Nonlocal exchange contribution to the free energy of inhomogeneous many-fermion systems. II: Second-order gradient coefficient for a Coulomb system

Abstract

The coefficient Bx(T), which determines the leading gradient contribution to the nonlocal free energy of an inhomogeneous many-fermion system, has been evaluated exactly to first order in the interparticle interaction, in the case of pure Coulomb interactions. The result is valid for all temperatures and is expressed in terms of Fermi–Dirac integrals having known properties. Explicit analytical results are given for the degenerate and nondegenerate limits and numerical results are given for the intermediate regime of temperature and density. The limiting value of Bx(T) at T → 0 differs from previous evaluations of this quantity based on ground-state perturbation theory. The reasons for this discrepancy are discussed.