Exact analytical formulas for the distribution functions of charged hard spheres in the mean spherical approximation

Exact analytical expressions are derived for the electrostatic part of the mean spherical approximation (MSA) radial distribution functions (RDFs) for a system of charged hard spheres. These expressions are valid for all distances. In addition, it is shown that these same expressions arise in the MSA description of the charge profile of charged hard spheres near a charged hard wall. We also derive analytical expressions for the nonelectrostatic part of the profile in this case, valid for z ≤ 5σ, and discuss a numerical method for obtaining results for z > 5 σ. Some simple approximate expressions are also considered. © 1978 Plenum Publishing Corporation.