The amplitude of the edge singularity in the spectra obtained by x-ray photoemission spectroscopy (XPS) is treated analytically. For a contact core-hole potential, the rigorous formula for the amplitude is obtained by deriving an analytical form for the overlap integral between the initial and final ground states of the conduction band and by giving a proof for the relation connecting the orthogonality theorem with the XPS intensity given by Feldkamp and Davis [Phys. Rev. B 22, 4994 (1980)]. Some numerical examples are presented for the XPS and the x-ray absorption spectra and the values for their intensities obtained recently by renormalization-group formalism are tested and shown to be accurate within an error of a few percent.

DOI:https://doi.org/10.1103/PhysRevB.32.2036