in the $E$1 process, assuming that the rotational invariance is preserved in the intermediate states of the scattering process. This is a reasonable assumption when the multiplet energy is larger than those of the CEF and the intersite interaction. On the basis of this expression, we have analyzed the RXS spectra in NpO$_2$. Assuming the $\Gamma_8$-quartet ground state, we have constructed the triple-**k** ordering ground state. The energy profiles have been calculated by taking full account of the multiplet structure in the intermediate state, in agreement with the experiment.

RXS signals on multipole ordering superlattice spots have also been observed and analyzed at L$_{2,3}$ edges of rare-earth metals in their compounds such as CeB$_{6}$ and DyB$_{2}$C$_{2}$.[@Nakao01; @Yakhou01; @Tanaka99; @Hirota00; @Matsumura05; @Nagao01; @Igarashi02; @Igarashi03] The intermediate state is created by the transition from the $2p$-core to $5d$ states. Since the $5d$ states are considerably delocalized with forming energy bands, the assumption that the intermediate state preserves the rotational invariance becomes less accurate. An extension of the formula is left in future study.

We thank M. Yokoyama and M. Takahashi for valuable discussions. This work was partially supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports and 