Long-time kinetics of the excited-state association-dissociation reaction with different lifetimes

We consider the long-time behaviour of the reversible diffusion-influenced reaction A+B -- C when A and C are immobile electronically excited states and B particles are in excess. A and C have different lifetimes. When C decays faster than A, the two leading terms of the asymptotic behaviour are obtained analytically by mapping this problem onto an effective irreversible reaction. The first term is exponential, and it coincides with that obtained from conventional rate equations with steady-state diffusion-influenced rate constants. The second term in the exponent is √t, as in the Smoluchowski irreversible kinetics