Contact pair correlation functions of binary mixtures of additive hard spheres from the virial expansion

Density expansions of the contact pair correlation functions for binary mixtures of additive hard spheres are obtained from the virial expansion of the equation of state. The procedure is based on the use consistency conditions. The resulting expansions are exact up to first order in the density. This corresponds to the third virial coefficient which is exactly known for these mixtures. Analytical expressions for the second and third order terms are obtained on the basis of very accurate approximate analytical expressions for the fourth and fifth virial coefficients. It is found that the series converge slowly, but the convergency can be accelerated by means of a resummation procedure.