Spin-Dependent Potential Functions in a Generalized Hartree-Fock Equation

Abstract

The exchange term in the generalized Hartree-Fock equation found by the Green's-function method is investigated with an electron gas in a metal in mind. This term contains a generalized exchange charge density and a generalized exchange potential function. The latter not only is shielded, but contains effects depending on the spin of the particle being described by the Hartree-Fock equation. This spin dependence is calculated for spin deviations periodic in the lattice, and also for the case of static spin density waves. The original Overhauser spin-density-wave integral equation, arising from a perturbation in the exchange charge density, now must incorporate the corresponding perturbation in the exchange potential function. It is shown that the two perturbations are of the same order of magnitude, and that the constant solution of the integral equation is no longer valid under the same type of approximation.