 
Summary: Chemical Physics 148 (1990) 1119
NorthHolland
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 coordinatedependent 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 diffusioninfluenced 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
