Excitation energy dependence of core-level x-ray-photoemission-spectra line shapes in metals

Abstract

Creation of a deep localized hole in the process of x-ray photoemission from metals is followed by a drastic rearrangement of the surrounding electrons in the Fermi sea. This rearrangement in which low-energy electron-hole pairs are produced, in analogy with gas-phase atomic shake-up processes, gives rise to a low-energy tail in the hole spectral density with an integrable (Mahan) singularity at the energy corresponding to zero-energy pair production. When the usual (symmetric) broadening of the hole is included, the resulting hole line shape becomes a skew resonance, with the asymmetry indices growing with the strength of the electron-hole interaction. The case in which the hole potential is switched on instantaneously (the sudden or impulse limit) has been treated by Doniach and Šunjić. However, the potential switching-on time is a function of the speed at which the excited electron leaves the region of the hole. In this paper we calculate the skew line shapes for finite hole-creation times, going continuously from the adiabatic to sudden limits. The photoemission line shape, for a given hole state, varies smoothly from the symmetric result given in the adiabatic approximation to the asymmetric result of Doniach and Šunjić obtained in the sudden approximation, as the photon energy is increased above the photoionization threshold value.