Multiple scattering and diffusion of scalar coherent waves in a group of small spheroidal particles with random orientations

In this manuscript we study multiple scattering and diffusion of scalar wave in a group of monodisperse spheroidal particles with random orientations. We begin by fixing a spheroid in a prolate spheroidal coordinate system, and attain the expansion of the scalar Green's function in this space. The expansion is firstly based on spheroidal wave functions, and then we transform it into the expansion of spherical wave functions. Next, we average the Green's function over the orientations of the spheroid to get the averaged transition operator. Finally, we calculate the transport mean free path and anisotropy factor for the spheroidal particles group, based on the irreducible vertex in the Bethe-Salpeter equation. The approaches to get the average transition operator and the mean free paths in this manuscript will be of benefit to the research area of multiple scattering by non-spherical particles.