---
abstract: 'We study resonant x-ray scattering (RXS) at Np M$_{4,5}$ edges in the triple-**k** multipole ordering phase in NpO$_2$, on the basis of a localized electron model. We derive an expression for RXS amplitudes to characterize the spectra under the assumption that a rotational invariance is preserved in the intermediate state of scattering process. This assumption is justified by the fact that energies of the crystal electric field and the intersite interaction is smaller than the energy of multiplet structures. This expression is found useful to calculate energy profiles with taking account of the intra-Coulomb and spin-orbit interactions. Assuming the $\Gamma_8$-quartet ground state, we construct the triple-**k** ground state, and analyze the RXS spectra. The energy profiles are calculated in good agreement with the experiment, providing a sound basis to previous phenomenological analyses.'
author:
- Tatsuya Nagao
- 'Jun-ichi Igarashi'
bibliography:
- 'paper.bib'
title: |
    Resonant x-ray scattering spectra from multipole orderings:\
    Np M$_{4,5}$ edges in NpO$_{2}$
---

\[sect.1\]Introduction
======================

Resonant x-ray scattering (RXS) technique has attracted much attention to study spin and orbital properties of 3d transition-metal compounds. RXS at the $K$-edge is described by a second-order optical process that an incident x-ray excites a $1s$ core electron 