The description of collective motions in terms of many-body perturbation theory III. The extension of the theory to the non-uniform gas

Abstract

The theory previously developed and applied to calculate the correlation energy of a free-electron gas is extended in this paper to calculate the energy of an electron gas in a potential field. Two new features arise: (i) the introduction of a self-consistent field which is a generalization of the ordinary Hartree field; (ii) the occurrence of ‘local field correction’ effects. It is shown that the energy of the gas can be expressed in terms of the eigenvalues of a certain homogeneous integral equation and a stationary principle for these eigenvalues is given. The theory is applied to crystals and an approximate expression for the correlation energy of a metal is derived neglecting Lorentz-Lorenz corrections effects.