and (iii) the differential operator which annihilates any angle-independent function. The operator has a large reflection symmetry group and in variables is an algebraic operator, which can be written in terms of generators of the hidden algebra . Thus, makes sense of the Hamiltonian of a quantum Euler–Arnold top in a constant magnetic field. It is conjectured that for any n, the similarity-transformed is the Laplace–Beltrami operator plus (effective) potential; thus, it describes a -dimensional quantum particle in curved space. This was verified for . After de-quantization the similarity-transformed becomes the Hamiltonian of the classical top with variable tensor of inertia in an external potential. This approach allows a reduction of the dn-dimensional spectral problem to a -dimensional spectral problem if the eigenfunctions depend only on relative distances. We prove that the ground state function of the n body problem depends on relative distances alone.
Estimating the critical determinants of a class of three-dimensional star bodies
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Nowak Werner Georg
2017-12-01
Full Text Available In the problem of (simultaneous Diophantine approximation in ℝ3 (in the spirit of Hurwitz’s theorem, lower bounds for the critical determinant of the special three-dimensional body K2 : (y2 + z2(x2 + y2 + z2 ≤ 1 play an important role; see [1], [6]. This article deals with estimates from below for the critical determinant ∆ (Kc of more general star bodies Kc : (y2 + z2c/2(x2 + y2 + z2 ≤ 1 ; where c is any positive constant. These are obtained by inscribing into Kc either a double cone, or an ellipsoid, or a double paraboloid, depending on the size of c.
Coulomb explosion of “hot spot”
Energy Technology Data Exchange (ETDEWEB)
Oreshkin, V. I., E-mail: oreshkin@ovpe.hcei.tsc.ru [Institute of High Current Electrons, SB, RAS, Tomsk (Russian Federation); Tomsk Polytechnic University, Tomsk (Russian Federation); Oreshkin, E. V. [P. N. Lebedev Physical Institute, RAS, Moscow (Russian Federation); Chaikovsky, S. A. [Institute of High Current Electrons, SB, RAS, Tomsk (Russian Federation); P. N. Lebedev Physical Institute, RAS, Moscow (Russian Federation); Institute of Electrophysics, UD, RAS, Ekaterinburg (Russian Federation); Artyomov, A. P. [Institute of High Current Electrons, SB, RAS, Tomsk (Russian Federation)
2016-09-15
The study presented in this paper has shown that the generation of hard x rays and high-energy ions, which are detected in pinch implosion experiments, may be associated with the Coulomb explosion of the hot spot that is formed due to the outflow of the material from the pinch cross point. During the process of material outflow, the temperature of the hot spot plasma increases, and conditions arise for the plasma electrons to become continuously accelerated. The runaway of electrons from the hot spot region results in the buildup of positive space charge in this region followed by a Coulomb explosion. The conditions for the hot spot plasma electrons to become continuously accelerated have been revealed, and the estimates have been obtained for the kinetic energy of the ions generated by the Coulomb explosion.
Coulomb explosion of “hot spot”
International Nuclear Information System (INIS)
Oreshkin, V. I.; Oreshkin, E. V.; Chaikovsky, S. A.; Artyomov, A. P.
2016-01-01
The study presented in this paper has shown that the generation of hard x rays and high-energy ions, which are detected in pinch implosion experiments, may be associated with the Coulomb explosion of the hot spot that is formed due to the outflow of the material from the pinch cross point. During the process of material outflow, the temperature of the hot spot plasma increases, and conditions arise for the plasma electrons to become continuously accelerated. The runaway of electrons from the hot spot region results in the buildup of positive space charge in this region followed by a Coulomb explosion. The conditions for the hot spot plasma electrons to become continuously accelerated have been revealed, and the estimates have been obtained for the kinetic energy of the ions generated by the Coulomb explosion.
Scattering and stopping of swift diatomic molecules under Coulomb explosion
International Nuclear Information System (INIS)
Sigmund, P.
1992-01-01
The scattering and stopping of the fragments of a fast diatomic molecule under Coulomb explosion has been analysed theoretically. The central assumption in the scheme is the dominance of Coulomb explosion, while electronic stopping (including wake forces) and elastic scattering are treated as perturbations. Charge exchange has been neglected. Coulomb images of penetration phenomena are heavily distorted. For small penetrated layer thicknesses, images appear contracted in the direction of the molecular axis, and expanded perpendicular to it. This distortion is described quantitatively by a linear transformation. General expressions have been derived for the effect of continuous and stochastic forces on the distribution of fragment velocities from Coulomb explosion (the ''ring pattern''). Moreover, relations have been found that allow to scale velocity distributions valid in the absence of Coulomb explosion into distributions allowing for Coulomb explosion. Applications concern the shift in ring pattern due to electronic stopping, the lateral broadening due to multiple scattering, and the effect of zero-point motion on the Coulomb image of a molecule. (orig.)
Scattering and stopping of swift diatomic molecules under Coulomb explosion
International Nuclear Information System (INIS)
Sigmund, P.
1991-01-01
The scattering and stopping of the fragments of a fast diatomic molecule under Coulomb explosion has been analyzed theoretically. The central assumption in the scheme is the dominance of Coulomb explosion, while electronic stopping (including wake forces) and elastic scattering are treated as perturbations. Charge exchange has been neglected. Coulomb images of penetration phenomena are heavily distorted. For small penetrated layer thicknesses, images appear contracted in the direction of the molecular axis, and expanded perpendicular to it. This distortion is described quantitatively by a linear transformation. General expressions have been derived for the effect of continuous and stochastic forces on the distribution of fragment velocities from Coulomb explosion (the ''ring pattern''). Moreover, relations have been found that allow to scale velocity distributions valid in the absence of Coulomb explosion into distributions allowing for Coulomb explosion. Applications concern the shift in ring pattern due to electronic stopping, the lateral broadening due to multiple scattering and the effect of zero-point motion on the Coulomb image of a molecule. 14 refs., 5 figs
Finite size and Coulomb corrections: from nuclei to nuclear liquid vapor phase diagram
International Nuclear Information System (INIS)
Moretto, L.G.; Elliott, J.B.; Phair, L.
2003-01-01
In this paper we consider the problem of obtaining the infinite symmetric uncharged nuclear matter phase diagram from a thermal nuclear reaction. In the first part we shall consider the Coulomb interaction which, because of its long range makes the definition of phases problematic. This Coulomb effect seems truly devastating since it does not allow one to define nuclear phase transitions much above A ∼ 30. However there may be a solution to this difficulty. If we consider the emission of particles with a sizable charge, we notice that a large Coulomb barrier Bc is present. For T << Bc these channels may be considered effectively closed. Consequently the unbound channels may not play a role on a suitably short time scale. Then a phase transition may still be definable in an approximate way. In the second part of the article we shall deal with the finite size problem by means of a new method, the complement method, which shall permit a straightforward extrapolation to the infinite system. The complement approach consists of evaluating the change in free energy occurring when a particle or cluster is moved from one (finite) phase to another. In the case of a liquid drop in equilibrium with its vapor, this is done by extracting a vapor particle of any given size from the drop and evaluating the energy and entropy changes associated with both the vapor particle and the residual liquid drop (complement)
Subcycle dynamics of Coulomb asymmetry in strong elliptical laser fields.
Li, Min; Liu, Yunquan; Liu, Hong; Ning, Qicheng; Fu, Libin; Liu, Jie; Deng, Yongkai; Wu, Chengyin; Peng, Liang-You; Peng, Liangyou; Gong, Qihuang
2013-07-12
We measure photoelectron angular distributions of noble gases in intense elliptically polarized laser fields, which indicate strong structure-dependent Coulomb asymmetry. Using a dedicated semiclassical model, we have disentangled the contribution of direct ionization and multiple forward scattering on Coulomb asymmetry in elliptical laser fields. Our theory quantifies the roles of the ionic potential and initial transverse momentum on Coulomb asymmetry, proving that the small lobes of asymmetry are induced by direct ionization and the strong asymmetry is induced by multiple forward scattering in the ionic potential. Both processes are distorted by the Coulomb force acting on the electrons after tunneling. Lowering the ionization potential, the relative contribution of direct ionization on Coulomb asymmetry substantially decreases and Coulomb focusing on multiple rescattering is more important. We do not observe evident initial longitudinal momentum spread at the tunnel exit according to our simulation.
Correlated Coulomb drag in capacitively coupled quantum-dot structures
DEFF Research Database (Denmark)
Kaasbjerg, Kristen; Jauho, Antti-Pekka
2016-01-01
We study theoretically Coulomb drag in capacitively coupled quantum dots (CQDs) -- a biasdriven dot coupled to an unbiased dot where transport is due to Coulomb mediated energy transfer drag. To this end, we introduce a master-equation approach which accounts for higher-order tunneling (cotunneling......) processes as well as energy-dependent lead couplings, and identify a mesoscopic Coulomb drag mechanism driven by nonlocal multi-electron cotunneling processes. Our theory establishes the conditions for a nonzero drag as well as the direction of the drag current in terms of microscopic system parameters...... on Coulomb drag in CQD systems....
International Nuclear Information System (INIS)
Brandao, S.B.
1987-01-01
The level structure of 189 Os has been studied by Coulomb excitation using 35 Cl, 28 Si, 16 O beams. GOSIA, a code written to analyze multiple Coulomb excitation, was used to obtain the reduced probabilities of transition B(E2). The results for interband and intraband turned out possible the classification of the states following Nilsson levels. Gamma-rays originating from deexcitation of 216.7 and 219.4 keV have been separated and the reduced probability of transition has been measured. (A.C.A.S.) [pt
Electron capture in proton collisions with alkali atoms as a three-body problem
International Nuclear Information System (INIS)
Avakov, G.V.; Blokhintsev, L.D.; Kadyrov, A.S.; Mukhamedzhanov, A.M.
1992-01-01
A previous paper proposed an approach to the calculation of electron transfer reactions in ion-atomic collisions based on the Faddeev three-body equations written in the Alt-Grassberger-Sandhas form. In the present work this approach is used to describe the electron capture in proton collisions with alkali atoms. The results of calculation of the total and partial cross sections for charge exchange in proton collisions with Li, Na, K and Rb atoms are presented. The calculated total cross sections are in good agreement with experiment for light target atoms. In going over to heavier targets, the theoretical total cross sections, while agreeing in form, tend to be larger than the experimental ones. The calculated partial cross sections for electron capture into the 2s state of the H atom are also in agreement with experiment. Some other partial cross sections were also calculated. (author)
International Nuclear Information System (INIS)
Almeida Ferreira, A.C. de.
1984-01-01
For problems with azimuthal symmetry in velocity space, the distribution function depends only on the speed and on the pitch angle. The angular dependence of the distribution function is expanded in Legendre polynomials, and the expansions of the collision integrals describing two-body Coulomb interactions in a plasma are determined through the use of the Rosenbluth potentials. The electron distribution function is written as a Maxwellian plus a deviation, and the representation in Legendre polynomials of the electron-electron collision term is given for both its linear and nonlinear part. To determine the representation of the electron-ion collision term it is assumed that the ion distribution is much narrower in velocity space than the electron distribution, and shifted from the origin by a flow velocity. The equations are presented in a form that is suitable for their use in a computer. (Author) [pt
QED effects in high-Z atoms; three-body potentials
International Nuclear Information System (INIS)
Zygelman, B.
1983-01-01
Electromagnetic three-body potentials were first studied by Primakoff and Holstein. Later, Chamugan and Schweber rederived these potentials and pointed out that they might be important in highly relativistic systems, however, their formulation was basically nonrelativistic. Mittleman, in a series of papers, constructed configuration space equations that included three-body potentials. His derivation started from first principles i.e. QED, and the resulting three-body potentials are more general than the Primakoff-Holstein potentials. In this thesis the contribution to the binding energy of a simple high-Z ion from the three-body potentials is calculated. In addition, the nature and structure of these potentials in greater detail are studied. Some ambiguities that arise when the transition from Fock to configuration space is made are studied in detail
A New Class of Solvable Many-Body Problems
Directory of Open Access Journals (Sweden)
Francesco Calogero
2012-10-01
Full Text Available A new class of solvable N-body problems is identified. They describe N unit-mass point particles whose time-evolution, generally taking place in the complex plane, is characterized by Newtonian equations of motion ''of goldfish type'' (acceleration equal force, with specific velocity-dependent one-body and two-body forces featuring several arbitrary coupling constants. The corresponding initial-value problems are solved by finding the eigenvalues of a time-dependent N×N matrix U(t explicitly defined in terms of the initial positions and velocities of the N particles. Some of these models are asymptotically isochronous, i.e. in the remote future they become completely periodic with a period T independent of the initial data (up to exponentially vanishing corrections. Alternative formulations of these models, obtained by changing the dependent variables from the N zeros of a monic polynomial of degree N to its N coefficients, are also exhibited.
