Sum-rule test for coherent and incoherent contributions to the photoelectron cross section near core-electron resonances in metallic Ni and Pt

The photoelectron currents emitted from the $d$ valence bands of Ni and Pt metal show strong modulation as the photon energy is scanned through, respectively, the $3p$ and $4f$ core-electron resonances. We demonstrate that the emitted electrons can be divided into three parts, a primary part which is coherent with the excitation step, and primary and Auger parts which are incoherent with the initial excitation. We find that effects due to hole-hole interactions in the $d$ bands are weak and we therefore neglect them. By calculating the energy dependence of the coherent and the Auger parts from previously published parameters obtained from analysis of electron-energy-loss spectroscopy and photo-absorption data, we demonstrate that a sum rule is obeyed in which the coherent and Auger parts add together with the incoherent primary emission to give the energy dependence of photoabsorption.