Spin Correlations in the Electron Liquid

An expression for the frequency- and wave-vector-dependent paramagnetic susceptibility of the electron gas at metallic densities is derived, using a previously given generalization of the random-phase approximation which takes short-range correlations between the electrons into account. The enhancement factor for the susceptibility is given as a functional of the difference between the correlation functions for pairs of electrons with parallel and antiparallel spins, which are determined in a self-consistent manner by means of the fluctuation-dissipation theorem. Explicit numerical calculations of these correlation functions are presented and compared with the results of previous theories. The present expression of the dynamic susceptibility for the paramagnetic case is a generalization of the expression given earlier by Izuyama, Kim, and Kubo, where the internal field is now a function of the wave vector.