Nearest-neighbor distribution functions in many-body systems

The probability of finding a nearest neighbor at some given distance from a reference point in a many-body system of interacting particles is of importance in a host of problems in the physical as well as biological sciences. We develop a formalism to obtain two different types of nearest-neighbor probability density functions (void and particle probability densities) and closely related quantities, such as their associated cumulative distributions and conditional pair distributions, for many-body systems of D-dimensional spheres. For the special case of impenetrable (hard) spheres, we compute low-density expansions of each of these quantities and obtain analytical expressions for them that are accurate for a wide range of sphere concentrations. Using these results, we are able to calculate the mean nearest-neighbor distance for distributions of D-dimensional impenetrable spheres. Our theoretical results are found to be in excellent agreement with computer-simulation data.