An unexpected symmetry of the coulomb potential in the debye-smoluchowski equation

Generalised diffusion processes are discussed using the theory of stochastic processes and several elementary results are proved for the survival probability of a pair of particles with an arbitrary potential. The reaction probability conditioned on reaction ultimately occurring is considered and its backward equation is determined. In the case of the Coulomb potential the probability is shown analytically to be identical in both the attractive and repulsive cases for a given absolute value of r_c. The utility of this result in numerical solutions of the Debye—Smoluchowski equation is discussed.