Multi-k multipole order analyzed by resonant X-ray scattering in the electric quadrupole transition

We introduce a convenient expression of the resonant X-ray scattering (RXS) amplitude, which is appropriate for the investigation of the multipole ordering phase in localized f electron system. The expression is applied to the calculation of the RXS spectra in the electric quadrupole transition around the Np M_2,3 edges from the longitudinal triple-k antiferrooctupolar ordering phase in NpO₂. The results demonstrate a possibility that analyzing the energy profile of the RXS spectrum is effective to identify the type of the order parameter.