NONLOCAL EXCHANGE CONTRIBUTION TO THE FREE-ENERGY OF INHOMOGENEOUS MANY-FERMION SYSTEMS .2. 2ND-ORDER GRADIENT COEFFICIENT FOR A COULOMB SYSTEM

The coefficient B(x)(T), which determines the leading gradient contrib ution to the nonlocal free energy of an inhomogeneous many-fermion sys tem, has been evaluated exactly to first order in the interparticle in teraction, in the case of pure Coulomb interactions. The result is val id for all temperatures and is expressed in terms of Fermi-Dirac integ rals having known properties. Explicit analytical results are given fo r the degenerate and nondegenerate limits and numerical results are gi ven for the intermediate regime of temperature and density. The limiti ng value of B(x)(T) at T --> 0 differs from previous evaluations of th is quantity based on ground-state perturbation theory. The reasons for this discrepancy are discussed.