Nearest-neighbor statistics in a one-dimensional random sequential adsorption process

The probability of finding a nearest neighbor at some radial distance from a reference point in many-particle systems is of fundamental importance in a host of fields in the physical as well as biological sciences. We have derived exact analytical expressions for nearest-neighbor probability functions for particles deposited on a line during a random sequential adsorption process for all densities, i.e., up to the jamming limit. Using these results, we find the mean nearest-neighbor distance λ as a function of the packing fraction, and discuss it in light of recent theorems derived for general ergodic and isotropic packings of hard spheres.