PAIRING CORRELATIONS IN DIFFUSION-LIMITED RECOMBINATION - COUPLED-CLUSTER STUDY IN FOCK SPACE

The purpose of the paper is to illustate bow the cluster method, introduced originally in classical statistical mechanics and later on generalized to describe correlation effects in quantum systems, can be extended for treating collective behaviour in diffusion limited recombination A + B --> 0. This involves exploring a many-body state vector in second quantization form with pairing correlations between particles only. An algebraic approach for deriving kinetics equations for pair correlation functions g(lambdalambda')(r,t) is proposed, where lambda, lambda'= a, b. Solution of those equations is presented. In two-body approximation, g(ab)(r,t) and the corresponding time-dependent rate constant reproduce the Smoluchowski results. Many-body effects are analysed both for a monomolecular regime (C(b) much greater than C(a)(t)) (MR) and a bimolecular regime (c(b)(t) = C(a)(t)) (BR). For MR at C(b) --> 0, g(ab)(r, t) is shown to have exponential screening on the characteristic length inversely propotional to square-root c(b), and the rate constant acquires additional correction, proportional to square-root c(b), to the Smoluchowski value. For BR at the later stage of recombination, the pair correlation function is predominantly determined by the initial condition, i.e. g(ab)(r,0), and the average concentration c(a) is found to exhibit time dependence almost-equal-to t -3/4 at the pre-asymptotic stage. However, at the true asymptotic, t --> infinity, the model gives c(a) almost-equal-to t-1. We confront these results with the previous analytical results and find a qualitative consistency in the MR case and some discrepancy for the BR case. The proposed description is rather simple and can be applied for exploring collective and correlation effects in other non-equilibrium classical systems.