Field-theoretical approach to scaling behavior of diffusion-controlled recombination

A diffusion-controlled recombination, A+A→O/ and/or A+A→A, is investigated on the basis of a field theory where initial conditions are explicitly taken into account. The renormalization is performed exactly to all orders in perturbation and a complete scaling form of Green (correlation) functions is derived. The asymptotic decay of a reactant density ρ, ρ(t)∝${\mathit{t}}^{\mathrm{-}\mathit{d}/2\mathrm{}}$, is confirmed. In addition, it becomes evident that ρ exhibits mean-field reaction rate dependence and is in inverse proportion to a reaction rate k, ρ∝${\mathit{k}}^{\mathrm{-}1}$. An explicit universal form of ρ is calculated perturbatively in two different ways, i.e., to first order of ε=${\mathit{d}}_{\mathit{c}}$-d=2-d and to first order of a scaling field X∼${\mathit{kt}}^{\mathit{d}/2\mathrm{}}$. Logarithmic corrections at d=${\mathit{d}}_{\mathit{c}}$=2 are also discussed.