Is it possible to "prescribe" the diffusion for a geminate pair in a force field?

Abstract

Given the difficulty of obtaining compact analytical solutions for diffusion of interacting geminate pairs (such as electron-hole pairs generated by ionization of liquid) it is common, following the original method of Mozumder, to "prescribe" this diffusion. With this approach, the survival probability of the pair is represented as a product of the survival probability for a freely diffusing pair and a suitably defined weighting function. This approach gives the correct limiting survival probability for a pair in the Coulomb field. The same approach was used for simulation of reaction dynamics in radiolytic spurs ("independent reaction times" approach of Pimblott) and solve other vexing diffusion problems that do not have analytical solution. A reasonable question is, can the same method be used for any other interaction potential than Coulomb? Here we demonstrate that such a prescription is generally impossible. The correct result given by the prescribed diffusion approach for the Coulomb potential is, actually, purely accidental. The method is inherently contradictory and it should be used with caution.