The Kramers approach to solving a problem in diffusion with a sink

A new method is proposed for calculating rate constants for liquid-phase re actions governed by a diffusion equation with a sink. Mathematically, the m ethod consists in the generalized Kramers approach to calculating the proce ss of high-barrier surmounting and applies when the reagents arrive in the reaction zone by the activation mechanism. For two typical cases of S-shape d and delocalized steeply growing sinks, simple mathematical manipulation y ields expressions for the distribution function and the rate constant. The derived expressions are valid over a wide range of values of the parameters and apply at an arbitrary ratio of the rates of diffusion-controlled relax ation and chemical conversion. The models considered adequately describe a great many processes, namely, charge transfer reactions, overbarrier transi tions during slow relaxation of the medium, biochemical reactions of ligand binding, etc.