The long time behavior of the rate of recombination

Abstract

Simple closed form expressions for the geminate and homogeneous recombination rates are given. These relations are valid for three‐dimensional, spherically symmetric systems with arbitrary potential interaction, space dependent diffusion coefficient, and reactivity; they contain the previously derived expressions as special cases. For extremely long times the familiar t^−3/2 (respectively, t^−1/2) behavior is obtained, but the relations are valid also for shorter times where deviations from the simple behavior are important. Also included are closed form expressions for the partially diffusion controlled recombination probability. All expressions are derived from one fundamental quantity: the diffusion controlled recombination probability, which is given as an asymptotic series.