Many-Pole Model Calculations of Inelastic Losses in XPS

Inelastic losses such as satellites in x-ray photo-emission spectra (XPS) are difficult to treat theoretically due to the importance of many-body effects beyond the quasi-particle approximation. Here we present an approach based on an exponential (i.e., cumulant) representation\footnote{M. Guzzo et al., Phys. Rev. Lett. {\bf 107}, 166401 (2011)} of the one-particle Green's function, together with\footnote{J. Kas et al., Phys. Rev. B {\bf 76}, 195116 (2007)} a many-pole model of the dielectric function, which incorporates dynamic effects beyond the GW approximation. In this method the photo-electron is treated as in inverted LEED state which couples to the system via neutral, quasi-boson excitations. The approach yields an approximation to the XPS in terms of a convolution of a quasi-particle calculation and a spectral function that includes contributions from both intrinsic and extrinsic excitations,\footnote{L. Hedin et al., Phys. Rev. B {\bf 58}, 15565 (1998)} as well as interference between them. The method is illustrated with recent experimental results.\footnote{Guzzo, op. cit.}