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

Amélie Juhin 1 , Christian Brouder 1 ,  and Frank Groot 2
  • 1 Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Sorbonne Universités, UMR CNRS 7590, UPMC Univ. Paris 06, Muséum National d’Histoire Naturelle, IRD UMR 206, 4 place Jussieu, F-75005, Paris, France
  • 2 Inorganic Chemistry and Catalysis, Department of Chemistry, Utrecht University, Universiteitsweg 99, 3584 CG, Utrecht, The Netherlands

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.

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