The effect of particle–hole interaction on the XPS core-hole spectrum

How the effective particle–hole interaction energy, U, or the polarization effect on a secondary electron in a final two-hole one-particle (2h1p) state created by the Coster–Kronig (CK) transition can solely affect the density of the CK particle states and consequently the core-hole spectral function, is discussed. The X-ray photoelectron spectroscopy (XPS) core-hole spectrum is predominantly governed by the unperturbed initial core-hole energy relative to the zero-point energy. At the latter energy, the real part of the initial core-hole self-energy becomes zero (no relaxation energy shift) and the imaginary part (the lifetime broadening) approximately maximizes. The zero-point energy relative to the double-ionization threshold energy is governed by the ratio of U relative to the bandwidth of the CK continuum. As an example, we study the 5p XPS spectra of atomic Ra (Z=88), Th (Z=90) and U (Z=92). The spectra are interpreted in terms of the change in the unperturbed initial core-hole energy relative to the zero-point energy. We explain why in general an ab initio atomic many-body calculation can provide an overall good description of solid-state spectra predominantly governed by the atomic-like localized core-hole dynamics. We explain this in terms of the change from free atom to metal in both U and the zero-point energy (self-energy).