Angular dependence of resonant inelastic x-ray scattering: a spherical tensor expansion

TL;DR

This paper develops a spherical tensor expansion for resonant inelastic x-ray scattering, including interference effects, and predicts observable circular dichroism in isotropic samples with polarized detection.

Contribution

It introduces a comprehensive tensor expansion that accounts for interference terms, extending previous models and enabling predictions of circular dichroism in isotropic samples.

Findings

Tensor expansion includes interference terms between dipole and quadrupole contributions.

Cross-section for isotropic samples expressed with only three fundamental spectra.

Circular dichroism predicted for isotropic samples with polarized scattered beam detection.

Abstract

A spherical tensor expansion is carried out to express the resonant inelastic scattering cross-section as a sum of products of fundamental spectra with tensors involving wavevectors and polarization vectors of incident and scattered photons. The expression presented in this paper differs from that of the influential article by Carra et al. (Phys. Rev. Lett. 74, 3700, 1995) because it does not omit interference terms between electric dipole and quadrupole contributions when coupling each photon to itself. Some specific cases of the spherical tensor expansion are discussed. For example the case of isotropic samples is considered and the cross-section is expressed as a combination of only three fundamental spectra for the situation where electric dipole or electric quadrupole transitions in the absorption process are followed by electric dipole transitions in the emission. This situation includes the case of untextured powder samples, which corresponds to the most frequent situation met experimentally. Finally, it is predicted that some circular dichroism may be observed on isotropic samples provided that the circular polarization of the scattered beam can be detected.