Survival probabilities and rates derived from an exact Green's function of the reversible diffusion-influenced reaction for an isolated pair in 2D

TL;DR

This paper derives exact expressions for survival probabilities and reaction rates in a 2D diffusion-influenced reaction system using a recently obtained Green's function, providing precise analytical tools for such processes.

Contribution

It introduces exact formulas for survival probabilities and reaction rates based on a newly derived Green's function for 2D diffusion-influenced reactions.

Findings

Exact expressions for survival probability and reaction rate coefficient.

Analytical formula for the survival probability of the bound state.

Derivation of an exact off-rate expression.

Abstract

Recently, an exact Green's function of the diffusion equation for a pair of spherical interacting particles in two dimensions subject to a backreaction boundary condition was derived. Here, we use the obtained Green's function to calculate exact expressions for the survival probability, the time-dependent reaction rate coefficient for the initially unbound pair and the survival probability of the bound state in the time domain. Moreover, we derive an exact expression for the off-rate.