On the mean separation of particles of finite size in one to three dimensions

Particles of finite size are assumed to move randomly in a gas or liquid, with their only interactions arising from their hard cores and excluded volume. The mean nearest neighbour separation of such particles is calculated exactly for one dimension (n = 1, rods) and quite accurately for two and three dimensions (n = 2, 3; hard discs and spheres). Results are exact for n = 2 and 3 in the limit of zero density or for any density when the particles are points. For finite-size particles the results are extended to the close-packed limiting densities. For n = 2 and 3, the present predictions differ very appreciably over the entire density range from those calculated by conventional approaches.