Mean Nearest-Neighbor Distance in Random Packings of Hard D -Dimensional Spheres

We derive the first nontrivial rigorous bounds on the mean distance between nearest neighbors λ in ergodic, isotropic packings of hard D-dimensional spheres that depend on the packing fraction and nearest-neighbor distribution function. Several interesting implications of these bounds for equilibrium as well as nonequilibrium ensembles are explored. For an equilibrium ensemble, we find accurate analytical approximations for λ for D0ex0ex=0ex0ex2 and 3 that apply up to random close packing. Our theoretical results are in excellent agreement with available computer-simulation data.