Alternative Treatment of Diffusion-Controlled Bulk Recombination

Abstract

It is shown that the Laplace transform of the diffusion-controlled bimolecular rate kernel can be directly obtained as the solution of a Riccati equation with the annihilation distance as the independent variable. This provides an efficient alternative to solving the Smoluchowski equation. The solution is expanded in powers of the square root of the Laplace variable; for the first time, the question of convergence is discussed and settled, and terms other than the first two are given explicitly and recursively by quadratures.