Generalization of the theory of Ichimaru. II. Particle correlations in a classical one-component plasma

In a previous paper the present authors have formulated a generalized theory of the dielectric function of an interacting electron liquid which was found to yield an almost exact satisfaction of the compressibility sum rule and fair results of the pair-correlation function $g(r)$. In the present paper we attempt to apply this generalized procedure to the case of a classical one-component plasma. Calculations are performed for the various physical quantities such as the pair-correlation function, compressibility, correlation energy, etc., and a substantial improvement upon the Debye-Huckel theory (classical random-phase approximation) is observed. The present study gives a remarkable improvement in the satisfaction of the compressibility sum rule in comparison to both the theory of Singwi et al. and of Ichimaru. The values of $g(r)$ show a close resemblance to the previous estimates.