A quantum mechanical exploration of phonon energy-loss spectroscopy using electrons in the aloof beam geometry

Phonon energy-loss spectroscopy using electrons has both high resolution and low resolution components, associated with short- and long-range interactions, respectively. In this paper, we discuss how these two contributions arise from a fundamental quantum mechanical perspective. Starting from a correlated model for the atomic motion we show how short range 'impact' scattering and long range 'dipole' scattering arises. The latter dominates in aloof beam imaging, an imaging geometry in which radiation damage can be avoided.