Wave propagation in a disordered array of monopole scatterers

We study scalar wave propagation in a disordered static array of spherical scatterers. Due to a hard core repulsion the scatterers do not overlap. The wave is scattered by a δ-function potential at the center of each of the spheres. To this monopole model we apply the previously developed cluster expansion for the self-energy. We find the root of the dispersion equation for the coherent wave for a range of volume fraction5. It turns out that the monopole model develops an instability when the scattering is too strong.