Dielectric formulation of strongly coupled electron liquids at metallic densities. VI. Analytic expression for the local-field correction

Through parametrization of the recent Monte Carlo results as well as those of the dielectric formulation by the present authors, we propose a simple, analytic formula for the static local-field correction which determines the screening function of the degenerate electron liquids at metallic and lower densities. The detailed features of the present theory agree well with the results of the Fermi hypernetted-chain variational calculations. It is shown that the resulting dielectric function satisfies the compressibility sum rule and the self-consistency condition in the short-range correlation significantly better than other existing theories.