Diffusion-Controlled Reactions with Mobile Traps

Abstract

A density expansion is obtained for the time dependence of the survival probability of diffusing particles in the presence of randomly distributed diffusing traps. The coefficients are expressed in terms of the exact survival probabilities in the presence of one trap, two traps, and so on. Its leading term coincides with the well-known Smoluchowski result which is shown to be exact for static particles and noninteracting mobile traps. As an application, the first correction term is calculated for a one-dimensional system and arbitrary ratios of particle and trap diffusion coefficients.