Three-body ΛNN force due to Λ-Σ coupling
International Nuclear Information System (INIS)
Myint, Khin Swe; Akaishi, Yoshinori
2003-01-01
The ΛNN three - body force due to coherent Λ - Σ Coupling effect was derived from realistic Nijmegen model D potential. Repulsive and attractive three - body ΛNN forces were reconcilably accounted. For 5 He, within one - channel description, ΛNN force is largely repulsive and its origin comes from Pauli forbidden terms. Within two - channel description, attractive Pauli allowed terms exist and resulting three - body force is always attractive. Large attractive ΛNN force effect due to coherent Λ - Σ coupling effect is predicted in neutron - rich nuclei. The attractive coherent Λ - Σ coupling effect is largely enhanced at high density neutron matter. The attractive three - body ΛNN force effect is essential dynamics of Λ - Σ coupling while the repulsive Nogami three - body effect arises from Pauli forbidden diagrams. (Y. Kazumata)
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.)
Three-M in Word Problem Solving
Hajra, Sayonita Ghosh; Kofman, Victoria
2018-01-01
We describe three activities that help undergraduates (pre-service teachers) to develop scientific vocabulary on measurable attributes and units of measurement. Measurable attributes are important features in understanding a word problem and solving the problem. These activities help students comprehend word problems better by identifying…
Optical Trapping of Ion Coulomb Crystals
Directory of Open Access Journals (Sweden)
Julian Schmidt
2018-05-01
Full Text Available The electronic and motional degrees of freedom of trapped ions can be controlled and coherently coupled on the level of individual quanta. Assembling complex quantum systems ion by ion while keeping this unique level of control remains a challenging task. For many applications, linear chains of ions in conventional traps are ideally suited to address this problem. However, driven motion due to the magnetic or radio-frequency electric trapping fields sometimes limits the performance in one dimension and severely affects the extension to higher-dimensional systems. Here, we report on the trapping of multiple barium ions in a single-beam optical dipole trap without radio-frequency or additional magnetic fields. We study the persistence of order in ensembles of up to six ions within the optical trap, measure their temperature, and conclude that the ions form a linear chain, commonly called a one-dimensional Coulomb crystal. As a proof-of-concept demonstration, we access the collective motion and perform spectrometry of the normal modes in the optical trap. Our system provides a platform that is free of driven motion and combines advantages of optical trapping, such as state-dependent confinement and nanoscale potentials, with the desirable properties of crystals of trapped ions, such as long-range interactions featuring collective motion. Starting with small numbers of ions, it has been proposed that these properties would allow the experimental study of many-body physics and the onset of structural quantum phase transitions between one- and two-dimensional crystals.
On the calculation of dynamic and heat loads on a three-dimensional body in a hypersonic flow
Bocharov, A. N.; Bityurin, V. A.; Evstigneev, N. M.; Fortov, V. E.; Golovin, N. N.; Petrovskiy, V. P.; Ryabkov, O. I.; Teplyakov, I. O.; Shustov, A. A.; Solomonov, Yu S.
2018-01-01
We consider a three-dimensional body in a hypersonic flow at zero angle of attack. Our aim is to estimate heat and aerodynamic loads on specific body elements. We are considering a previously developed code to solve coupled heat- and mass-transfer problem. The change of the surface shape is taken into account by formation of the iterative process for the wall material ablation. The solution is conducted on the multi-graphics-processing-unit (multi-GPU) cluster. Five Mach number points are considered, namely for M = 20-28. For each point we estimate body shape after surface ablation, heat loads on the surface and aerodynamic loads on the whole body and its elements. The latter is done using Gauss-type quadrature on the surface of the body. The comparison of the results for different Mach numbers is performed. We also estimate the efficiency of the Navier-Stokes code on multi-GPU and central processing unit architecture for the coupled heat and mass transfer problem.
International Nuclear Information System (INIS)
Nissen, K.L.
1988-06-01
Two computer codes for the analysis of fuel rod behavior have been developed. Fuel rod mechanics is treated by a two-dimensional, axisymmetric finite element method. The program KONTAKT is used for detailed examinations on fuel rod sections, whereas the second program METHOD2D allows instationary calculations of whole fuel rods. The mechanical contact of fuel and cladding during heating of the fuel rod is very important for it's integrity. Both computer codes use a Newton-Raphson iteration for the solution of the nonlinear solid body contact problem. A constitutive equation is applied for the dependency of contact pressure on normal approach of the surfaces which are assumed to be rough. If friction is present on the contacting surfaces, Coulomb's friction law is used. Code validation is done by comparison with known analytical solutions for special problems. Results of the contact algorithm for an elastic ball pressing against a rigid surface are confronted with Hertzian theory. Influences of fuel-pellet geometry as well as influences of discretisation of displacements and stresses of a single fuel pellet are studied. Contact of fuel and cladding is calculated for a fuel rod section with two fuel pellets. The influence of friction forces between fuel and cladding on their axial expansion is demonstrated. By calculation of deformations and temperatures during an instationary fuel rod experiment of the CABRI-series the feasibility of two-dimensional finite element analysis of whole fuel rods is shown. (orig.) [de
On calculations of the ground state energy in quantum mechanics
International Nuclear Information System (INIS)
Efimov, G.V.
1991-02-01
In nonrelativistic quantum mechanics the Wick-ordering method called the oscillator representation suggested to calculate the ground-state energy for a wide class of potentials allowing the existence of a bound state. The following examples are considered: the orbital excitations of the ground-state in the Coulomb plus linear potential, the Schroedinger equation with a ''relativistic'' kinetic energy √p 2 +m 2 , the Coulomb three-body problem. (author). 22 refs, 2 tabs
Coulomb dissociation of N-20,N-21
Roeder, Marko; Adachi, Tatsuya; Aksyutina, Yulia; Alcantara, Juan; Altstadt, Sebastian; Alvarez-Pol, Hector; Ashwood, Nicholas; Atar, Leyla; Aumann, Thomas; Avdeichikov, Vladimir; Barr, M.; Beceiro, Saul; Bemmerer, Daniel; Benlliure, Jose; Bertulani, Carlos; Boretzky, Konstanze; Borge, Maria J. G.; Burgunder, G.; Caamano, Manuel; Caesar, Christoph; Casarejos, Enrique; Catford, Wilton; Cederkall, Joakim; Chakraborty, S.; Chartier, Marielle; Chulkov, Leonid; Cortina-Gil, Dolores; Crespo, Raquel; Pramanik, Ushasi Datta; Diaz-Fernandez, Paloma; Dillmann, Iris; Elekes, Zoltan; Enders, Joachim; Ershova, Olga; Estrade, A.; Farinon, F.; Fraile, Luis M.; Freer, Martin; Freudenberger, M.; Fynbo, Hans; Galaviz, Daniel; Geissel, Hans; Gernhaeuser, Roman; Goebel, Kathrin; Kalantar-Nayestanaki, Nasser; Najafi, Mohammad Ali; Rigollet, Catherine; Stoica, V.; Streicher, Branislav; Van de Walle, J.
2016-01-01
Neutron-rich light nuclei and their reactions play an important role in the creation of chemical elements. Here, data from a Coulomb dissociation experiment on N-20,N-21 are reported. Relativistic N-20,N-21 ions impinged on a lead target and the Coulomb dissociation cross section was determined in a
The Quantum N-Body Problem and the Auxiliary Field Method
International Nuclear Information System (INIS)
Semay, C.; Buisseret, F.; Silvestre-Brac, B.
2011-01-01
Approximate analytical energy formulas for N-body semirelativistic Hamiltonians with one- and two-body interactions are obtained within the framework of the auxiliary field method. We first review the method in the case of nonrelativistic two-body problems. A general procedure is then given for N-body systems and applied to the case of baryons in the large-N c limit. (author)
Calculation of electromagnetic observables in few-body systems
International Nuclear Information System (INIS)
Gibson, B.F.
1986-10-01
An introduction to the calculation of electromagnetic observables in few-body systems is given by studying two examples in the trinucleon system: (1) the elastic electron scattering charge form factor in configuration space and momentum space and (2) the two-body photodisintegration of 3 H leading to a neutron-deuteron final state in a separable potential formalism. In the discussion of charge form factor calculations, a number of related topics are touched upon: the relation of structure in Psi to the properties of simple NN forces, the Faddeev and Schroedinger solution to the harmonic oscillator problem, the Rosenbluth formula for electron scattering from a spin-1/2 nuclear target (e.g., the proton or 3 H), and the charge density operator. Formulae for 3 He and 3 H charge form factors in a central force approximation are given in configuration and momentum space. The physics of these form factors is discussed in light of results from realistic nucleon-nucleon potential model calculations, including the effects of two-pion-exchange three-body force models. Topics covered are the rms charge densities, and the Coulomb energy of 3 He. In the discussion of the 3 H photodisintegration, the Siegert form of the electric dipole operator (in the long wave length limit) is derived as are the separable potential equations which describe the off-shell transition amplitudes which connect nucleon-plus-corrected-pair states. Expressions for the Born amplitudes required to complete the two-body photodisintegration amplitude calculation are given. Numerical results for a model central force problem are discussed and compared with an approximate calculation. Comparisons with 3 H(γ,n)d and 3 He(γ,p)d data are made, and the significant features of the exact theoretical calculation are outlined. 61 refs., 26 figs
Coulomb Distortion in the Inelastic Regime
Energy Technology Data Exchange (ETDEWEB)
Patricia Solvignon, Dave Gaskell, John Arrington
2009-09-01
The Coulomb distortion effects have been for a long time neglected in deep inelastic scattering for the good reason that the incident energies were very high. But for energies in the range of earlier data from SLAC or at JLab, the Coulomb distortion could have the potential consequence of affecting the A-dependence of the EMC effect and of the longitudinal to transverse virtual photon absorption cross section ratio $R(x,Q^2)$.
Exact calculation of three-body contact interaction to second order
International Nuclear Information System (INIS)
Kaiser, N.
2012-01-01
For a system of fermions with a three-body contact interaction the second-order contributions to the energy per particle anti E(k f ) are calculated exactly. The three-particle scattering amplitude in the medium is derived in closed analytical form from the corresponding two-loop rescattering diagram. We compare the (genuine) second-order three-body contribution to anti E(k f )∝k f 10 with the second-order term due to the density-dependent effective two-body interaction, and find that the latter term dominates. The results of the present study are of interest for nuclear many-body calculations where chiral three-nucleon forces are treated beyond leading order via a density-dependent effective two-body interaction. (orig.)
Effect of Coulomb collision on the negative ion extraction mechanism in negative ion sources.
Goto, I; Miyamoto, K; Nishioka, S; Mattei, S; Lettry, J; Abe, S; Hatayama, A
2016-02-01
To improve the H(-) ion beam optics, it is necessary to understand the energy relaxation process of surface produced H(-) ions in the extraction region of Cs seeded H(-) ion sources. Coulomb collisions of charged particles have been introduced to the 2D3V-PIC (two dimension in real space and three dimension in velocity space particle-in-cell) model for the H(-) extraction by using the binary collision model. Due to Coulomb collision, the lower energy part of the ion energy distribution function of H(-) ions has been greatly increased. The mean kinetic energy of the surface produced H(-) ions has been reduced to 0.65 eV from 1.5 eV. It has been suggested that the beam optics of the extracted H(-) ion beam is strongly affected by the energy relaxation process due to Coulomb collision.
