Perturbation Correction to the Radial Distribution Function

Abstract

The effect on the radial distribution function $g\left(r\right)\mathrm{}$ of adding a small, long-range interaction to a short-range potential is investigated. Two equations are obtained for the corrected $g$, corresponding to approximations similar to those used in obtaining the Percus-Yevick and convolution hypernetted chain integral equations. The equations relate the "short-range" $g$ (assumed known) and the long-range perturbing potential to the $g$ corresponding to the complete potential. These equations and equations previously obtained by Broyles, Sahlin, and Carley and Hemmer have been tested numerically for a model having a negative Gaussian-Mayer $f$ function, for which near-exact solutions are available from the work of Helfand and Kornegay.