Bivalent nearest-available-neighbor distribution in n dimensions: A Monte Carlo calculation

The bivalent nearest-available-neighbor distribution PNAN,n in n dimensions is of interest in the statistics of recombining particles. We generalize to arbitrary dimension a calculation of PNAN,3 due to Dunstan. This derivation, however, is shown to be based on an invalid approximation. A Monte Carlo calculation of PNAN,n for n=1,2, and 3 gives results significantly different from the Dunstan form. We propose the asymptotic form PNAN,1(r)~r^-32 for large r.