Theory underpinning multislice simulations with plasmon energy losses

The theoretical conditions for small-angle inelastic scattering where the incident electron can effectively be treated as a particle moving in a uniform potential is examined. The motivation for this work is the recent development of a multislice method that combines plasmon energy losses with elastic scattering using Monte Carlo methods. Since plasmon excitation is delocalized, it was assumed that the Bloch wave nature of the incident electron in the crystal does not affect the scattering cross-section. It is shown here that for a delocalized excitation the mixed dynamic form factor term of the scattering cross-section is zero and the scattered intensities follow a Poisson distribution. These features are characteristic of particle-like scattering and validate the use of Monte Carlo methods to model plasmon losses in multislice simulations.