On the theory and simulation of multiple elastic scattering of electrons

Abstract Multiple elastic scattering of electrons in matter is analyzed on the basis of accurate single scattering differential cross sections obtained from partial wave calculations. We give a brief derivation of Moliere's multiple scattering theory that clarifies its physical content and points out its limitations. In particular, it is shown that transport mean free paths calculated from the Moliere single scattering cross section differ significantly from the values obtained from partial wave calculations. We present a mixed simulation algorithm that overcomes most of the limitations of the currently available condensed Monte Carlo codes. This algorithm takes advantage of the fact that most of the collisions experienced by a high-energy electron along a given path length are soft, i.e. the scattering angle is less than a selected small value χs. The global effect of these soft collisions is described by using a multiple scattering approximation. Hard collisions, with scattering angle larger than χs, occur in a moderately small number and are described as in detailed simulations. This mixed algorithm can be applied to any single scattering differential cross section, it leads to the correct spatial distributions and it completely avoids problems related to boundary crossing. Moreover, when the single scattering law underlying Moliere's theory is adopted, the algorithm can be formulated in a completely analytical way.