Model of phonon excitation by fast electrons in a crystal with correlated atomic motion

hen fast electrons are used to study matter at subnanometer length scales, it is often necessary to model the inelastic cross section and the absorptive effect of phonon excitation on elastically scattered electrons. The inelastic cross section for the excitation of a phonon in a crystal by a fast electron is well modeled by using an effective absorptive potential. In this paper, the absorption potential for phonon excitation by fast electrons is rigorously derived from many-body quantum mechanics taking into account correlated atomic motion. This potential is calculated for a silicon crystal at room temperature from the force constants and dispersion curves for the crystal. It is shown that the total absorption for a crystal at room temperature predicted by a phonon model with correlated atomic motion agrees with the Einstein-model potential, based on independent atomic motions.