Excitation Pathways in Resonant Inelastic X-ray Scattering from Many-Body Perturbation Theory

Resonant inelastic x-ray scattering (RIXS) spectroscopy is a powerful tool to unravel the nature of elementary excitations in a wide range of crystalline materials. In the RIXS process, a core electron is excited through the absorption of an x-ray photon. Subsequently, a valence electron fills the core hole via the emission of a x-ray photon. The final many-body state contains an excited electron and a valence hole. Through resonant x-ray absorption and emission, RIXS offers an elemental and orbital selective probe of the electronic valence excitations. In this talk, we present a novel many-body approach to RIXS. We use explicit many-body excited states in the optical and x-ray region, as obtained from full diagonalization of the Bethe-Salpeter equation in an all-electron framework, to obtain an expression for the RIXS cross section. The RIXS cross section is expressed in terms of pathways between intermediate many-body states containing a core hole, and final many-body states containing a valence hole. We apply our in-depth analysis to the RIXS spectra of the flour K edge of LiF and carbon K edge of diamond. Our results show that the excitation pathways determine the spectral shape of the emission, and the importance of electron-hole correlation in the spectra.