Electron Correlations at Metallic Densities

The dielectric function of a degenerate electron gas in the random-phase approximation, and the one proposed by Hubbard, which takes exchange effects into account, have been extensively used in the study of metallic properties. However, both dielectric functions lead to an overestimate of the short-range correlations between particles. This is manifest from the fact that the pair-correlation function is negative for small interparticle separations over the whole range of metallic densities, and implies an overestimate of the correlation energy. An improved expression of the dielectric function is given, which includes explicitly, in an approximate way, the short-range correlations arising from both Coulomb and exchange effects by being a functional of the structure factor. The structure factor and the dielectric function can then be determined in a self-consistent manner. The numerical solution of the self-consistent scheme yields a pair-correlation function which is positive for all values of the density up to $r_s=4\mathrm{}$. For $r_s>4\mathrm{}$, it is very slightly negative at small separations, but it is so small that it can be considered to be zero for all practical purposes. New estimates of the correlation energy are given for the entire metallic density range, and are smaller than the earlier estimates. These results are used to recalculate the cohesive energy of the alkali metals. A discussion of the plasmon dispersion relation, the compressibility, and the liquid-solid transition, both for the electron system and for an astrophysically interesting system of protons over a background of electrons, is also given.