On the role of inner-shell ionization in the scattering of fast electrons by crystals

A new, simpler and more general derivation is given of the cross-section for inelastic scattering of a fast electron, whose interaction with the thin crystal through which it passes causes inner-shell ionization of some atom. It is assumed that an individual scattering can be associated with ionization of a particular atom and that previous derivations, based on a tight-binding model of the crystal electrons, have failed to recognize this. Bloch-wave sums are used to describe the fast electron before and after ionization and it is suggested that analyses of extended X-ray absorption fine structure and extended energy loss fine structure experiments might lead to an improved description of the excited state of the crystal.