Multiple scattering of classical waves in systems with liquidlike correlations: Formulation as a liquid-state theory.

Abstract

The multiple-scattering theory for wave propagation in a medium with spherical inclusions is examined for the case where these exhibit liquidlike correlations. By adopting graphical methods previously employed in the context of disordered tight-binding models, the determination of the ensemble-averaged amplitude (one-particle) Green function is reduced to the solution of two central equations. One of these is an operator analog of the Ornstein-Zernike (OZ) equation of liquid-state theory. The other describes the self-consistent determination of an effective single-scatterer T matrix. This formalism leads naturally to the definition of a direct and a total propagator, the former being identified with what is generally termed the medium propagator. It is demonstrated that a number of existing theories may be derived as closure approximations to the (exact) pseudo-OZ equation. By generalizing previous treatments of a given (effective medium) approximation, it is then shown how the intensity (two-particle) Green function may be derived in a manner that ensures energy conservation.