Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review C

Ground-state energy of nuclear matter

George Allen Baker Jr., L. P. Benofy, Mauricio Fortes

Published Jul 1, 1988• 3 citations
Publisher

Abstract

The low-density expansion of the ground-state energy for spin-dependent forces is given, through order ${k}_{F}^{6}$ for the ladder approximation and through order ${k}_{F}^{6}$ln${k}_{F}$ for the complete energy, in terms of derivatives with respect to the strength of the attractive part of the interaction defined by the Baker-Hind-Kahane potential. The ladder approximation is also computed by the numerical solution of the K-matrix equation. The resulting series gives a satisfactory representation of the energy at interesting densities. Using Pad\'e extrapolation techniques, both in the density and in the attractive part of the interaction, we obtain the ground-state energy of nuclear matter.

DOI
10.1103/physrevc.38.329

Related papers

Study of the Perturbation Series for the Ground-State Energy of a Many-Fermion System

George Allen Baker Jr., J. L. Gammel, Bob Hill

In order to investigate the validity of the Brueckner and the simple sum of the ladder diagrams approximations to the energy of an infinite system of fermions, we have calculated as a function of density all the terms in the perturbation expansion through the fourth order in the strength of the potential. We have done this for a repulsive, square-well, two-body potential spin-\textonehalf{} fermions. We are able to construct rigorous upper and lower bounds from the coefficients for the value of the ladder approximation and find that the standard solution procedures give reasonably accurate results (within a few percent). We find that the error in the solution as obtained in practice to the equations of the Brueckner approximation is large compared to the size of its departure from the ladder approximation. We further find for low-to-moderate densities and for low-to-moderate potential strengths that the Brueckner approximation both as a sum of a certain class of diagrams and as computed in practice lies above the ladder approximation while the complete perturbation theory lies below it. This result arises from the neglect of the ring diagrams by the Brueckner approximation.

Physical Review•Nov 1, 1963•29 citations

Ground-state energy of a hard-sphere Fermi fluid. II. Spin and isospin

L. P. Benofy, J. L. Gammel, Robert M. Delaney +1 more

We evaluate the fourth-order Hugenholtz diagrams from the Rayleigh-Schr\"odinger many-body perturbation series for a repulsive, square-well potential. We consider a system containing four different equal-mass identically interacting particle species, similar to nuclear matter when only the repulsive core is considered. We use the results of these calculations to extend the L expansion of the ground-state energy of a Fermi fluid by one more term. From this extension, we are able to provide accurate values of the ground-state energy over a density range which includes that for infinite nuclear matter.

Physical Review C•Dec 1, 1993•1 citation

Constructive methods for the ground-state energy of fully interacting fermion gases

V.C Aguilera Navarro, George Allen Baker Jr., L. P. Benofy +2 more

A perturbation scheme based not on the ideal gas but on a system of purely repulsive cores is applied to a typical fully interacting fermion gas. This is ``neutron matter'' interacting via (a) the repulsive ``Bethe homework-problem'' potential, (b) a hard-core--plus--square-well potential, and (c) the Baker-Hind-Kahane modification of the latter, suitable for describing a more accurate two-nucleon potential. Pad\'e extrapolation techniques and generalizations thereof are employed to represent both the density dependence as well as the attractive coupling dependence of the perturbation expansion. Equations of state are constructed and compared with Jastrow--Monte Carlo calculations as well as expectations based on semiempirical mass formulas. Excellent agreement is found with the latter.

Physical Review A•Nov 1, 1987•11 citations

Ground State Energy of Bose Particle System

Ryuzo Abe

The ground state energy of the Bose particle system at low densities is investigated by using the method which is based on summing up the terms of the conventional perturbation series giving rise to the lowest order with respect to the density. The summation is shown to be greatly simplified if the scattering matrix is introduced, and a simple example is demonstrated for the repulsive square well potential by calculating a few terms of the series first directly and secondly with the aid of scattering matrix. The final result is shown to be valid both for weak and strong interactions and the calculation is carried out analytically for some types of potential function. The connection of the present method with the pseudopotential method and with the Brueckner theory is investigated and some problems associated with the attractive interactions are discussed.

Progress of Theoretical Physics•Dec 1, 1958•2 citations

Constructive approach to the ground-state energy of a hard-core square-well fermion system

George Allen Baker Jr.

I am looking at the old problem of the ground-state energy of quantum many-Fermion systems. My tools will be a version of perturbation theory. It is plain that the ordinary, low-density rearrangement can not be used directly to compute the saturation energy and density of a system for which the two-body potential has a strong repulsive core and an attractive portion beyond the core, because the path of continuation from low-density to saturation density passes through the two-phase (vacuum, liquid) region. Likewise it is difficult to supply an expansion directly in lambda for fixed rho (density) because of the difficulty of the strong repulsive core and the tediousness of the calculations. My approach here is to expand the energy in a double series in k/sub F/, the Fermi momentum, and lambda, the strength of the attractive part of the potential. The plan is then to sum up, by the Pade method or a generalization of it, the k/sub F/ expansions of the coefficients of each power of lambda into a function of k/sub F/. The coefficient of lambda/sup 0/ is just the repulsive-core energy itself.

