Second-order Percus-Yevick theory for the radial distribution functions of a mixture of hard spheres in the limit of zero concentration of the large spheres

The radial distribution functions of a mixture of hard spheres are quite interesting when the ratio of diameters is large and the concentration of the large spheres is very small. In this regime, the radial distrbution functions change rapidly with concentration. The usual Percus-Yevick theory, which is adequate over most of the concentration range, fails at low concentrations of the large spheres. Values are reported of the radial distribution functions for zero concentration of the large spheres using the most accurate theory presently available, second-order Percus-Yevick theory. Agreement with recent formulae for the contact values of these functions is very good except for the contact value for a pair of large spheres, where the agreement is fairly good. It is possible that the radial distribution function for a pair of large spheres may be a little larger than the already large values given by this recent formula.