X-ray absorption spectroscopy (XAS) and resonant inelastic x-ray scattering (RIXS) are powerful probes of electronic structure owing to their chemical and orbital selectivity. For powder samples, however, interpreting RIXS spectral intensities remains challenging as the measured signal is an average over all orientations. Existing theoretical treatments rely largely on spherical-tensor formalisms, which often involve complex derivations and case-specific analyses. Meanwhile, recent advances in quantum-chemistry methods have made the evaluation of transition tensors in Cartesian coordinates both accurate and straightforward. Here, we present a general theoretical framework that translates Cartesian transition tensors into physically meaningful, orientation-averaged intensities for powder samples. The formalism allows predicting angular and polarization dependences ab initio for both XAS and RIXS and is extendable to other spectroscopies. The resulting predictions show excellent agreement with RIXS experimental data at the Ce ${\mathrm{L}}_3$ edge.

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• Polarization in interactions & scattering
• Quantum chemistry methods
• Resonant inelastic x-ray scattering
• X-ray absorption spectroscopy