•Sep 1, 1984•0 citations

Thermodynamic perturbation scheme for the ground-state energy of Lennard-Jones bosons

M. A. Sol̆s, Valdir C. Aguilera-Navarro, MANUEL DE LLANO +1 more

The thermodynamic perturbation scheme so successful for classical-liquid equations of state is applied to the ground-state energy of a many-boson system interacting pairwise via the Lennard-Jones intermolecular potential. The ensuing density and attractive-coupling double expansion for the energy is series analyzed with Pad\'e techniques, as well as generalizations thereof. Results through sixth order compare with Green's-function Monte Carlo simulations at the 1% level of accuracy.

Physical Review Letters•Nov 16, 1987•13 citations
The low-density expansion of the ground-state energy for spin-dependent forces is given, through order kF6{k}_{F}^{6}kF6​ for the ladder approximation and through order kF6{k}_{F}^{6}kF6​lnkF{k}_{F}kF​ for the complete energy, in terms of derivatives with respect to the strength of the attractive part of the interaction defined by the Baker-Hind-Kahane potential. The ladder approximation is also computed by the numerical solution of the K-matrix equation. The resulting series gives a satisfactory representation of the energy at interesting densities. Using Pad'e extrapolation techniques, both in the density and in the attractive part of the interaction, we obtain the ground-state energy of nuclear matter.
In order to investigate the validity of the Brueckner and the simple sum of the ladder diagrams approximations to the energy of an infinite system of fermions, we have calculated as a function of density all the terms in the perturbation expansion through the fourth order in the strength of the potential. We have done this for a repulsive, square-well, two-body potential spin-\textonehalf{} fermions. We are able to construct rigorous upper and lower bounds from the coefficients for the value of the ladder approximation and find that the standard solution procedures give reasonably accurate results (within a few percent). We find that the error in the solution as obtained in practice to the equations of the Brueckner approximation is large compared to the size of its departure from the ladder approximation. We further find for low-to-moderate densities and for low-to-moderate potential strengths that the Brueckner approximation both as a sum of a certain class of diagrams and as computed in practice lies above the ladder approximation while the complete perturbation theory lies below it. This result arises from the neglect of the ring diagrams by the Brueckner approximation.
We evaluate the fourth-order Hugenholtz diagrams from the Rayleigh-Schr\"odinger many-body perturbation series for a repulsive, square-well potential. We consider a system containing four different equal-mass identically interacting particle species, similar to nuclear matter when only the repulsive core is considered. We use the results of these calculations to extend the L expansion of the ground-state energy of a Fermi fluid by one more term. From this extension, we are able to provide accurate values of the ground-state energy over a density range which includes that for infinite nuclear matter.
A perturbation scheme based not on the ideal gas but on a system of purely repulsive cores is applied to a typical fully interacting fermion gas. This is ``neutron matter'' interacting via (a) the repulsive ``Bethe homework-problem'' potential, (b) a hard-core--plus--square-well potential, and (c) the Baker-Hind-Kahane modification of the latter, suitable for describing a more accurate two-nucleon potential. Pad\'e extrapolation techniques and generalizations thereof are employed to represent both the density dependence as well as the attractive coupling dependence of the perturbation expansion. Equations of state are constructed and compared with Jastrow--Monte Carlo calculations as well as expectations based on semiempirical mass formulas. Excellent agreement is found with the latter.
The ground state energy of the Bose particle system at low densities is investigated by using the method which is based on summing up the terms of the conventional perturbation series giving rise to the lowest order with respect to the density. The summation is shown to be greatly simplified if the scattering matrix is introduced, and a simple example is demonstrated for the repulsive square well potential by calculating a few terms of the series first directly and secondly with the aid of scattering matrix. The final result is shown to be valid both for weak and strong interactions and the calculation is carried out analytically for some types of potential function. The connection of the present method with the pseudopotential method and with the Brueckner theory is investigated and some problems associated with the attractive interactions are discussed.
I am looking at the old problem of the ground-state energy of quantum many-Fermion systems. My tools will be a version of perturbation theory. It is plain that the ordinary, low-density rearrangement can not be used directly to compute the saturation energy and density of a system for which the two-body potential has a strong repulsive core and an attractive portion beyond the core, because the path of continuation from low-density to saturation density passes through the two-phase (vacuum, liquid) region. Likewise it is difficult to supply an expansion directly in lambda for fixed rho (density) because of the difficulty of the strong repulsive core and the tediousness of the calculations. My approach here is to expand the energy in a double series in k/sub F/, the Fermi momentum, and lambda, the strength of the attractive part of the potential. The plan is then to sum up, by the Pade method or a generalization of it, the k/sub F/ expansions of the coefficients of each power of lambda into a function of k/sub F/. The coefficient of lambda/sup 0/ is just the repulsive-core energy itself.