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 Sunjic-acute. 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 S-caronunjic-acute obtained in the sudden approximation, as the photon energy is increased above the photoionization threshold value.
Citation: Physical Review B (Condensed Matter and Materials Physics)
Pub Type: Journals