Interparticle distribution functions and rate equations for diffusion-limited reactions

We study the spatial interparticle distribution function in diffusion-limited reactions and its effect on the macroscopic reaction rate. For an exactly soluble model we find that a universal scaling interparticle distribution function is achieved regardless of initial conditions, and that the macroscopic kinetics is described by an autonomous polynomial rate equation only when the initial distribution of particles is of the functional form of the scaling distribution. Monte Carlo simulations are used to verify the analysis, as well as to investigate interparticle distribution functions for some other reactions