Nearest-neighbor distribution functions for impenetrable particles in one to three dimensions

Abstract

In several interesting recent papers, S. Torquato and his associates presented specific expressions for the dimensional hard-sphere nearest-neighbor probability density distribution function, P NN , and the mean nearest-neighbor particle separation, R NN , for D=1, 2, and 3. These expressions, which have been known since 1981, are closely related to general expressions of scaled particle theory given by Reiss and co-workers in 1959 and 1974. Here, the consequences of four different choices for the basic probability function, G, needed in calculating P NN and R NN , are explored with particular emphasis on the D=3 situation