Sine-Gordon mean field theory of a Coulomb gas
Energy Technology Data Exchange (ETDEWEB)
Diehl, Alexandre; Barbosa, Marcia C.; Levin, Yan
1997-12-31
Full text. The Coulomb gas provides a paradigm for the study of various models of critical phenomena. In particular, it is well known that the two dimensional (2 D). Coulomb gas can be directly used to study the superfluidity transition in {sup 4} He films, arrays of Josephson junctions, roughening transition, etc. Not withstanding its versatility, our full understanding of the most basic model of Coulomb gas, namely an ensemble of hard spheres carrying either positive or negative charges at their center, is still lacking. It is now well accepted that at low density the two dimensional plasma of equal number of positive and negative particles undergoes a Kosterlitz-Thouless (KT) metal insulator transition. This transition is of an infinite order and is characterized by a diverging Debye screening length. As the density of particles increases, the validity of the KT theory becomes questionable and the possibility of the KT transition being replaced by some kind of first order discontinuity has been speculated for a long time. In this work sine-Gordon field theory is used to investigate the phase diagram of a neutral Coulomb gas. A variational mean-field free energy is constructed and the corresponding phase diagrams in two and three dimensions are obtained. When analyzed in terms of chemical potential, the sine-Gordon theory predicts the phase diagram topologically identical to the Monte Carlo simulations and a recently developed Debye-Huckel-Bjerrum theory. In 2D, we find that the infinite-order Kosterlitz-Thouless line terminates in a tricritical point, after which the metal-insulator transition becomes first order. However, when the transformation from chemical potential to the density is made the whole insulating phase is mapped onto zero density. (author)
Heggie, D.; Hut, P.
2003-10-01
, Dynamical Evolution of Globular Clusters, or that the standard reference on the observational properties of stellar systems is Binney and Merrifield's Galactic Astronomy. A minor irritation is that many concepts are discussed several times before they are defined, and the index provides no pointer to the primary discussion; thus, for example, there are ten index entries for 'phase mixing' and no indication that the fourth of these refers to the actual definition. The book is intended as a graduate textbook but more likely it will be used mainly in other contexts: by theoretical researchers, as an indispensable reference on the dynamics of gravitational N-body systems; by observational astronomers, as a readable summary of the theory of star cluster evolution; and by physicists seeking a well-written and accessible introduction to a simple problem that remains fascinating and incompletely understood after three centuries. Scott Tremaine
Two-body quantum mechanical problem on spheres
Shchepetilov, Alexey V.
2005-01-01
The quantum mechanical two-body problem with a central interaction on the sphere ${\\bf S}^{n}$ is considered. Using recent results in representation theory an ordinary differential equation for some energy levels is found. For several interactive potentials these energy levels are calculated in explicit form.
Maximal superintegrability of the generalized Kepler-Coulomb system on N-dimensional curved spaces
International Nuclear Information System (INIS)
Ballesteros, Angel; Herranz, Francisco J
2009-01-01
The superposition of the Kepler-Coulomb potential on the 3D Euclidean space with three centrifugal terms has recently been shown to be maximally superintegrable (Verrier and Evans 2008 J. Math. Phys. 49 022902) by finding an additional (hidden) integral of motion which is quartic in the momenta. In this paper, we present the generalization of this result to the N-dimensional spherical, hyperbolic and Euclidean spaces by making use of a unified symmetry approach that makes use of the curvature parameter. The resulting Hamiltonian, formed by the (curved) Kepler-Coulomb potential together with N centrifugal terms, is shown to be endowed with 2N - 1 functionally independent integrals of the motion: one of them is quartic and the remaining ones are quadratic. The transition from the proper Kepler-Coulomb potential, with its associated quadratic Laplace-Runge-Lenz N-vector, to the generalized system is fully described. The role of spherical, nonlinear (cubic) and coalgebra symmetries in all these systems is highlighted
Coulomb drag in coherent mesoscopic systems
DEFF Research Database (Denmark)
Mortensen, Asger; Flensberg, Karsten; Jauho, Antti-Pekka
2001-01-01
We present a theory for Coulomb drag between two mesoscopic systems. Our formalism expresses the drag in terms of scattering matrices and wave functions, and its range of validity covers both ballistic and disordered systems. The consequences can be worked out either by analytic means, such as th......We present a theory for Coulomb drag between two mesoscopic systems. Our formalism expresses the drag in terms of scattering matrices and wave functions, and its range of validity covers both ballistic and disordered systems. The consequences can be worked out either by analytic means......, such as the random matrix theory, or by numerical simulations. We show that Coulomb drag is sensitive to localized states. which usual transport measurements do not probe. For chaotic 2D systems we find a vanishing average drag, with a nonzero variance. Disordered 1D wires show a finite drag, with a large variance...
Scaling laws governing the multiple scattering of diatomic molecules under Coulomb explosion
International Nuclear Information System (INIS)
Sigmund, P.
1992-01-01
The trajectories of fast molecules during and after penetration through foils are governed by Coulomb explosion and distorted by multiple scattering and other penetration phenomena. A scattering event may cause the energy available for Coulomb explosion to increase or decrease, and angular momentum may be transferred to the molecule. Because of continuing Coulomb explosion inside and outside the target foil, the transmission pattern recorded at a detector far away from the target is not just a linear superposition of Coulomb explosion and multiple scattering. The velocity distribution of an initially monochromatic and well-collimated, but randomly oriented, beam of molecular ions is governed by a generalization of the standard Bothe-Landau integral that governs the multiple scattering of atomic ions. Emphasis has been laid on the distribution in relative velocity and, in particular, relative energy. The statistical distributions governing the longitudinal motion (i.e., the relative motion along the molecular axis) and the rotational motion can be scaled into standard multiple-scattering distributions of atomic ions. The two scaling laws are very different. For thin target foils, the significance of rotational energy transfer is enhanced by an order of magnitude compared to switched-off Coulomb explosion. A distribution for the total relative energy (i.e., longitudinal plus rotational motion) has also been found, but its scaling behavior is more complex. Explicit examples given for all three distributions refer to power-law scattering. As a first approximation, scattering events undergone by the two atoms in the molecule were assumed uncorrelated. A separate section has been devoted to an estimate of the effect of impact-parameter correlation on the multiple scattering of penetrating molecules
Empirical Coulomb matrix elements and the mass of 22Al
International Nuclear Information System (INIS)
Whitehead, R.R.; Watt, A.; Kelvin, D.; Rutherford, H.J.
1976-01-01
An attempt has been made to obtain a set of Coulomb matrix elements which fit the known Coulomb energy shifts in the nuclei of mass 18 to 22. The interaction obtained fits the data well with only a few exceptions, one of these being the Coulomb shift of the notorious third 0 + state in 18 Ne. These Coulomb matrix elements are used together with the Chung-Wildenthal interaction to obtain a new prediction for the mass excess of 22 Al. The results indicate that 22 Al should be bound against proton emission. (Auth.)
Resonances in the two centers Coulomb system
International Nuclear Information System (INIS)
Seri, Marcello
2012-01-01
In this work we investigate the existence of resonances for two-centers Coulomb systems with arbitrary charges in two and three dimensions, defining them in terms of generalized complex eigenvalues of a non-selfadjoint deformation of the two-center Schroedinger operator. After giving a description of the bifurcation of the classical system for positive energies, we construct the resolvent kernel of the operators and we prove that they can be extended analytically to the second Riemann sheet. The resonances are then defined and studied with numerical methods and perturbation theory.
Resonances in the two centers Coulomb system
Energy Technology Data Exchange (ETDEWEB)
Seri, Marcello
2012-09-14
In this work we investigate the existence of resonances for two-centers Coulomb systems with arbitrary charges in two and three dimensions, defining them in terms of generalized complex eigenvalues of a non-selfadjoint deformation of the two-center Schroedinger operator. After giving a description of the bifurcation of the classical system for positive energies, we construct the resolvent kernel of the operators and we prove that they can be extended analytically to the second Riemann sheet. The resonances are then defined and studied with numerical methods and perturbation theory.
The few-body problem - some thoughts after the 1980 International Conference
International Nuclear Information System (INIS)
Moravcsik, M.J.; Oregon Univ., Eugene
1981-01-01
Recent progress in the few-body problem, as considered at the Ninth International Conference on the Few-body Problem, Eugene, Oregon, August 1980, is discussed. It is shown that these developments help to-wards the understanding of some of the systems properties of these few-body configurations, contribute to the testing of quark theories, give evidence for the validity or violation of conservation laws, add to the present knowledge of nuclear properties, off-shell nucleon-nucleon interaction and other component laws and provide reliable predictions which may be useful in applications extrinsic to the few-body itself, such as astrophysics, space physics or chemistry. (U.K.)
Energy Technology Data Exchange (ETDEWEB)
Marganiec, Justyna [ExtreMe Matter Institute EMMI, GSI Darmstadt, Darmstadt (Germany); Aumann, Thomas; Heil, Michael; Plag, Ralf; Wamers, Felix [Kernreaktionen und Nuklear Astrophysik, GSI Darmstadt, Darmstadt (Germany)
2010-07-01
For the production of proton-rich nuclei during the rp process two-proton capture plays an important role. This process can bridge long-lived waiting points which otherwise hamper the mass flow between CNO material and the FeNi mass region. One of these waiting points is {sup 15}O. The three-body radiative capture can proceed sequentially or directly from the three-body continuum. The rate of the {sup 15}O(2p,{gamma}){sup 17}Ne reaction obtained using the two-successive-proton-capture model has been discussed in J. Goerres et al. (Phys. Rev. C 51, 392, 1995). The role of continuum states ({sup 15}O+2p) for the rate calculation has been demonstrated in L.V Grigorenko, M.V. Zhukov (Phys. Rev. C 72, 015803, 2005). It has been suggested that the reaction rate can be enhanced by a few orders of magnitude by taking into account the three-body continuum. In order to verify these calculations, we have deduced the {sup 15}O(2p,{gamma}){sup 17}Ne cross section by studying the time-reversed process, the Coulomb dissociation of {sup 17}Ne, at the LAND/R{sup 3}B setup at GSI, using a {sup 17}Ne secondary beam from the fragment separator FRS.
Coulomb Dissociation as a Tool of Nuclear Astrophysics
International Nuclear Information System (INIS)
Utsunomiya, H.
2000-01-01
My talk will begin with an introduction of the Coulomb dissociation method, proceed to discussions on Coulomb breakup of 7 Li with respect to the big-bang nucleosynthesis and end with the revision of astrophysical S-factors. The methodology based on the virtual photon source will be introduced in view of experimental techniques. The discussion will include the quantum tunnelling effect in non-resonant breakup, the lifetime of continuum states, and Coulomb distortion of relevant cross sections. Roles of multi-step processes and different multipolarities will also be discussed on the basis of solving a time-dependent Schroedinger equation. My talk will present quantitative results. The theoretical framework of the Coulomb dissociation method and a broad scope of its applications are given by G. Baur. Applications to radioactive nuclei which have quickly become vogue are discussed in the related lecture of J. Kiener. (author)
Pairing from dynamically screened Coulomb repulsion in bismuth
Ruhman, Jonathan; Lee, Patrick A.
2017-12-01
Recently, Prakash et al. have discovered bulk superconductivity in single crystals of bismuth, which is a semimetal with extremely low carrier density. At such low density, we argue that conventional electron-phonon coupling is too weak to be responsible for the binding of electrons into Cooper pairs. We study a dynamically screened Coulomb interaction with effective attraction generated on the scale of the collective plasma modes. We model the electronic states in bismuth to include three Dirac pockets with high velocity and one hole pocket with a significantly smaller velocity. We find a weak-coupling instability, which is greatly enhanced by the presence of the hole pocket. Therefore we argue that bismuth is the first material to exhibit superconductivity driven by retardation effects of Coulomb repulsion alone. By using realistic parameters for bismuth we find that the acoustic plasma mode does not play the central role in pairing. We also discuss a matrix element effect, resulting from the Dirac nature of the conduction band, which may affect Tc in the s -wave channel without breaking time-reversal symmetry.
Wang, J.; Xu, C.; Furlong, K.; Zhong, B.; Xiao, Z.; Yi, L.; Chen, T.
