Multiple Scattering by Arbitrary Configurations in Three Dimensions

Abstract

This paper provides the extension to three dimensions of our previous treatment of two-dimensional problems. Thus we derive a system of integral equations which specifies the multiple-scattering amplitudes for many objects in terms of corresponding functions for the isolated objects. For arbitrary configurations and large spacings, the amplitudes are expanded as series of single scattered functions and their derivatives; ``closed forms'' involving differential operators are derived for two objects. For arbitrary spacings, the amplitudes are expanded as series of spherical harmonics to obtain algebraic sets of equations relating the multiple and single scattering coefficients. Series expansions are available for arbitrary configurations, and closed forms are given for two small objects.