The role of pair correlations in diffusion limited recombination A+B-->0

For the reaction A+B→0, the algebraic approach for deriving the kinetic equations for the pair correlation functions g_λλ′ ( r, t), with λ, λ′= a, b, is discussed in the general context of the coupled cluster approach assuming that pair correlations are favored. For the unimolecular regime, c_a( t)≪ c_b( t)≪1, an exponential cutoff of g_ab( r, t) at a length of ≈ {1}/{√c _b} is found, as well as the additional contribution ≈√ c_b to the Smoluchowski rate constant. For the bimolecular regime, c_b( t)= c_a( t), the model gives a decreasing c _a≈t ^{- {3}/{4}} for preasymptotic t< D^-1c_a^-4(0), and c_a≈ t^-1 for t→∞, with D being the mutual diffusion rate.