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The approach of Refs. 41 and 42 considers the dynamical structure factor in terms of a product of electron and hole single-particle spectral functions. The relationship with our approach can be understood by noting that the Dyson orbital considered in this paper is related to the hole wave function while the ejected electron goes in a high-energy continuous state
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Equation (9) assumes the atom to be completely ionized and the ejected electron characterized by its wave function
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