$2.0$ eV, respectively, from bottom to top panels. ](Fig.6.eps){width="8.0cm"}

Absorption coefficient
----------------------

The absorption coefficient is proportional to $-{\rm Im} \ \alpha_0(\omega)$. We calculate $\alpha_0(\omega)$ from Eq. (A.4) in the same way as in the calculation of $\alpha_1(\omega)$ and $\alpha_2(\omega)$. The calculated results are shown in Fig. \[Fig.alpha\_0\] at the $M_4$ and $M_5$ edges. The present calculation confirms the previous multiplet calculation by Lovesey [*et al*]{}., in which $-\textrm{Im} \ \alpha_0(\omega)$ has been calculated at the $M_{\textrm 4}$ edge for $\Gamma=0.7$ eV.[@Lovesey03] With increasing values of $\Gamma$, the multiplet structure merges into a single peak. The peak position at the $M_4$ edge with $\Gamma=2$ eV is about $0.35$ eV higher than that in $|\alpha_2(\omega)|^2$.

![\[Fig.alpha\_0\] Absorption coefficients as functions of the photon energy at the Np $M_4$ (right panel) and $M_5$ (left panel) edges. The bold solid and dotted lines represent the calculated results for $\Gamma=0.5$ and $2.0$ eV, respectively. The vertical bars represent $\delta$-functions with $\Gamma=0$. ](Fig.7.eps){width="8.0cm"}

\[sect.4\] Concluding remarks
=============================

In this paper, we have studied the RXS spectra at the Np M$_{4,5}$ edges in the triple-**k** multipole ordering phase of NpO$_2$, on the basis of a localized electron model. We have derived an expression of scattering amplitudes 