Abstract
X-ray photoemission line shapes of $2s$ and $2p$ electrons from Al, Mg, and Na have been analyzed in terms of the theory of Mahan and of Nozi\`eres and De Dominicis. The resultant singularity indices, 0.115, 0.13, and 0.19, respectively, require that all x-ray threshold exponents, save that for the Na $K$ edge, be positive.
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