Electron Correlations at Metallic Densities. IV

This paper presents an extension of an earlier theory of the dielectric function of the electron liquid in the metallic density range, which took into account the short-range correlations arising from both Coulomb and exchange effects through a local-field correction depending on the pair correlation function. The extension consists in allowing for the adjustment of the pair correlation function to the external field and results in a screening of the Coulomb potential entering the local field. Self-consistent numerical calculations have been carried out to evaluate the dielectric function and the density correlation function in the metallic-density range. Results are presented for the static pair correlation function, the correlation energy, the compressibility, the plasmon dispersion, and the screening of a static point charge. In contrast to the earlier theories, the present theory satisfies closely the compressibility sum rule and also gives reasonable values for the pair correlation function. The same approximation has been straightforwardly applied to treat the spin correlations in the paramagnetic state. The calculation yields fair values for the static paramagnetic susceptibility and for the internal field as a function of wave vector. A simple analytic representation is presented for the numerical values of the local-field correction as a function of wave vector over the metallic density range, which should prove useful for applications.