Exchange and correlation in the theory of simple metals

Abstract

A unified approach for including the effects of exchange and correlation in the theory of simple metals is presented. It is first demonstrated that the indirect potential acting on a conduction electron can be described approximately by a function of the scattering momentum G(q), and that this result follows directly from general theoretical results. Exchange and correlation corrections to the Hartree expressions for model (or pseudo) potential form factors and energy-wavenumber characteristics are derived and these corrections are shown to have a simple dependence on G(q). The selfconsistent theory of Singwi et al. (1968) is used to obtain a pair of transform relations between G(q) and the pair correlation function g(r) which permit G(q) to be calculated directly from g(r). The pair correlation function for a tenuous electron gas is used to compute a G(q) which is found to be selfconsistent. A simple approximate form of G(q), which is also selfconsistent, is suggested.