Optical potential of a disordered array of scatterers

We study the propagation of scalar waves in a disordered array of static scatters. We derive a cluster expansion for the optical potential in analogy to that for the dielectric constant of a polarizable suspension. It is shown that the long range of the free space Green function leads to divergence of the cluster integrals at low energy. The divergences are removed by a resummation procedure analogous to the resummation of Mayer cluster integrals in the theory of electrolytes. We derive expressions for the most important contributions to the optical potential.