Microstructure of two-phase random media. V. The n-point matrix probability functions for impenetrable spheres

We examine the two- and three-point matrix probability functions for a two-phase random and homogeneous system of impenetrable spheres. For such a system, we give an exact analytical expression for the two-point matrix function S₂ through second order in the number density of particles. Moreover, the two-point matrix function is evaluated, for the first time, for a very wide range of densities. We also discuss the evaluation of the three-point matrix function S₃ for an impenetrable-sphere system and provide new expressions that may be used to estimate it.