Sum rules for resonant inelastic x-ray scattering: Explicit form and angular dependence in perpendicular geometry

Resonant inelastic x-ray scattering (RIXS) and resonant photoemission spectroscopy (RPES) can be used to selectively measure the ground-state properties of atoms in solid materials. For the two types of experiment we compare the sum rules developed in the past years to extract quantitative information from the measured spectra. We show that if the measurements are not sensitive to the emitted photon polarization state (in RIXS) or to the photoelectron spin orientation (in RPES), the two experiments exhibit the same angular dependence of the spectral intensities but differ in some numerical coefficients in the sum rules. In particular we give explicit expressions for the RIXS sum rules in the so-called perpendicular geometry for all the cases of practical interest. These rules can serve, in combination with the well-known x-ray magnetic circular dichroism sum rules in absorption, to evaluate the quadrupole and octupole moments of the scattering atoms.