Multiple scattering

The purpose of this work is to find the time-dependent distributions of directions and positions of a particle that undergoes multiple elastic scattering. The angular cross section is given and the scatterers are randomly placed. The distribution of directions is found. As for the second distribution we find an exact expression for isotropic cross section in two dimensions. For the same cross section we find its Fourier–Laplace transform in three dimensions. For the general case we devise a method to compute the Fourier–Laplace transform with arbitrary precision. This work is based not on the Boltzmann transport equation but on an integral equation formulation of the problem. The results are general in the sense that any initial condition is a linear combination of the cases considered in this article