A simple type of expansion is presented for the x-ray photoemission spectroscopy (XPS) excitation distribution of the Mahan-Nozi\`eres---de Dominicis x-ray model. No assumption about any special form of the potential is used. The exact threshold behavior for the XPS spectrum is correctly given by the lowest-order term in the expansion. The results are compared with exact numerical solutions in case of a contact potential. The agreement is good for one of the approximations presented.
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Hänsch et al. (1982) studied this question.
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