Perturbative solution to order βε of the Percus–Yevick equation for the square-well potential

Abstract

The radial distribution function (RDF) of a fluid is considered for the case of the square‐well potential. If the RDF is expanded in powers of the depth of the square‐well, ε, the first two terms are, in most applications, the most important. The Percus–Yevick (PY) integral equation for the RDF is examined and the resulting integral equations for these terms obtained. The first set of equations are just the PY equations for hard spheres which have been solved analytically. In this paper, the remaining equations for the terms of order βε, where β=1/k_BT, are solved analytically and the results examined. We have speculated in the past that the PY theory could be used to obtain estimates of higher‐order terms in a perturbation expansion of the RDF. We find that the PY theory cannot give reliable estimates of these higher‐order terms for the square‐well potential at high densities.