Unified theory of orientation averaging in X-ray spectroscopies: understanding polarization dependence in a Cartesian tensor approach

TL;DR

This paper introduces a unified Cartesian tensor framework for understanding orientation averaging in X-ray spectroscopies, enabling accurate polarization dependence predictions for powder samples.

Contribution

It develops a general theoretical approach translating Cartesian transition tensors into orientation-averaged intensities, improving interpretation of powder XAS and RIXS spectra.

Findings

Predictions match experimental RIXS data at Ce L3 edge.

Framework accurately predicts angular and polarization dependencies.

Method is extendable to other spectroscopic techniques.

Abstract

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 \textit{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 L$_3$ edge.