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Chemical Physics 148 (1990) 11-19 North-Holland

Summary: Chemical Physics 148 (1990) 11-19
The slow diffusion limit for the survival probability
in reactive diffusion equations
Savely Rabinovich and Noam Agmon
Department of Physical Chemistry and The Fritz Haber Centerfor Molecular Dynamics, TheHebrew University.
Jerusalem 91904, Israel
Received 25 May 1990
We consider the Smoluchowski equation with a coordinate-dependent reactivity and obtain asymptotic expansions for the
survival probability and the mean lifetime as power series in the diffusion constant. The coefficients in this expansion may depend
on both temporal and spatial variables. Using the present results together with the previously derived expansion for the fast
diffusion limit, we are able to obtain useful Pad6 approximations for the dependence of the mean lifetime on the diffusion coefficient.
1. Introduction
The kinetics of diffusion-influenced reactions has
been studied since the early twentieth century by a
variety of mathematical techniques and indeed a large
number of applications in physical and chemical ki-
netic phenomena have been found [ 1,2]. A rela-
tively simple model consists of a particle diffusing in
the presence of a potential field with a spatially vary-


Source: Agmon, Noam - Institute of Chemistry, Hebrew University of Jerusalem


Collections: Chemistry