2017-12-01
Although Coulomb stress changes induced by earthquake events have been used to quantify stress transfers and to retrospectively explain stress triggering among earthquake sequences, realistic reliable prospective earthquake forecasting remains scarce. To generate a robust Coulomb stress map for earthquake forecasting, uncertainties in Coulomb stress changes associated with the source fault, receiver fault and friction coefficient and Skempton's coefficient need to be exhaustively considered. In this paper, we specifically explore the uncertainty in slip models of the source fault of the 2011 Mw 9.0 Tohoku-oki earthquake as a case study. This earthquake was chosen because of its wealth of finite-fault slip models. Based on the wealth of those slip models, we compute the coseismic Coulomb stress changes induced by this mainshock. Our results indicate that nearby Coulomb stress changes for each slip model can be quite different, both for the Coulomb stress map at a given depth and on the Pacific subducting slab. The triggering rates for three months of aftershocks of the mainshock, with and without considering the uncertainty in slip models, differ significantly, decreasing from 70% to 18%. Reliable Coulomb stress changes in the three seismogenic zones of Nanki, Tonankai and Tokai are insignificant, approximately only 0.04 bar. By contrast, the portions of the Pacific subducting slab at a depth of 80 km and beneath Tokyo received a positive Coulomb stress change of approximately 0.2 bar. The standard errors of the seismicity rate and earthquake probability based on the Coulomb rate-and-state model (CRS) decay much faster with elapsed time in stress triggering zones than in stress shadows, meaning that the uncertainties in Coulomb stress changes in stress triggering zones would not drastically affect assessments of the seismicity rate and earthquake probability based on the CRS in the intermediate to long term.
Some threshold spectral problems of Schroedinger operators
International Nuclear Information System (INIS)
Jia, X.
2009-01-01
This Ph.D. thesis deals with some spectral problems of the Schroedinger operators. We first consider the semi-classical limit of the number of bound states of unique two-cluster N-body Schroedinger operator. Then we use Dirichlet-Neumann bracket to get semi-classical limit of Riesz means of the discrete eigenvalues of N-body Schroedinger operator. The effective potential of N-body Schroedinger operator with Coulomb potential is also considered and we find that the effective potential has critical decay at infinity. Thus, the Schroedinger operator with critical potential is studied in this thesis. We study the coupling constant threshold of Schroedinger operator with critical potential and the asymptotic expansion of resolvent of Schroedinger operator with critical potential. We use that expansion to study low-energy asymptotics of derivative of spectral shift function for perturbation with critical decay. After that, we use this result and the known result for high-energy asymptotic expansion of spectral shift function to obtain the Levinson theorem. (author)
Coulomb sum rules in the relativistic Fermi gas model
International Nuclear Information System (INIS)
Do Dang, G.; L'Huillier, M.; Nguyen Giai, Van.
1986-11-01
Coulomb sum rules are studied in the framework of the Fermi gas model. A distinction is made between mathematical and observable sum rules. Differences between non-relativistic and relativistic Fermi gas predictions are stressed. A method to deduce a Coulomb response function from the longitudinal response is proposed and tested numerically. This method is applied to the 40 Ca data to obtain the experimental Coulomb sum rule as a function of momentum transfer
Equilibria of the three-body problem with rigid dumb-bell satellite
International Nuclear Information System (INIS)
Elipe, A.; Palacios, M.; Pretka-Ziomek, H.
2008-01-01
This paper is concerned with the orbital-rotational motion of an asymmetric dumb-bell (two masses with fixed distance among them) under the attraction of a central body. For this model, we find some equilibria and give sufficient conditions for their stability
Similar solutions for viscous hypersonic flow over a slender three-fourths-power body of revolution
Lin, Chin-Shun
1987-01-01
For hypersonic flow with a shock wave, there is a similar solution consistent throughout the viscous and inviscid layers along a very slender three-fourths-power body of revolution The strong pressure interaction problem can then be treated by the method of similarity. Numerical calculations are performed in the viscous region with the edge pressure distribution known from the inviscid similar solutions. The compressible laminar boundary-layer equations are transformed into a system of ordinary differential equations. The resulting two-point boundary value problem is then solved by the Runge-Kutta method with a modified Newton's method for the corresponding boundary conditions. The effects of wall temperature, mass bleeding, and body transverse curvature are investigated. The induced pressure, displacement thickness, skin friction, and heat transfer due to the previously mentioned parameters are estimated and analyzed.
Omidvar, K.
1972-01-01
Three charged particles 1, 2, 3 collide according to the reaction 1+(2+3) yields (1+3)+2, where (2+3) and (1+3) are hydrogenlike bound states. It is shown when (1+3) is in a highly excited state n, due to the repulsive potential, the cross section in the first Born approximation behaves as 1/n which makes the total cross section to diverge like ln n. The total cross sections in the higher orders of the Born approximation are similarly divergent logarithmically.
Heavy flavor baryons in hypercentral model
Indian Academy of Sciences (India)
Keywords. Hypercentral constituent quark model; charmed and beauty baryons; hyper-Coulomb plus power potential. Abstract. Heavy flavor baryons containing single and double charm (beauty) quarks with light flavor combinations are studied using the hypercentral description of the three-body problem. The confinement ...
Coulomb displacement energies in nuclei: a new approach
International Nuclear Information System (INIS)
Auerbach, N.; Tel Aviv Univ.; Bernard, V.; Nguyen, V.G.
1978-04-01
The neutron core polarization gives rise to an important correction to the direct Coulomb contribution when one calculates the Coulomb displacement energies. In the Hartree-Fock model it is shown that this correction is about 2% to 4.5% in medium and heavy nuclei. The core polarization as well as other higher order effects can be included by using a selfconsistent description of the analog state in a complete proton particle-neutron hole space. The Coulomb displacement energies in 48 Ca, 88 Sr and 208 Pb have been calculated using Skyrme interactions SIII and SIV. A good agreement with experiment is obtained
Assessment of mechanical and three-body abrasive wear peculiarity ...
Indian Academy of Sciences (India)
The three-body abrasive wear characteristic of fabricated composites has been assessed under different operating conditions. For this, the three-body abrasion test is done on dry abrasion test rig (TR-50)and analysed using Taguchi's experimental design scheme and analysis of variance. The results obtained from these ...
Ginzburg criterion for ionic fluids: the effect of Coulomb interactions.
Patsahan, O
2013-08-01
The effect of the Coulomb interactions on the crossover between mean-field and Ising critical behavior in ionic fluids is studied using the Ginzburg criterion. We consider the charge-asymmetric primitive model supplemented by short-range attractive interactions in the vicinity of the gas-liquid critical point. The model without Coulomb interactions exhibiting typical Ising critical behavior is used to calibrate the Ginzburg temperature of the systems comprising electrostatic interactions. Using the collective variables method, we derive a microscopic-based effective Hamiltonian for the full model. We obtain explicit expressions for all the relevant Hamiltonian coefficients within the framework of the same approximation, i.e., the one-loop approximation. Then we consistently calculate the reduced Ginzburg temperature t(G) for both the purely Coulombic model (a restricted primitive model) and the purely nonionic model (a hard-sphere square-well model) as well as for the model parameters ranging between these two limiting cases. Contrary to the previous theoretical estimates, we obtain the reduced Ginzburg temperature for the purely Coulombic model to be about 20 times smaller than for the nonionic model. For the full model including both short-range and long-range interactions, we show that t(G) approaches the value found for the purely Coulombic model when the strength of the Coulomb interactions becomes sufficiently large. Our results suggest a key role of Coulomb interactions in the crossover behavior observed experimentally in ionic fluids as well as confirm the Ising-like criticality in the Coulomb-dominated ionic systems.
Appleberry, W. T.
1983-01-01
Standard hydraulic shock absorber modified to form coulomb (linear friction) damper. Device damps very small velocities and is well suited for use with large masses mounted on soft springs. Damping force is easily adjusted for different loads. Dampers are more reliable than fluid dampers and also more economical to build and to maintain.
Three-body and four-body photodisintegrations of the 4He nuclei in the Δ region
International Nuclear Information System (INIS)
Niki, Kazuaki
1991-01-01
The differential and total cross sections were measured for the three-body (pnd) and four-body (ppnn) final states in photodisintegration of 4 He in an energy range between 125 and 445 MeV. The kinematic variables were determined in an almost complete way, using a large acceptance spectrometer together with the use of tagged photons of an energy resolution of 10 MeV. We have found that the three-body reaction 4 He(γ, pn)d makes a dominant contribution among various processes which lead to non-mesonic final states. The behavior of the 4 He(γ, pn)d cross section is well described by the quasi-deuteron model (QDM). On the other hand, the four-body breakup cross sections are not consistent with the prediction of the QDM. For these four-body reactions, photon absorption by three-nucleon clusters seems to give a dominant effect. The four-body cross sections also show a broad enhancement around 300 to 400 MeV, indicating a possible participation of the Δ to the reactions. (author)
International Nuclear Information System (INIS)
Petrov, N.M.; Pushkash, A.M.
1985-01-01
In accordance with the main idea of the phase function method the two-body off-shell scattering amplitudes are considered as the limit of the scattering amplitude sequence corresponding to the sequence of the R-radius cut-off potentials. The explicit analytical expression for the scattering amplitudes function is obtained in the case of separable potentials, due to which the three-body problem is investigated
Renormalizable Non-Covariant Gauges and Coulomb Gauge Limit
Baulieu, L
1999-01-01
To study ``physical'' gauges such as the Coulomb, light-cone, axial or temporal gauge, we consider ``interpolating'' gauges which interpolate linearly between a covariant gauge, such as the Feynman or Landau gauge, and a physical gauge. Lorentz breaking by the gauge-fixing term of interpolating gauges is controlled by extending the BRST method to include not only the local gauge group, but also the global Lorentz group. We enumerate the possible divergences of interpolating gauges, and show that they are renormalizable, and we show that the expectation value of physical observables is the same as in a covariant gauge. In the second part of the article we study the Coulomb-gauge as the singular limit of the Landau-Coulomb interpolating gauge. We find that unrenormalized and renormalized correlation functions are finite in this limit. We also find that there are finite two-loop diagrams of ``unphysical'' particles that are not present in formal canonical quantization in the Coulomb gauge. We verify that in the ...
Three-body interactions and the Landau levels using Nikiforov ...
Indian Academy of Sciences (India)
In this article, the eigenvalues for the three-body interactions on the line and the Landau levels in the presence of topological defects have been regenerated by the Nikiforov–Uvarov (NU) method. Two exhaustive lists of such exactly solvable potentials are given. Keywords. Nikiforov–Uvarov (NU) method; three-body ...
Activation measurements of α-induced reactions at sub-Coulomb energies
Energy Technology Data Exchange (ETDEWEB)
Scholz, Philipp; Dewald, Alfred; Heinze, Stefan; Mayer, Jan; Mueller-Gatermann, Claus; Netterdon, Lars; Zilges, Andreas [Institute for Nuclear Physics, University of Cologne (Germany); Endres, Anne [Institute for Applied Physics, Goethe University Frankfurt am Main (Germany)
2015-07-01
Network calculations of the γ process rely almost completely on theoretically predicted reaction rates within the scope of the Hauser-Feshbach Statistical Model. Especially the prediction of cross sections for (γ,α)-reactions at energies within or close to the astrophysically relevant energy window remains a problem due to the uncertainties in the underlying α-optical-model potentials. Although experimental values far above the Coulomb-barrier are well reproduced, commonly used α-optical potentials often fail to describe the trend at energies comparable to those at astrophysical sites of the γ process. Improvements of the adopted optical-model potentials are hampered by the lack of experimental cross sections at sub-Coulomb energies. In order to enlarge the experimental data base, cross sections of the {sup 187}Re(α,n) and {sup 108}Cd(α,n) reactions were investigated using the activation technique with the Cologne Clover Counting Setup. Besides recent experimental results, future plans for more sensitive cross-section studies applying Accelerator Mass Spectrometry using CologneAMS are presented.
