We review the theory of the excitation of electrons from atomic inner<br />shells in crystals as relevant to microanalysis in the transmission<br />electron microscope and suggest several improvements and generalizations.<br />The orthodox theory, originating with Kainuma, represents the fast<br />electrons as Bloch waves and the core and ejected electrons as tight-binding<br />wavefunctions. For several reasons we consider it more satisfactory<br />to represent the core electron as a purely atomic wavefunction and<br />the ejected electron as a sum of spherical waves centred on the atom<br />in question. This formulation is ideally suited for generalization<br />to calculate fine-structure effects such as those observed in extended<br />electron energy-loss fine structure and electron energy-loss near-edge<br />structure. We show that the apparent lack of momentum conservation<br />in the excitation process, commented on by Maslen and Rossouw (1983)<br />and Meekison and Whelan (1983) has a simple explanation based on<br />the character of the core wavefunction.
Saldin, D. K., & Rez, P. (1987). The theory of the excitation of atomic inner-shells in crystals by fast electrons. Philosophical Magazine B: Physics of Condensed Matter; Statistical Mechanics, Electronic, Optical and Magnetic Properties, 55(4), 481–489. https://doi.org/10.1080/13642818708217957