A note on the forms for the integrals of the Percus–Yevick expression for g(R) for hard spheres

Abstract

A new method is presented for evaluating the integrals of the Lennard-Jones potential and the Percus–Yevick (PY) radial distribution function which occur in the Barker–Henderson perturbation theory of liquids. It is shown that the PY g(R) has a simple dependence on R which allows it to be separated into a number of terms of which the integrals with the LJ potential may then be evaluated “computationally” exactly using simple formulae. Some results for pure substances are presented. The method is generally applicable to obtaining the integral of the product of any inverse Laplace transform, obtained by the method of residues, with an inverse power of the argument. The formulae presented here allow the evaluation of residues of up to 4th order poles.