Real-space Green's function theory of non-resonant core-level two-photon x-ray absorption

We present a real-space Green's function approach (RSGF) for core-level two-photon x-ray absorption (TPA), with illustrative calculations for metallic Cu. The theory is based on a Green's function treatment of the Kramers-Heisenberg equation and an efficient approximation that includes only non-resonant intermediate states. The resulting theory is expressed in terms of an effective, static quadrupole transition operator. Calulations of K-shell TPA are carried out using an extension of the FEFF10 RSGF x-ray spectroscopy code, yielding results similar in spectral shape to the one-particle L₃ x-ray absorption spectra, and in reasonable agreement with TPA experiment at pulsed XFEL sources.