Unification of the methods of Onsager and Monchick for calculating the probabilities of various fates in diffusion-controlled reactions, with applications to diffusion in space and in a plane

We have unified the methods of Onsager and Monchick for calculating the probabilities for the various fates (reaction, escape, re-encounter, etc.) of a particle undergoing a diffusion-controlled reaction in three dimensions; the unified treatment applies also to diffusion in a plane and leads easily to some results which have either not been derived before or have required considerable labor. Finally, explicit solutions for a specific force field representing both attraction and repulsion are given.