Analysis of a Unilateral Contact Problem with Normal Compliance
Directory of Open Access Journals (Sweden)
Touzaline Arezki
2014-06-01
Full Text Available The paper deals with the study of a quasistatic unilateral contact problem between a nonlinear elastic body and a foundation. The contact is modelled with a normal compliance condition associated to unilateral constraint and the Coulomb's friction law. The adhesion between contact surfaces is taken into account and is modelled with a surface variable, the bonding field, whose evolution is described by a first-order differential equation. We establish a variational formulation of the mechanical problem and prove an existence and uniqueness result in the case where the coefficient of friction is bounded by a certain constant. The technique of the proof is based on arguments of time-dependent variational inequalities, differential equations and fixed-point theorem.
Phase diagram, correlation gap, and critical properties of the Coulomb glass
Palassini, Matteo; Goethe, Martin
2009-03-01
We investigate the lattice Coulomb glass model in three dimensions via extensive Monte Carlo simulations. 1. No evidence for an equilibrium glass phase is found down to very low temperatures, contrary to mean-field predictions, although the correlation length increases rapidly near T=0. 2. The single-particle density of states near the Coulomb gap satisfies the scaling law g(e,T)=T^λf(e/T) with λ 2.2. 3. A charge-ordered phase exists at low disorder. The phase transition from the fluid to the charge ordered phase is consistent with the Random Field Ising universality class, which shows that the interaction is effectively screened at moderate temperature. Results from nonequilibrium simulations will also be briefly discussed. Reference: M.Goethe and M.Palassini, arXiv:0810.1047
An initial boundary value problem for modeling a piezoelectric dipolar body
Marin, Marin; Öchsner, Andreas
2018-03-01
This study deals with the first initial boundary value problem in elasticity of piezoelectric dipolar bodies. We consider the most general case of an anisotropic and inhomogeneous elastic body having a dipolar structure. For two different types of restrictions imposed on the problem data, we prove two results regarding the uniqueness of solution, by using a different but accessible method. Then, the mixed problem is transformed in a temporally evolutionary equation on a Hilbert space, conveniently constructed based on the problem data. With the help of a known result from the theory of semigroups of operators, the existence and uniqueness of the weak solution for this equation are proved.
Key to good fit: body measurement problems specific to key ...
African Journals Online (AJOL)
Key to good fit: body measurement problems specific to key dimensions. ... to explore and describe the problems that the South African Clothing Industry currently ... A postal survey was conducted among South African apparel and footwear ...
Observation of a Coulomb flux tube
Greensite, Jeff; Chung, Kristian
2018-03-01
In Coulomb gauge there is a longitudinal color electric field associated with a static quark-antiquark pair. We have measured the spatial distribution of this field, and find that it falls off exponentially with transverse distance from a line joining the two quarks. In other words there is a Coulomb flux tube, with a width that is somewhat smaller than that of the minimal energy flux tube associated with the asymptotic string tension. A confinement criterion for gauge theories with matter fields is also proposed.
Structures of two-dimensional three-body systems
International Nuclear Information System (INIS)
Ruan, W.Y.; Liu, Y.Y.; Bao, C.G.
1996-01-01
Features of the structure of L = 0 states of a two-dimensional three-body model system have been investigated. Three types of permutation symmetry of the spatial part, namely symmetric, antisymmetric, and mixed, have been considered. A comparison has been made between the two-dimensional system and the corresponding three-dimensional one. The effect of symmetry on microscopic structures is emphasized. (author)
Efimov resonances in atomic three-body systems
International Nuclear Information System (INIS)
Mezei, J. Zs.; Papp, Z.
2006-01-01
In a recent work [Phys. Rev. Lett. 94, 143201 (2005)], we reported an accumulation of three-body resonant states attached to n=2 and higher two-body thresholds. A more careful investigation revealed that there are resonances of the same kind above the n=1 threshold as well. This suggests that the resonances attached to the thresholds are Efimov resonances
Three-body calculation of Be double-hypernuclei
Indian Academy of Sciences (India)
Energy levels and bond energy of the double- hypernucleus are calculated by considering two- and three-cluster interactions. Interactions between constituent particles are contact interactions for reproducing the low binding energy of nuclei. The effective action is constructed to involve three-body forces. In this paper ...
Dimensional regularization and renormalization of Coulomb gauge quantum electrodynamics
International Nuclear Information System (INIS)
Heckathorn, D.
1979-01-01
Quantum electrodynamics is renormalized in the Coulomb gauge with covariant counter terms and without momentum-dependent wave-function renormalization constants. It is shown how to dimensionally regularize non-covariant integrals occurring in this guage, and prove that the 'minimal' subtraction prescription excludes non-covariant counter terms. Motivated by the need for a renormalized Coulomb gauge formalism in certain practical calculations, the author introduces a convenient prescription with physical parameters. The renormalization group equations for the Coulomb gauge are derived. (Auth.)
Coulomb Mediated Hybridization of Excitons in Coupled Quantum Dots.
Ardelt, P-L; Gawarecki, K; Müller, K; Waeber, A M; Bechtold, A; Oberhofer, K; Daniels, J M; Klotz, F; Bichler, M; Kuhn, T; Krenner, H J; Machnikowski, P; Finley, J J
2016-02-19
We report Coulomb mediated hybridization of excitonic states in optically active InGaAs quantum dot molecules. By probing the optical response of an individual quantum dot molecule as a function of the static electric field applied along the molecular axis, we observe unexpected avoided level crossings that do not arise from the dominant single-particle tunnel coupling. We identify a new few-particle coupling mechanism stemming from Coulomb interactions between different neutral exciton states. Such Coulomb resonances hybridize the exciton wave function over four different electron and hole single-particle orbitals. Comparisons of experimental observations with microscopic eight-band k·p calculations taking into account a realistic quantum dot geometry show good agreement and reveal that the Coulomb resonances arise from broken symmetry in the artificial semiconductor molecule.
Planar density of vacuum charge induced by a supercritical Coulomb potential
Directory of Open Access Journals (Sweden)
V.R. Khalilov
2017-06-01
Full Text Available Analytical expressions for the planar density of an induced vacuum charge are obtained in a strong Coulomb potential in coordinate space. Treatment is based on a self-adjoint extension approach for constructing of the Green's function of a charged fermion in an external electromagnetic field. Induced vacuum charge density is calculated and analyzed in subcritical and supercritical Coulomb potentials for massless and massive fermions. We argue that the virtual and so-called real vacuum polarizations contribute in an induced vacuum charge in a supercritical Coulomb potential. The behavior of the polarization vacuum charge density is investigated at long and short distances from the Coulomb center. The induced vacuum charge has a screening sign. Screening of a Coulomb impurity in graphene is briefly discussed. The real vacuum polarization charge density that acquires the quantum electrodynamics vacuum in a supercritical Coulomb potential due to the real vacuum polarization is calculated. It is shown that the vacuum charge densities essentially differ in massive and massless cases. We expect that our results can, as a matter of principle, be tested in graphene with a supercritical Coulomb impurity.
Planar density of vacuum charge induced by a supercritical Coulomb potential
Energy Technology Data Exchange (ETDEWEB)
Khalilov, V.R., E-mail: khalilov@phys.msu.ru; Mamsurov, I.V.
2017-06-10
Analytical expressions for the planar density of an induced vacuum charge are obtained in a strong Coulomb potential in coordinate space. Treatment is based on a self-adjoint extension approach for constructing of the Green's function of a charged fermion in an external electromagnetic field. Induced vacuum charge density is calculated and analyzed in subcritical and supercritical Coulomb potentials for massless and massive fermions. We argue that the virtual and so-called real vacuum polarizations contribute in an induced vacuum charge in a supercritical Coulomb potential. The behavior of the polarization vacuum charge density is investigated at long and short distances from the Coulomb center. The induced vacuum charge has a screening sign. Screening of a Coulomb impurity in graphene is briefly discussed. The real vacuum polarization charge density that acquires the quantum electrodynamics vacuum in a supercritical Coulomb potential due to the real vacuum polarization is calculated. It is shown that the vacuum charge densities essentially differ in massive and massless cases. We expect that our results can, as a matter of principle, be tested in graphene with a supercritical Coulomb impurity.
On low energy scattering theory with Coulomb potentials
International Nuclear Information System (INIS)
Gibson, A.G.
1985-09-01
The scattering length is a very useful characteristic of the scattering phenomena. But in the presence of a combined potential (e.g. in nuclear physics, when Coulomb, the polarization and the strong potentials are to be added), the analytical definition of the scattering length in not unambigous and strictly defined. This problem is discussed in detail, the various alternatives are examined and compared. A practical suggestion is given for the proper choice of the definition and for the calculation of scattering length. Numerical solutions of the Schroedinger equation are compared with the results of different definitions. Some questions of application to nuclear physics are discussed. (D.Gy.)
The statistical mechanics of the classical two-dimensional Coulomb gas is exactly solved
International Nuclear Information System (INIS)
Samaj, L
2003-01-01
The model under consideration is a classical 2D Coulomb gas of pointlike positive and negative unit charges, interacting via a logarithmic potential. In the whole stability range of temperatures, the equilibrium statistical mechanics of this fluid model is exactly solvable via an equivalence with the integrable 2D sine-Gordon field theory. The exact solution includes the bulk thermodynamics, special cases of the surface thermodynamics and the large-distance asymptotic behaviour of the two-body correlation functions
Cavity QED experiments with ion Coulomb crystals
DEFF Research Database (Denmark)
Herskind, Peter Fønss; Dantan, Aurélien; Marler, Joan
2009-01-01
Cavity QED experimental results demonstrating collective strong coupling between ensembles of atomic ions cooled into Coulomb crystals and optical cavity fields have been achieved. Collective Zeeman coherence times of milliseconds have furthermore been obtained.......Cavity QED experimental results demonstrating collective strong coupling between ensembles of atomic ions cooled into Coulomb crystals and optical cavity fields have been achieved. Collective Zeeman coherence times of milliseconds have furthermore been obtained....
Influence of effective three-body force on the spectroscopy of 19O
International Nuclear Information System (INIS)
Haung, W.; Song, H.; Wang, Z.; Kuo, T.T.S.
1983-01-01
The purpose of the present paper is to investigate the influence of effective three-body force on the spectroscopy of 19 O. The model space was chosen as the configuration space which consists of the j-j coupling states of three valence neutrons in the s-d shell. The effective interaction including two- and three-body forces was then derived in the framework of the folded diagram method (FDM). Besides two traditional three-body terms, there is another kind of three-body force, the folded one constructed with two two-body diagrams, in FDM. The G-matrix elements of soft core Reid force were used in the numerical calculations. In the case of lacking the G-matrix elements, we adopted the matrix elements of M-3Y force as the equivalents. The results show that the influence of the effective three-body forces on the spectrum of 19 O is not of importance, but the part coming from the folded three-body term is worth noting
Coulomb dissociation of N 20,21
Röder, Marko; Adachi, Tatsuya; Aksyutina, Yulia; Alcantara, Juan; Altstadt, Sebastian; Alvarez-Pol, Hector; Ashwood, Nicholas; Atar, Leyla; Aumann, Thomas; Avdeichikov, Vladimir; Barr, M.; Beceiro, Saul; Bemmerer, Daniel; Benlliure, Jose; Bertulani, Carlos
2016-01-01
Neutron-rich light nuclei and their reactions play an important role in the creation of chemical elements. Here, data from a Coulomb dissociation experiment on N20,21 are reported. Relativistic N20,21 ions impinged on a lead target and the Coulomb dissociation cross section was determined in a kinematically complete experiment. Using the detailed balance theorem, the N19(n,γ)N20 and N20(n,γ)N21 excitation functions and thermonuclear reaction rates have been determined. The N19(n,γ)N20 rate is...
Coulomb singularity effects in tunnelling spectroscopy of individual impurities
Arseyev, P. I.; Maslova, N. S.; Panov, V. I.; Savinov, S. V.
2002-01-01
Non-equilibrium Coulomb effects in resonant tunnelling processes through deep impurity states are analyzed. It is shown that Coulomb vertex corrections to the tunnelling transfer amplitude lead to a power-law singularity in current- voltage characteristics
Exact solution of the three-boson problem at vanishing energy
International Nuclear Information System (INIS)
Mora, Ch.; Gogolin, A.O.; Egger, R.
