interaction can be safely neglected in the intermediate state, because they are much smaller than the intra-atomic Coulomb interaction. Therefore, it may be reasonable to assume that the intermediate state preserves the rotational invariance. Under the assumption, we derive an expression for the RXS amplitude in the $E$1 process to characterize the spectra. Although the expression is essentially the same as the formula by Hannon [*et al*]{}.,[@Hannon88] the present form is useful to calculate energy profiles with taking full account of multiplet structures. Using this expression together with a microscopic model, we calculate the RXS spectra in the triple-**k** multipole ordering phase in NpO$_2$.

NpO$_2$ undergoes a second-order phase transition below $T_{\textrm 0}=25.5$ K. [@Osborne53; @Erdos80] Since Np ions are Kramers ions in the $(5f)^3$ configuration, a magnetic ground state is naturally expected. However, neither Mössbauer spectroscopy[@Dunlap68; @Friedt85] nor neutron diffraction experiments[@Cox67; @Heaton67] could detect any evidence of the sizable magnetic moment. Actually, the former experiment gave an estimate of the upper limit of the magnitude of the magnetic moment $\sim 0.01 \mu_{\textrm B}$, which was too small to explain the effective paramagnetic moment $\sim 2.95 \mu_{\textrm B}$.[@Ross67] Another complication is that a muon spin relaxation ($\mu$SR) experiment has suggested 