Abstract
We derive an expression for the double differential scattering cross section for inner-shell excitation of atoms by fast electrons. Using the augmented plane-waves approach for description of the photo electron, we find the inelastic scattering cross section to be a function of energy loss and momentum transfer, which is a priori not proportional to the local symmetry-projected unoccupied density of states. We show the importance of symmetries and choice of coordinate systems, which may necessitate the consideration of cross terms in the expression for the inelastic scattering cross section, coupling different angular momenta of the final state. This has important consequences for the interpretation of energy loss near-edge structure and its counterpart x-ray absorption near edge structure.
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