 
Summary: Unified theory of reversible target reactions
Noam Agmona)
and Alexander V. Popovb)
Department of Physical Chemistry and the Fritz Haber Research Center, The Hebrew University,
Jerusalem 91904, Israel
Received 3 April 2003; accepted 1 July 2003
We discuss two fundamental reversible diffusion influenced reactions: i A B C and ii A
B C D. In the pseudounimolecular case, we prove that reaction i is a special case of ii ,
which thus constitutes a unified reversible problem of multiparticle kinetics. For static A and C the
``target'' limit , we suggest to treat this problem as follows. First we generalize the Smoluchowski
theory to reaction ii . In Laplace space, we combine this with a powerlaw theory, determining the
combination coefficient so that the unified theory reduces correctly in all known limits. We also
show how to rewrite it in the time domain, with the generalized Smoluchowski theory as the leading
term. Comparison with Brownian simulations shows near perfect agreement for both versions of our
theory under all conditions. © 2003 American Institute of Physics. DOI: 10.1063/1.1603717
I. INTRODUCTION
Chemical reactions are reversible. Yet, traditionally the
study of diffusion influenced reactions has focused on irre
versible reactions,1
A B
