Statistical geometry of hard-sphere systems

Abstract

The statistical geometry of a system of hard spheres is discussed in terms of the volumes V_j which lie within one diameter of j, and only j, sphere centres. The equation of state can be written as p/ρkT= 1 + [graphic omitted]where S₀ is the surface area of V₀ and D is the dimensionality of the system. Relations between the V_j are derived and numerical values are estimated for hard discs at all densities.