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Physical Review C

Choice of finite-temperature single-particle potential and preservation of thermodynamic relations

Shen Yang, Meng Jiang, J. Heyer, T.T.S. Kuo

Published May 1, 1989• 3 citations
Publisher

Abstract

A method for choosing and deriving a suitable single-particle potential for many-body calculations at finite temperature is suggested. With this potential one can readily determine the self-consistent correlated chemical potential and consequently the resulting equations of state rigorously satisfy a number of basic thermodynamic relations. Application of our method to a Brueckner-Hartree-Fock nuclear matter calculation yields results in remarkably good agreement with the Hugenholtz--Van Hove theorem.

DOI
10.1103/physrevc.39.2065

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A method for choosing and deriving a suitable single-particle potential for many-body calculations at finite temperature is suggested. With this potential one can readily determine the self-consistent correlated chemical potential and consequently the resulting equations of state rigorously satisfy a number of basic thermodynamic relations. Application of our method to a Brueckner-Hartree-Fock nuclear matter calculation yields results in remarkably good agreement with the Hugenholtz--Van Hove theorem.
This paper investigates the criteria for maintenance of the macroscopic conservation laws of number, momentum, and energy by approximate two-particle correlation functions in many-body systems. The methods of generating such approximations are the same as in a previous paper. However, the derivations of the conservation laws given here clarify both why the approximation method works and the connection between the macroscopic conservation laws and those at the vertices.Conserving nonequilibrium approximations are based on self-consistent approximations to the one-particle Green's function. The same condition that ensures that the nonequilibrium theory be conserving also ensures that the equilibrium approximation has the following properties. The several common methods for determining the partition function from the one-particle Green's function all lead to the same result. When applied to a zero-temperature normal fermion system, the approximation procedure maintains the Hugenholtz-Van Hove theorem. Consequently, the self-consistent version of Brueckner's nuclear matter theory obeys this theorem.
Conserving approximations lead to thermodynamically consistent expressions for Fermi-liquid properties such as compression modulus, symmetry energy and Landau parameters. We will emphasize the need for the precision experiment to determine the density of states at the Fermi surface by discussing nuclear matter approximations in terms of thermodynamic consistency (the Hugenholtz-Van Hove theorem and the virial theorem). The density of states is the primary self-consistent observable to be determined from nuclear many-body approximations. The precise measurement of this observable will establish a rigorous criterion on the validity of nuclear matter approximations.
A systematic study of the microscopic and thermodynamical properties of pure neutron matter at finite temperature within the self-consistent Green's-function approach is performed. The model dependence of these results is analyzed by both comparing the results obtained with two different microscopic interactions, the CD Bonn and the Argonne V18 potentials, and by analyzing the results obtained with other approaches, such as the Brueckner-Hartree-Fock approximation, the variational approach, and the virial expansion.
We present calculations of the energy per particle of pure neutron and symmetric nuclear matter with simplified Argonne nucleon-nucleon potentials for different many-body theories. We compare critically the Brueckner-Hartree-Fock results to other formalisms, such as the Brueckner-Bethe-Goldstone expansion up to third order, self-consistent Green's functions, auxiliary field diffusion Monte Carlo, and Fermi hypernetted chain. We evaluate the importance of spin-orbit and tensor correlations in the equation of state and find these to be important in a wide range of densities.