Real-space Green's function approach for intrinsic losses in x-ray spectra
Intrinsic inelastic losses in x-ray spectra originate from excitations in an interacting electron system due to a suddenly created core-hole. These losses characterize the features observed in x-ray photoemission spectra (XPS), as well as many-body effects such as satellites and edge-singularities in x-ray absorption spectra (XAS). However, they are usually neglected in practical calculations. As shown by Langreth these losses can be treated within linear response in terms of a cumulant Green's function in momentum space. Here we present a complementary ab initio real-space Green's function generalization of the Langreth cumulant in terms of the dynamically screened core-hole interaction W c (ω) and the independent particle response function. Here we find that the cumulant kernel β(ω) is analogous to XAS, but with the transition operator replaced by the core-hole potential with monopole selection rules. The behavior reflects the analytic structure of the loss function, with peaks near the zeros of the dielectric function, consistent with delocalized quasiboson excitations. The approach simplifies when W c (ω) is localized and spherically symmetric. In conclusion, illustrative results and comparisons are presented for the electron gas, sodium, and some early transition metal compounds.