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 Here we present a complementary {\it ab initio} real-space Green's function (RSGF) generalization of the Langreth cumulant in terms of the dynamically screened core-hole interaction $W_c(\omega)$ and the independent particle response function. We find that the cumulant kernel $\beta(\omega)$ 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 quasi-boson excitations. The approach simplifies when $W_c(\omega)$ is localized and spherically symmetric. Illustrative results and comparisons are presented for the electron gas, sodium, and some early transition metal compounds.