2011-01-01
A zero-range approach is used to model resonant two-body interactions between three identical bosons. A dimensionless phase parameterizes the three-body boundary condition while the scattering length enters the Bethe-Peierls boundary condition. The model is solved exactly at zero energy for any value of the scattering length, positive or negative. From this solution, an analytical expression for the rate of three-body recombination to the universal shallow dimer is extracted. (authors)
Effect of Coulomb collision on the negative ion extraction mechanism in negative ion sources
Energy Technology Data Exchange (ETDEWEB)
Goto, I., E-mail: goto@ppl.appi.keio.ac.jp; Nishioka, S.; Abe, S.; Hatayama, A. [Graduate School of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522 (Japan); Miyamoto, K. [Naruto University of Education, 748 Nakashima, Takashima, Naruto-cho, Naruto-shi, Tokushima 772-8502 (Japan); Mattei, S.; Lettry, J. [CERN, 1211 Geneva 23 (Switzerland)
2016-02-15
To improve the H{sup −} ion beam optics, it is necessary to understand the energy relaxation process of surface produced H{sup −} ions in the extraction region of Cs seeded H{sup −} ion sources. Coulomb collisions of charged particles have been introduced to the 2D3V-PIC (two dimension in real space and three dimension in velocity space particle-in-cell) model for the H{sup −} extraction by using the binary collision model. Due to Coulomb collision, the lower energy part of the ion energy distribution function of H{sup −} ions has been greatly increased. The mean kinetic energy of the surface produced H{sup −} ions has been reduced to 0.65 eV from 1.5 eV. It has been suggested that the beam optics of the extracted H{sup −} ion beam is strongly affected by the energy relaxation process due to Coulomb collision.
3He(d,p)4He reaction calculation with three-body Faddeev equations
International Nuclear Information System (INIS)
Oryu, S.; Uzu, E.; Sunahara, H.; Yamada, T.; Tabaru, G.; Hino, T.
1998-01-01
In order to investigate the 3 He-n-p system as a three-body problem, we have formulated 3 He-n and 3 H-p effective potentials using both a microscopic treatment and a phenomenological approach. In the microscopic treatment, potentials are generated by means of the resonating group method (RGM) based on the Minnesota nucleon-nucleon potential. These potentials are converted into separable form by means of the microscopic Pauli correct (MPC) method. The MPC potentials are properly formulated to avoid Pauli forbidden states. The phenomenological potentials are obtained by modifying parameters of the EST approximation to the Paris nucleon-nucleon potential, such that they fit the low-energy 3 He-n, 3 H-p, and 3 He-p phase shifts. Therefore, they describe the 3 He-n differential cross section, the polarization observables, and the energy levels of 4 He. The 3 He-n-p Faddeev equations are solved numerically. We reproduce correctly the ground state and the first excited state of 5 Li. Furthermore, the Paris-type potential is used to investigate the 3 He(d,p) 4 He reaction at a deuteron bombarding energy of 270 MeV, where the system is treated as a three-body problem. Results for the polarized and unpolarized differential cross sections demonstrate convergence of the Born series. (orig.)
The Coulomb Branch of 3d N= 4 Theories
Bullimore, Mathew; Dimofte, Tudor; Gaiotto, Davide
2017-09-01
We propose a construction for the quantum-corrected Coulomb branch of a general 3d gauge theory with N=4 supersymmetry, in terms of local coordinates associated with an abelianized theory. In a fixed complex structure, the holomorphic functions on the Coulomb branch are given by expectation values of chiral monopole operators. We construct the chiral ring of such operators, using equivariant integration over BPS moduli spaces. We also quantize the chiral ring, which corresponds to placing the 3d theory in a 2d Omega background. Then, by unifying all complex structures in a twistor space, we encode the full hyperkähler metric on the Coulomb branch. We verify our proposals in a multitude of examples, including SQCD and linear quiver gauge theories, whose Coulomb branches have alternative descriptions as solutions to Bogomolnyi and/or Nahm equations.
Resolution of identity approximation for the Coulomb term in molecular and periodic systems
Burow, Asbjörn M.; Sierka, Marek; Mohamed, Fawzi
2009-12-01
A new formulation of resolution of identity approximation for the Coulomb term is presented, which uses atom-centered basis and auxiliary basis functions and treats molecular and periodic systems of any dimensionality on an equal footing. It relies on the decomposition of an auxiliary charge density into charged and chargeless components. Applying the Coulomb metric under periodic boundary conditions constrains the explicit form of the charged part. The chargeless component is determined variationally and converged Coulomb lattice sums needed for its determination are obtained using chargeless linear combinations of auxiliary basis functions. The lattice sums are partitioned in near- and far-field portions which are treated through an analytical integration scheme employing two- and three-center electron repulsion integrals and multipole expansions, respectively, operating exclusively in real space. Our preliminary implementation within the TURBOMOLE program package demonstrates consistent accuracy of the method across molecular and periodic systems. Using common auxiliary basis sets the errors of the approximation are small, in average about 20 μhartree per atom, for both molecular and periodic systems.
Ma, Pan; Wang, Chuncheng; Luo, Sizuo; Yu, Xitao; Li, Xiaokai; Wang, Zhenzhen; Hu, Wenhui; Yu, Jiaqi; Yang, Yizhang; Tian, Xu; Cui, Zhonghua; Ding, Dajun
2018-05-01
We studied the relative yields and dissociation dynamics for two- and three-body Coulomb explosion (CE) channels from highly charged carbonyl sulfide molecules in intense laser fields using the CE imaging technique. The electron recollision contributions are evaluated by comparing the relative yields for the multiple ionization process in linearly polarized and circularly polarized (LP and CP) laser fields. The nonsequential multiple ionization is only confirmed for the charge states of 2 to 4 because the energy for further ionization from the inner orbital is much larger than the maximum recollision energy, 3.2U p . The novel deviations of kinetic energy releases distributions between LP and CP pulses are observed for the charge states higher than 4. It can be attributed to the stronger molecular bending in highly charged states before three-body CE with CP light, in which the bending wave packet is initialed by the triple or quartic ionization and spread along their potential curves. Compared to LP light, CP light ionizes a larger fraction of bending molecules in the polarization plane.
Directory of Open Access Journals (Sweden)
P. P. Hallan
2008-01-01
Full Text Available The effect of perturbations in Coriolis and cetrifugal forces on the nonlinear stability of the equilibrium point of the Robe's (1977 restricted circular three-body problem has been studied when the density parameter K is zero. By applying Kolmogorov-Arnold-Moser (KAM theory, it has been found that the equilibrium point is stable for all mass ratios μ in the range of linear stability 8/9+(2/3((43/25ϵ1−(10/3ϵ<μ<1, where ϵ and ϵ1 are, respectively, the perturbations in Coriolis and centrifugal forces, except for five mass ratios μ1=0.93711086−1.12983217ϵ+1.50202694ϵ1, μ2 = 0.9672922−0.5542091ϵ+ 1.2443968ϵ1, μ3=0.9459503−0.70458206ϵ+ 1.28436549ϵ1, μ4=0.9660792−0.30152273ϵ + 1.11684064ϵ1, μ5=0.893981−2.37971679ϵ + 1.22385421ϵ1, where the theory is not applicable.
Coulomb energy of uniformly charged spheroidal shell systems.
Jadhao, Vikram; Yao, Zhenwei; Thomas, Creighton K; de la Cruz, Monica Olvera
2015-03-01
We provide exact expressions for the electrostatic energy of uniformly charged prolate and oblate spheroidal shells. We find that uniformly charged prolate spheroids of eccentricity greater than 0.9 have lower Coulomb energy than a sphere of the same area. For the volume-constrained case, we find that a sphere has the highest Coulomb energy among all spheroidal shells. Further, we derive the change in the Coulomb energy of a uniformly charged shell due to small, area-conserving perturbations on the spherical shape. Our perturbation calculations show that buckling-type deformations on a sphere can lower the Coulomb energy. Finally, we consider the possibility of counterion condensation on the spheroidal shell surface. We employ a Manning-Oosawa two-state model approximation to evaluate the renormalized charge and analyze the behavior of the equilibrium free energy as a function of the shell's aspect ratio for both area-constrained and volume-constrained cases. Counterion condensation is seen to favor the formation of spheroidal structures over a sphere of equal area for high values of shell volume fractions.
Relativistic Dirac-Fock and many-body perturbation calculations on He, He-like ions, Ne, and Ar
International Nuclear Information System (INIS)
Ishikawa, Y.
1990-01-01
Relativistic Dirac-Fock and diagrammatic many-body perturbation-theory calculations have been performed on He, several He-like ions, Ne, and Ar. The no-pair Dirac-Coulomb Hamiltonian is taken as the starting point. A solution of the Dirac-Fock equations is obtained by analytic expansion in basis sets of Gaussian-type functions. Many-body perturbation improvements of Coulomb correlation are done to third order
On an efficient and accurate method to integrate restricted three-body orbits
Murison, Marc A.
1989-01-01
This work is a quantitative analysis of the advantages of the Bulirsch-Stoer (1966) method, demonstrating that this method is certainly worth considering when working with small N dynamical systems. The results, qualitatively suspected by many users, are quantitatively confirmed as follows: (1) the Bulirsch-Stoer extrapolation method is very fast and moderately accurate; (2) regularization of the equations of motion stabilizes the error behavior of the method and is, of course, essential during close approaches; and (3) when applicable, a manifold-correction algorithm reduces numerical errors to the limits of machine accuracy. In addition, for the specific case of the restricted three-body problem, even a small eccentricity for the orbit of the primaries drastically affects the accuracy of integrations, whether regularized or not; the circular restricted problem integrates much more accurately.
THE MIND BODY PROBLEM: THE HERMENEUTICS OF AFRICAN ...
African Journals Online (AJOL)
principles in explaining the mind –body problem due to deep seated criticisms from the ..... over duly by his mathematical intercourse with mere materials and this made him to found his .... Ed. (New York: McGraw Hill), 1993, p. 90. 19 Emefie ...
Coherent Destruction of Tunneling of Bosons with Effective Three-Body Interactions
International Nuclear Information System (INIS)
Niu Zhen-Xia; Yu Zi-Fa; Xue Ju-Kui
2015-01-01
The tunneling dynamics of dilute boson gases with three-body interactions in a periodically driven double wells are investigated both theoretically and numerically. In our findings, when the system is with only repulsive two-body interactions or only three-body interactions, the tunneling will be suppressed; while in the case of the coupling between two- and three-body interactions, the tunneling can be either suppressed or enhanced. Particularly, when attractive three-body interactions are twice large as repulsive two-body interactions, CDT occurs at isolated points of driving force, which is similar to the linear case. Considering different interaction, the system can experience different transformation from coherent tunneling to coherent destruction of tunneling (CDT). The quasi-energy of the system as the function of the periodically driving force shows a triangular structure, which provides a deep insight into the tunneling dynamics of the system. (paper)
Characterization of ion Coulomb crystals in a linear Paul trap
International Nuclear Information System (INIS)
Okada, K.; Takayanagi, T.; Wada, M.; Ohtani, S.; Schuessler, H. A.
2010-01-01
We describe a simple and fast method for simulating observed images of ion Coulomb crystals. In doing so, cold elastic collisions between Coulomb crystals and virtual very light atoms are implemented in a molecular dynamics (MD) simulation code. Such an approach reproduces the observed images of Coulomb crystals by obtaining density plots of the statistics of existence of each ion. The simple method has the advantage of short computing time in comparison with previous calculation methods. As a demonstration of the simulation, the formation of a planar Coulomb crystal with a small number of ions has been investigated in detail in a linear ion trap both experimentally and by simulation. However, also large Coulomb crystals including up to 1400 ions have been photographed and simulated to extract the secular temperature and the number of ions. For medium-sized crystals, a comparison between experiments and calculations has been performed. Moreover, an MD simulation of the sympathetic cooling of small molecular ions was performed in order to test the possibility of extracting the temperature and the number of refrigerated molecular ions from crystal images of laser-cooled ions. Such information is basic to studying ultracold ion-molecule reactions using ion Coulomb crystals including sympathetically cooled molecular ions.
Ultrafast dynamics of Coulomb correlated excitons in GaAs quantum wells
Energy Technology Data Exchange (ETDEWEB)
Mycek, M.A. [Univ. of California, Berkeley, CA (United States). Dept. of Physics]|[Lawrence Berkeley National Lab., CA (United States). Materials Sciences Div.
