Pair Correlation Functions in Classical and Quantal Electron Gases

Abstract

We solve four integral equations including the hypernetted chain (HNC) equation and also their quantum versions, which are extensions of the mean-spherical model, for a classical and a degenerate electron gas. In treating these integral equations, a degenerate electron gas specified by the conventional parameter rs is shown to be regarded approximately as a classical electron gas with the plasma parameter Γ\doteqdot0.815rs. In the classical electron gas, the comparison of the results obtained from these equations with the Monte Carlo calculations shows that the HNC equation gives rise to the best results both for the radial distribution function and for the isothermal compressibility. This comparison and the correspondence of a degenerate electron gas to a classical one suggest that the quantum version of the HNC equation gives the best results both for the density distribution n(r|v) around a fixed electron in the system and for the isothermal compressibility.