Exact Solution of the Percus Yevick Approximation for Hard Spheres .and Beyond
One of the milestones of the statistical mechanical theory of liquids in equilibrium was the exact analytical solution of the Percus Yevick integral equation for three dimensional hard spheres by, independently, Wertheim and Thiele in 1963. The solution was later extended to mixtures, hard hyperspheres in odd dimensions, and sticky hard spheres. This chapter presents some of those solutions within the framework of the rational function approximation, which lends itself to generalizations beyond the Percus Yevick approximation.