Nonzero temperature variational calculation for the quantum electron gas Slater sum

Abstract

A nonzero temperature variational principle (NZTVP) for the Slater sum has previously been derived. The Slater sum is written in the form of a Boltzmann factor. The effects of Fermi statistics may be included by Lado’s method. The effective potentials in the Boltzmann factor are approximated by parameterized pair potentials and the parameters are determined by the NZTVP. These effective pair potentials can be used to determine the particle distributions and the thermodynamic properties using the methods developed for classical fluids. This paper presents the results of a sample calculation on the quantum electron gas at three densities which simulates a real calculation on a complicated system in order to see whether calculations using the NZTVP are feasible and to determine what problems may arise in such a calculation. Several simplifying approximations are made so that another calculation which does not restrict the temperature dependence of the parameter may also be done as a test of the results of the sample calculation. These exploratory calculations for the electron gas indicate that calculations using the NZTVP are feasible and that the NZTVP may provide a practical means for computing the properties of matter at all temperatures and densities.