Self-consistent cluster expansion for wave propagation and diffusion-controlled reactions in a random medium

Abstract

We formulate a self-consistent cluster expansion for the self-energy of a wave propagating in a disordered system of scatterers. The self-energy of the effective medium is determined from a self-consistency condition which requires the optical potential to vanish. In lowest order this leads to a self-consistent equation first formulated by Klauder which involves the T-matrix of only a single scatterer. In next order the self-energy is modified by pair corrections. We apply the theory to the problem of diffusion-controlled reactions and calculate the rate coefficient for a system of perfectly absorbing spheres.