LOCALIZATION OF CLASSICAL WAVES IN A RANDOM MEDIUM - A SELF-CONSISTENT THEORY

We study localization of classical waves in a model of point scatterer s, idealizing a random arrangement of dielectric spheres (epsilon = 1 + DELTAepsilon) of volume V(s) and mean spacing a in a matrix (epsilon = 1). At distances >>a energy transport is diffusive. A self-consiste nt equation for the frequency-dependent diffusion coefficient is obtai ned and evaluated in the approximation where noncritical quantities ar e calculated in the coherent potential approximation. The velocity of energy transport and the phase velocity are renormalized in a similar way, even for finite-size scatterers. We find localization for d = 3 d imensions in a frequency window centered at omega congruent-to 2pi/a, and for values of the average change in the dielectric constant DELTAe psilonBAR = (V(s)a-3)DELTAepsilon exceeding approximately 1.7.