Implications of (e, 2e) scattering for inelastic electron diffraction in crystals I. Theoretical

Abstract

A formal expression, within the first Born approximation and taking account of the (e, 2e) nature of the event, has been derived for the inelastic differential cross-section associated with scattering of a fast electron which traverses a thin crystal, causing ionization of a crystal atom. In contrast to comparable scattering by an isolated atom, the differential cross-section depends on the phase of the matrix element describing ionization. Formulae are provided which enable this cross-section to be evaluated when a tight binding model crystal of hydrogenic atoms can be used to describe the inelastic event. Applications of the expression and formulae to electron diffraction are the subject of the following paper.