The theory of the excitation of atomic inner-shells in crystals by fast electrons

We review the theory of the excitation of electrons from atomic inner shells in crystals as relevant to microanalysis in the transmission electron microscope and suggest several improvements and generalizations. The orthodox theory, originating with Kainuma, represents the fast electrons as Bloch waves and the core and ejected electrons as tight-binding wavefunctions. For several reasons we consider it more satisfactory to represent the core electron as a purely atomic wavefunction and the ejected electron as a sum of spherical waves centred on the atom in question. This formulation is ideally suited for generalization to calculate fine-structure effects such as those observed in extended electron energy-loss fine structure and electron energy-loss near-edge structure. We show that the apparent lack of momentum conservation in the excitation process, commented on by Maslen and Rossouw (1983) and Meekison and Whelan (1983) has a simple explanation based on the character of the core wavefunction.