Resonant inelastic x-ray scattering (RIXS) is a synchrotron-based spectroscopy that has seen growing interest across a range of scientific disciplines beyond fundamental physics. The interpretation of experimental RIXS data requires theoretical calculations based on the Kramers–Heisenberg formula. However, because of the dependence of RIXS on both the incident and scattered photon properties, a tractable treatment of the angular dependence in this formula has been lacking. In this work, within the electric-dipole approximation, we determine the number of fundamental spectra contributing to the RIXS cross section for all crystallographic point groups. We then derive a general expression for the RIXS cross section of isotropic samples such as untextured powders, homogeneous glasses or liquids, explicitly accounting for the polarization and propagation directions of both the incident and scattered photons. Simplified forms of the RIXS expressions are subsequently obtained for the most common point groups. Finally, we demonstrate the applicability of our formalism through two cases: $2p3d$ RIXS of ${\mathrm{Ni}}^{\mathrm{II}}$ and the study of uranium $3d4f$ RIXS.

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• Crystal symmetry
• Total cross sections
• Resonant inelastic x-ray scattering