Mean-spherical model for soft potentials: The hard core revealed as a perturbation

Abstract

The mean-spherical approximation for fluids is extended to treat the case of dense systems interacting via soft potentials. The extension takes the form of a generalized statement concerning the behavior of the direct-correlation function $c\left(r\right)\mathrm{}$ and the radial-distribution function $g\left(r\right)\mathrm{}$. From a detailed analysis that views the hard-core portion of a potential as a perturbation on the whole, a specific model is proposed which possesses analytic solutions for both Coulomb and Yukawa potentials, in addition to certain other remarkable properties. A variational principle for the model leads to a relatively simple method for obtaining numerical solutions.