1995-12-01
The author measures the transient nonlinear optical response of room temperature excitons in gallium arsenide quantum wells via multi-wave mixing experiments. The dynamics of the resonantly excited excitons is directly reflected by the ultrafast decay of the induced nonlinear polarization, which radiates the detected multi-wave mixing signal. She characterizes this ultrafast coherent emission in both amplitude and phase, using time- and frequency-domain measurement techniques, to better understand the role of Coulomb correlation in these systems. To interpret the experimental results, the nonlinear optical response of a dense medium is calculated using a model including Coulomb interaction. She contributes three new elements to previous theoretical and experimental studies of these systems. First, surpassing traditional time-integrated measurements, she temporally resolves the amplitude of the ultrafast coherent emission. Second, in addition to measuring the third-order four-wave mixing signal, she also investigates the fifth-order six-wave mixing response. Third, she characterizes the ultrafast phase dynamics of the nonlinear emission using interferometric techniques with an unprecedented resolution of approximately 140 attoseconds. The author finds that effects arising from Coulomb correlation dominate the nonlinear optical response when the density of excitons falls below 3 {times} 10{sup 11} cm{sup {minus}2}, the saturation density. These signatures of Coulomb correlation are investigated for increasing excitation density to gradually screen the interactions and test the validity of the model for dense media. The results are found to be qualitatively consistent with both the predictions of the model and with numerical solutions to the semiconductor Bloch equations. Importantly, the results also indicate current experimental and theoretical limitations, which should be addressed in future research.
Periodic Solutions for Circular Restricted -Body Problems
Directory of Open Access Journals (Sweden)
Xiaoxiao Zhao
2013-01-01
Full Text Available For circular restricted -body problems, we study the motion of a sufficiently small mass point (called the zero mass point in the plane of equal masses located at the vertices of a regular polygon. By using variational minimizing methods, for some , we prove the existence of the noncollision periodic solution for the zero mass point with some fixed wingding number.
Wang, Jing; Tian, Xue-Dong; Liu, Yi-Mou; Cui, Cui-Li; Wu, Jin-Hui
2018-06-01
We investigate the stationary entanglement properties in a hybrid system consisting of an optical cavity, a mechanical resonator, a charged object, and an atomic ensemble. Numerical results show that this hybrid system exhibits three kinds of controllable bipartite entanglements in an experimentally accessible parameter regime with the help of the charged object. More importantly, it is viable to enhance on demand each bipartite entanglement at the expense of reducing others by modulating the Coulomb coupling strength. Last but not least, these bipartite entanglements seem more robust against on the environmental temperature for the positive Coulomb interaction.
Computational assignment of redox states to Coulomb blockade diamonds.
Olsen, Stine T; Arcisauskaite, Vaida; Hansen, Thorsten; Kongsted, Jacob; Mikkelsen, Kurt V
2014-09-07
With the advent of molecular transistors, electrochemistry can now be studied at the single-molecule level. Experimentally, the redox chemistry of the molecule manifests itself as features in the observed Coulomb blockade diamonds. We present a simple theoretical method for explicit construction of the Coulomb blockade diamonds of a molecule. A combined quantum mechanical/molecular mechanical method is invoked to calculate redox energies and polarizabilities of the molecules, including the screening effect of the metal leads. This direct approach circumvents the need for explicit modelling of the gate electrode. From the calculated parameters the Coulomb blockade diamonds are constructed using simple theory. We offer a theoretical tool for assignment of Coulomb blockade diamonds to specific redox states in particular, and a study of chemical details in the diamonds in general. With the ongoing experimental developments in molecular transistor experiments, our tool could find use in molecular electronics, electrochemistry, and electrocatalysis.
Correlated Coulomb Drag in Capacitively Coupled Quantum-Dot Structures.
Kaasbjerg, Kristen; Jauho, Antti-Pekka
2016-05-13
We study theoretically Coulomb drag in capacitively coupled quantum dots (CQDs)-a bias-driven dot coupled to an unbiased dot where transport is due to Coulomb mediated energy transfer drag. To this end, we introduce a master-equation approach that accounts for higher-order tunneling (cotunneling) processes as well as energy-dependent lead couplings, and identify a mesoscopic Coulomb drag mechanism driven by nonlocal multielectron cotunneling processes. Our theory establishes the conditions for a nonzero drag as well as the direction of the drag current in terms of microscopic system parameters. Interestingly, the direction of the drag current is not determined by the drive current, but by an interplay between the energy-dependent lead couplings. Studying the drag mechanism in a graphene-based CQD heterostructure, we show that the predictions of our theory are consistent with recent experiments on Coulomb drag in CQD systems.
Coulomb interactions in charged fluids.
Vernizzi, Graziano; Guerrero-García, Guillermo Iván; de la Cruz, Monica Olvera
2011-07-01
The use of Ewald summation schemes for calculating long-range Coulomb interactions, originally applied to ionic crystalline solids, is a very common practice in molecular simulations of charged fluids at present. Such a choice imposes an artificial periodicity which is generally absent in the liquid state. In this paper we propose a simple analytical O(N(2)) method which is based on Gauss's law for computing exactly the Coulomb interaction between charged particles in a simulation box, when it is averaged over all possible orientations of a surrounding infinite lattice. This method mitigates the periodicity typical of crystalline systems and it is suitable for numerical studies of ionic liquids, charged molecular fluids, and colloidal systems with Monte Carlo and molecular dynamics simulations.
Monotonicity of energy eigenvalues for Coulomb systems
International Nuclear Information System (INIS)
Englisch, R.
1983-01-01
Generalising results by earlier workers for a large class of Hamiltonians (among others, Hamiltonians of Coulomb systems) which can be written in the form H(α) = H 0 + αH' the present works shows that their eigenvalues decrease with increasing α. This result is applied to Coulomb systems in which the distances between the infinitely heavy particles are varying and also is used to obtain a completion and simplification of proof for the stability of the biexciton. (author)
FaCE: a tool for Three Body Faddeev calculations with core excitation
Thompson, I. J.; Nunes, F. M.; Danilin, B. V.
2004-01-01
FaCE is a self contained programme, with namelist input, that solves the three body Faddeev equations. It enables the inclusion of excitation of one of the three bodies, whilst the other two remain inert. It is particularly useful for obtaining the binding energies and bound state structure compositions of light exotic nuclei treated as three-body systems, given the three effective two body interactions. A large variety of forms for these interactions may be defined, and supersymmetric transf...
Emerging bosons with three-body interactions from spin-1 atoms in optical lattices
International Nuclear Information System (INIS)
Mazza, L.; Rizzi, M.; Cirac, J. I.; Lewenstein, M.
2010-01-01
We study two many-body systems of bosons interacting via an infinite three-body contact repulsion in a lattice: a pairs quasicondensate induced by correlated hopping and the discrete version of the Pfaffian wave function. We propose to experimentally realize systems characterized by such interaction by means of a proper spin-1 lattice Hamiltonian: spin degrees of freedom are locally mapped into occupation numbers of emerging bosons, in a fashion similar to spin-1/2 and hardcore bosons. Such a system can be realized with ultracold spin-1 atoms in a Mott insulator with a filling factor of 1. The high versatility of these setups allows us to engineer spin-hopping operators breaking the SU(2) symmetry, as needed to approximate interesting bosonic Hamiltonians with three-body hardcore constraint. For this purpose we combine bichromatic spin-independent superlattices and Raman transitions to induce a different hopping rate for each spin orientation. Finally, we illustrate how our setup could be used to experimentally realize the first setup, that is, the transition to a pairs quasicondensed phase of the emerging bosons. We also report on a route toward the realization of a discrete bosonic Pfaffian wave function and list some open problems for reaching this goal.
4-center STO interelectron repulsion integrals with Coulomb Sturmians
DEFF Research Database (Denmark)
Avery, James Emil; Avery, John Scales
2018-01-01
Abstract We present a method for evaluating 4-center electron repulsion integrals (ERI) for Slater-type orbitals by way of expansions in terms of Coulomb Sturmians. The ERIs can then be evaluated using our previously published methods for rapid evaluation of Coulomb Sturmians through hyperspherical...
Controllability of the Coulomb charging energy in close-packed nanoparticle arrays.
Duan, Chao; Wang, Ying; Sun, Jinling; Guan, Changrong; Grunder, Sergio; Mayor, Marcel; Peng, Lianmao; Liao, Jianhui
2013-11-07
We studied the electronic transport properties of metal nanoparticle arrays, particularly focused on the Coulomb charging energy. By comparison, we confirmed that it is more reasonable to estimate the Coulomb charging energy using the activation energy from the temperature-dependent zero-voltage conductance. Based on this, we systematically and comprehensively investigated the parameters that could be used to tune the Coulomb charging energy in nanoparticle arrays. We found that four parameters, including the particle core size, the inter-particle distance, the nearest neighboring number, and the dielectric constant of ligand molecules, could significantly tune the Coulomb charging energy.
International Nuclear Information System (INIS)
Lin, C.Y.; Ho, Y.K.
2010-01-01
The screening effects due to the exponential-cosine-screened Coulomb and screened Coulomb (Yukawa) potentials on photoionization processes are explored within the framework of complex coordinate rotation method. The energy levels of H and He + in both screened potentials shifted with various Debye screening lengths are presented. The photoionization cross sections illustrate the considerable screening effects on photoionization processes in low energy region. The shape resonances can be found near ionization thresholds for certain of Debye screening lengths. The relations between the appearance of resonances and the existence of quasi-bound states under shielding conditions are discussed. (authors)
The Kantian Attempt to Solve the Mind-Body Problem. A Critical Approach
Directory of Open Access Journals (Sweden)
Pedro Jesús Teruel
2014-11-01
Full Text Available The mind-body problem is one of the perennial challenges in the history of ideas. Immanuel Kant (1724-1804 tried to solve it through an approach with several modulations –parallel to his intellectual evolution– that brought him into contact with both the later projection of the theoretical issue (the mind brain problem and its practical side (the immortality question. In this paper I face the Kantian approach to the mind-body problem from a triple perspective: descriptive, appraising and critical.
Health Behaviour and Body Mass Index Among Problem Gamblers
DEFF Research Database (Denmark)
Holst Algren, Maria; Ekholm, Ola; Davidsen, Michael
2015-01-01
Problem gambling is a serious public health issue. The objective of this study was to investigate whether past year problem gamblers differed from non-problem gamblers with regard to health behaviour and body mass index (BMI) among Danes aged 16 years or older. Data were derived from the Danish...... pattern and obesity was higher among problem gamblers than among non-problem gamblers. The associations found in this study remained significant after adjustment for sex, age, educational and cohabiting status as well as other risk factors. Our findings highlight the presence of a potential, public health...... Health and Morbidity Surveys in 2005 and 2010. Past year problem gambling was defined using the lie/bet questionnaire. Logistic regression analyses were used to examine the association between past year problem gambling and health behaviour and BMI. Problem gambling was associated with unhealthy...
Three-Body Antikaon-Nucleon Systems
Czech Academy of Sciences Publication Activity Database
Shevchenko, Nina V.
2017-01-01
Roč. 58, č. 1 (2017), č. článku UNSP 6. ISSN 0177-7963 R&D Projects: GA ČR(CZ) GA15-04301S Institutional support: RVO:61389005 Keywords : three-body * antikaon-nucleon * K p interactions Subject RIV: BE - Theoretical Physics OBOR OECD: Atom ic, molecular and chemical physics (physics of atom s and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 0.877, year: 2016
Known-to-Unknown Approach to Teach about Coulomb's Law
Thamburaj, P. K.
2007-01-01
Analogies from life experiences help students understand various relationships presented in an introductory chemistry course. Coulomb's law is a complex relationship encountered in introductory general chemistry. A proper understanding of the relationships between the quantities involved in Coulomb's law is necessary in order for students to…
Antilocalization of Coulomb Blockade in a Ge-Si Nanowire
DEFF Research Database (Denmark)
Higginbotham, Andrew P.; Kuemmeth, Ferdinand; Larsen, Thorvald Wadum
2014-01-01
The distribution of Coulomb blockade peak heights as a function of magnetic field is investigated experimentally in a Ge-Si nanowire quantum dot. Strong spin-orbit coupling in this hole-gas system leads to antilocalization of Coulomb blockade peaks, consistent with theory. In particular, the peak...
