Bimolecular annihilation reactions with immobile reactants

Abstract

We study the bimolecular annihilation reaction A+B→0 with immobile reactants in arbitrary dimension. For this we derive a closed set of integrodifferential equations by using Kirkwood’s superposition approximation to decouple the infinite hierarchy of equations for the many-center correlation functions. We find that for exchange-type interactions and equal numbers of A and B species the reactant concentration n decays as n∼ξ−d/2, where ξ is time-dependent, ξ=ln t, and may be interpreted to be an effective reaction radius. A comparison to numerical simulations shows very good agreement to the theoretical expressions, both for the temporal evolution of particle concentrations and also for the pair-correlation functions; this confirms the validity of the superposition approximation.