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Green's function for reversible geminate reaction with volume reactivity

### Abstract

The kinetics of a diffusing particle near a reversible trap may be described by an extension of the Feynman-Kac equation to the case of reversible binding, which can occur within a finite reaction sphere. We obtain the Green's function solution for the Laplace transform of this equation when the particle is initially either bound or unbound. We study the solution in the time-domain by either inverting the Laplace transform numerically or propagating the partial differential equation in the time-domain. We show that integrals of this solution over the reaction sphere agree with previously obtained solutions.

© 2012 American Institute of Physics

Received 27 September 2012
Accepted 15 October 2012
Published online 12 November 2012

Acknowledgments:
Research supported by The Israel Science Foundation (Grant No. 122/08). The Fritz Haber Research Center is supported by the Minerva Gesellschaft für die Forschung, München, FRG.

Article outline:

I. INTRODUCTION
II. THE REVERSIBLE FEYNMAN-KAC EQUATION
A. Initially unbound particle
B. Initially bound particle
III. THE GREEN’S FUNCTION SOLUTION
A. Unbound particle, initially outside: *r* _{0} > σ
B. Unbound particle, initially inside: *r* _{0} < σ
C. Bound particle, initially inside: *r* _{0} < σ
IV. DEMONSTRATIVE CALCULATIONS
V. CONCLUSION