 
Summary: VOLUME 84, NUMBER 12 P H Y S I C A L R E V I E W L E T T E R S 20 MARCH 2000
Rigorous Derivation of the LongTime Asymptotics for Reversible Binding
Irina V. Gopich and Noam Agmon
Department of Physical Chemistry, The Hebrew University, Jerusalem 91904, Israel
(Received 20 July 1999)
Using an iterative solution in LaplaceFourier space, we supply a rigorous mathematical proof for
the longtime asymptotics of reversible binding in one dimension. The asymptotic power law and its
concentration dependent prefactor result from diffusional and manybody effects which, unlike for the
corresponding irreversible reaction and in classical chemical kinetics, play a dominant role in shaping
the approach to equilibrium.
PACS numbers: 82.20.Mj
Are manybody and mobility effects important for bi
molecular reactions in condensed phases? The simplest ir
reversible diffusion influenced reaction, A 1 B ! C, has
been studied by von Smoluchowski [1] in the pseudouni
molecular limit where c B far exceeds A , the con
centration of A. It has since been demonstrated several
times [24] that for the "target problem" [5] of a static A
molecule, the von Smoluchowski theory is equivalent to an
exact solution of a pair problem. Even when A is mobile