9Be+120Sn scattering at near-barrier energies within a four-body model
Arazi, A.; Casal, J.; Rodríguez-Gallardo, M.; Arias, J. M.; Lichtenthäler Filho, R.; Abriola, D.; Capurro, O. A.; Cardona, M. A.; Carnelli, P. F. F.; de Barbará, E.; Fernández Niello, J.; Figueira, J. M.; Fimiani, L.; Hojman, D.; Martí, G. V.; Martínez Heimman, D.; Pacheco, A. J.
2018-04-01
Cross sections for elastic and inelastic scattering of the weakly bound 9Be nucleus on a 120Sn target have been measured at seven bombarding energies around and above the Coulomb barrier. The elastic angular distributions are analyzed with a four-body continuum-discretized coupled-channels (CDCC) calculation, which considers 9Be as a three-body projectile (α +α +n ). An optical model analysis using the São Paulo potential is also shown for comparison. The CDCC analysis shows that the coupling to the continuum part of the spectrum is important for the agreement with experimental data even at energies around the Coulomb barrier, suggesting that breakup is an important process at low energies. At the highest incident energies, two inelastic peaks are observed at 1.19(5) and 2.41(5) MeV. Coupled-channels (CC) calculations using a rotational model confirm that the first inelastic peak corresponds to the excitation of the 21+ state in 120Sn, while the second one likely corresponds to the excitation of the 31- state.
McClarty, P. A.; O'Brien, A.; Pollmann, F.
2014-05-01
We consider a classical model of charges ±q on a pyrochlore lattice in the presence of long-range Coulomb interactions. This model first appeared in the early literature on charge order in magnetite [P. W. Anderson, Phys. Rev. 102, 1008 (1956), 10.1103/PhysRev.102.1008]. In the limit where the interactions become short ranged, the model has a ground state with an extensive entropy and dipolar charge-charge correlations. When long-range interactions are introduced, the exact degeneracy is broken. We study the thermodynamics of the model and show the presence of a correlated charge liquid within a temperature window in which the physics is well described as a liquid of screened charged defects. The structure factor in this phase, which has smeared pinch points at the reciprocal lattice points, may be used to detect charge ice experimentally. In addition, the model exhibits fractionally charged excitations ±q/2 which are shown to interact via a 1/r potential. At lower temperatures, the model exhibits a transition to a long-range ordered phase. We are able to treat the Coulombic charge ice model and the dipolar spin ice model on an equal footing by mapping both to a constrained charge model on the diamond lattice. We find that states of the two ice models are related by a staggering field which is reflected in the energetics of these two models. From this perspective, we can understand the origin of the spin ice and charge ice ground states as coming from a dipolar model on a diamond lattice. We study the properties of charge ice in an external electric field, finding that the correlated liquid is robust to the presence of a field in contrast to the case of spin ice in a magnetic field. Finally, we comment on the transport properties of Coulombic charge ice in the correlated liquid phase.
Frictional Coulomb drag in strong magnetic fields
DEFF Research Database (Denmark)
Bønsager, Martin Christian; Flensberg, Karsten; Hu, Ben Yu-Kuang
1997-01-01
A treatment of frictional Coulomb drag between two two-dimensional electron layers in a strong perpendicular magnetic field, within the independent electron picture, is presented. Assuming fully resolved Landau levels, the linear response theory expression for the transresistivity rho(21) is eval......A treatment of frictional Coulomb drag between two two-dimensional electron layers in a strong perpendicular magnetic field, within the independent electron picture, is presented. Assuming fully resolved Landau levels, the linear response theory expression for the transresistivity rho(21...
Physics of the Non-Abelian Coulomb Phase
DEFF Research Database (Denmark)
Ryttov, Thomas A.; Shrock, Robert
2018-01-01
are applied to obtain further estimates of $\\gamma_{\\bar\\psi\\psi,IR}$ and $\\beta'_{IR}$ for several SU($N_c$) groups and representations $R$, and comparisons are made with lattice measurements. We apply our results to obtain new estimates of the extent of the respective non-Abelian Coulomb phases in several....... It is shown that an expansion of $\\gamma_{\\bar\\psi\\psi,IR}$ to $O(\\Delta_f^4)$ is quite accurate throughout the entire non-Abelian Coulomb phase of this supersymmetric theory....
Efimov Physics and the Three-Body Parameter within a Two-Channel Framework
DEFF Research Database (Denmark)
Sørensen, Peder Klokmose; V. Fedorov, D.; S. Jensen, A.
2012-01-01
scaling laws. We recover known results for broad Feshbach resonances with small effective range, whereas in the case of narrow resonances we find a distinct non-monotonic behavior of the threshold at which the lowest Efimov trimer merges with the three-body continuum. To address the issue of the physical...... origin of the three-body parameter we provide a physically clear model for the relation between three-body physics and typical two-body atom-atom interactions. Our results demonstrate that experimental information from narrow Feshbach resonances and/or mixed systems are of vital importance to pin down...... the relation of two- and three-body physics in atomic systems....
Coulomb Logarithm in Nonideal and Degenerate Plasmas
Filippov, A. V.; Starostin, A. N.; Gryaznov, V. K.
2018-03-01
Various methods for determining the Coulomb logarithm in the kinetic theory of transport and various variants of the choice of the plasma screening constant, taking into account and disregarding the contribution of the ion component and the boundary value of the electron wavevector are considered. The correlation of ions is taken into account using the Ornstein-Zernike integral equation in the hypernetted-chain approximation. It is found that the effect of ion correlation in a nondegenerate plasma is weak, while in a degenerate plasma, this effect must be taken into account when screening is determined by the electron component alone. The calculated values of the electrical conductivity of a hydrogen plasma are compared with the values determined experimentally in the megabar pressure range. It is shown that the values of the Coulomb logarithm can indeed be smaller than unity. Special experiments are proposed for a more exact determination of the Coulomb logarithm in a magnetic field for extremely high pressures, for which electron scattering by ions prevails.
Coulomb corrections to nuclear scattering lengths and effective ranges for weakly bound systems
International Nuclear Information System (INIS)
Mur, V.D.; Popov, V.S.; Sergeev, A.V.
1996-01-01
A procedure is considered for extracting the purely nuclear scattering length as and effective range rs (which correspond to a strong-interaction potential Vs with disregarded Coulomb interaction) from the experimentally determined nuclear quantities acs and rcs, which are modified by Coulomb interaction. The Coulomb renormalization of as and rs is especially strong if the system under study involves a level with energy close to zero (on the nuclear scale). This applies to formulas that determine the Coulomb renormalization of the low-energy parameters of s scattering (l=0). Detailed numerical calculations are performed for coefficients appearing in the equations that determine Coulomb corrections for various models of the potential Vs(r). This makes it possible to draw qualitative conclusions that the dependence of Coulomb corrections on the form of the strong-interaction potential and, in particular, on its small-distance behavior. A considerable enhancement of Coulomb corrections to the effective range rs is found for potentials with a barrier
Coulomb collisions in the solar wind
Klein, L. W.; Ogilvie, K. W.; Burlaga, L. F.
1985-01-01
A major improvement of the present investigation over previous studies of the subject is related to the use of helium temperatures obtained from helium ion measurements uncontaminated by the high-velocity tail of the proton distribution. More observations, covering a large parameter range, were employed, and the effects of interspecies drift were taken into account. It is shown in a more definite way than has been done previously, that Coulomb collisions provide the most important mechanism bringing about equilibrium between helium and protons in the solar wind. Other mechanisms may play some part in restricted regions, but Coulomb collisions are dominant on the macroscale.
Three-body recombination of cold fermionic atoms
International Nuclear Information System (INIS)
Suno, H; Esry, B D; Greene, Chris H
2003-01-01
Recombination of identical, spin-polarized fermions in cold three-body collisions is investigated. We parametrize the mechanisms for recombination in terms of the 'scattering volume' V p and another length scale r 0 . Model two-body interactions were used within the framework of the adiabatic hyperspherical representation. We examine the recombination rate K 3 as a function of the collision energy E for various values of V p . Not only do we consider the dominant J Π = 1 + case, but also the next-leading order contributions from J Π = 1 - and 3 - . We discuss the behaviour near a two-body resonance and the expected universality of fermionic recombination. Comparisons with boson recombination are considered in detail
Pavlov and the mind-body problem.
Windholz, G
1997-01-01
I. P. Pavlov claimed that the mind-body problem would ultimately be resolved by empirical methods, rather than by rational arguments. A committed monist, Pavlov was confronted by dualism in the case of an hysterical person. Under normal conditions, her body's left side was insensitive to pain, but when she was hypnotized, there was a reversal of her sensitivity to pain, with the right side becoming insensitive. Pavlov acknowledged that the divergence between stimulation and response suggested dualism, yet condemned his disciple G.P. Zelenyĭ as well as Charles S. Sherrington, for their dualistic tendencies. Pavlov's continuous adherence to monism it attributed to the influence of popular scientific books that he read during his adolescence. The books maintained that science was based upon monism. Pavlov proposed that by introducing the concept of emotions, an hysterical person's condition could be explained within the framework of his theory of higher nervous activity, thereby obviating the need to change his paradigm.
Using Analogy to Solve a Three-Step Physics Problem
Lin, Shih-Yin; Singh, Chandralekha
2010-10-01
In a companion paper, we discuss students' ability to take advantage of what they learn from a solved problem and transfer their learning to solve a quiz problem that has different surface features but the same underlying physics principles. Here, we discuss students' ability to perform analogical reasoning between another pair of problems. Both the problems can be solved using the same physics principles. However, the solved problem provided was a two-step problem (which can be solved by decomposing it into two sub-problems) while the quiz problem was a three-step problem. We find that it is challenging for students to extend what they learned from a two-step problem to solve a three-step problem.
Fast Electron Repulsion Integrals for Molecular Coulomb Sturmians
DEFF Research Database (Denmark)
Avery, James Emil
2013-01-01
A new method is presented for calculating interelectron repulsion integrals for molecular Coulomb Sturmian basis sets. This makes use of an expansion of densities in terms of 2k-Sturmians, and the interelectron repulsion integrals are then calculated by a method based on the theory of hyperspheri......A new method is presented for calculating interelectron repulsion integrals for molecular Coulomb Sturmian basis sets. This makes use of an expansion of densities in terms of 2k-Sturmians, and the interelectron repulsion integrals are then calculated by a method based on the theory...... of hyperspherical harmonics. A rudimentary software library has been implemented and preliminary benchmarks indicate very good performance: On average 40 ns, or approximately 80 clock cycles, per electron repulsion integral. This makes molecular Coulomb Sturmians competitive with Gaussian type orbitals in terms...
Critical opalescence in the pure Coulomb system
Bobrov, V. B.; Trigger, S. A.
2011-04-01
Based on the dielectric formalism and quantum field theory methods, the phenomenon of critical opalescence is explained for light scattering in pure matter as a two-component electron-nuclear system with Coulomb interaction. A similar phenomenon is shown to occur in the case of neutron scattering in pure substances as well. The obtained results are valid for quantum case and arbitrary strong Coulomb interaction. Thus, the relations between structure factors derived for the electron-nuclear system are the exact result of the quantum statistical mechanics.
Efficient Non-Linear Finite Element Implementation of Elasto-Plasticity for Geotechnical Problems
DEFF Research Database (Denmark)
Clausen, Johan
-Coulomb yield criterion and the corresponding plastic potential possess corners and an apex, which causes numerical difficulties. A simple, elegant and efficient solution to these problems is presented in this thesis. The solution is based on a transformation into principal stress space and is valid for all...... linear isotropic plasticity models in which corners and apexes are encountered. The validity and merits of the proposed solution are examined in relation to the Mohr-Coulomb and the Modified Mohr-Coulomb material models. It is found that the proposed method compares well with existing methods......-Brown material. The efficiency and validity are demonstrated by comparing the finite-element results with well-known solutions for simple geometries. A common geotechnical problem is the assessment of slope stability. For slopes with simple geometries and consisting of a linear Mohr-Coulomb material, this can...