Real-space Green's function approach for intrinsic losses in x-ray spectra

Intrinsic losses in x-ray spectra originate from excitations in a system due to a suddenly created core-hole. These losses give rise to many-body effects such as satellites and edge singularities in x-ray photoemission spectra (XPS) and x-ray absorption spectra (XAS). As shown by Langreth, these effects can be treated within linear response and the RPA in terms of a cumulant Green’s function in momentum space. Here we present a complementary ab initio real-space Green’s function (RSGF) approach in terms of the dynamically screened core-hole W_c(ω) and the independent particle response function. We show that the cumulant kernel β(ω), which characterizes the excitation spectrum, is analogous to XAS, but with the transition operator replaced by the core-hole potential and monopole selection rules. Assuming spherical symmetry about each site, the calculations can be carried out using a discrete site-radial coordinate basis, in parallel with RSGF calculations of XAS. The behavior of W_c(ω) and β(ω) reflect the analytic structure of the loss function, with peaks in β(ω) arising from the zeros of the dielectric matrix. This behavior is consistent with the interpretation of these quasi-boson peaks as plasmons or charge-transfer excitations. The approach further simplifies when W_c(ω) is localized and spherically symmetric. Illustrative results are presented for several systems and compared with other methods.