VV and CV correlation effects in CVV Auger-electron and appearance-potential spectroscopy: exact results for limiting cases

Abstract

The authors investigate the influence of correlations among the valence-band electrons (VV correlations) and correlations between the valence-band and core electrons (CV correlations) in CVV Auger-electron spectroscopy (AES) and appearance-potential spectroscopy (APS). The AES and APS intensities are given by properly defined three-particle spectral densities, which are exactly determined for the limiting cases of the completely filled and empty valence bands. They solve the equations of motion for the corresponding three-particle Green functions within the framework of the single-band Hubbard model, which is extended to include, in addition to the on-site Coulomb interaction U among the valence-band electrons, the on-site Coulomb interaction Uc between valence-band and core electrons as well. For AES the calculation can be done analytically, yielding the same result as in the Cini-Sawatzky model except for an additional energetic shift of the spectrum by 2Uc. For APS the calculation has to be performed numerically. The role of the core-hole potential turns out to be qualitatively different from that for AES. The APS spectrum may exhibit up to three different features, which are ascribed to effects of final-state correlations: the band-like part of the spectrum corresponds to final states in which both valence-band electrons are moving independently through the lattice. In the case of strong correlations two satellites are additionally observed. The first one corresponds to two-electron bound states that are more or less localized at the site where the transition takes place. It has a small width and takes almost the whole spectral weight as soon as it is split off. The second one has a width equal to the width of the free Bloch band and quite a small spectral weight. It is interpreted as belonging to final states in which one electron is localized in the core-hole potential while the other one is moving through the lattice. Apart from this rather weak satellite feature, the APS line shape is qualitatively well described within the Cini-Sawatzky model, provided that the coupling parameter U is replaced by an effective coupling Ueff=U-2Uc.