multiplescattering

Multiplescattering refers to the propagation of waves or particles through a medium in which they undergo more than one scattering event. It contrasts with single-scattering, where only one interaction occurs. In many natural and engineered materials the path length is long and the wave loses memory of its initial direction, leading to diffuse transport rather than ballistic travel.

Key quantities include the scattering mean free path l, the average distance between consecutive scattering events, and the transport mean free path l*, which accounts for the angular distribution of scattering. If the medium is optically thick with many scattering events, the intensity behaves approximately as a diffusion process with a diffusion coefficient D ~ v l*/3, where v is the particle speed in the medium. The anisotropy factor g = <cos θ> characterizes the tendency for forward scattering.

The standard mathematical framework comprises the radiative transfer equation and, in the multiple-scattering limit, the diffusion approximation. For coherent effects, the Bethe-Salpeter equation or other diagrammatic approaches describe interference phenomena. Numerical methods often rely on Monte Carlo simulation of photon packets or electrons to model complex media and geometries.

Applications span atmospheric optics, astronomy, and computer graphics, where multiple scattering shapes sky color, haze, and translucency. In biomedical imaging, multiple scattering limits resolution but is exploited in diffuse optical tomography to probe tissue properties. In materials science and neutron scattering, it provides information about structure and dynamics. Phenomena such as coherent backscattering arise from interference among multiple scattered waves.