state, then the excited electron falls into the core state emitting a photon having the same energy, wavevector ${\textbf k}'$, and polarization vector $\mbox{\boldmath{$\epsilon$}}'$. For example, at $M_{4,5}$ edges in actinide compounds, a $3d$ core electron is promoted to partially filled $5f$ states at each site by the $E$1 transition. The definition of a geometrical arrangement adopted here is found in Fig. \[fig.geom\]. The RXS amplitude is assumed as a sum of contributions from individual ions. Since the dipole matrix element involves well-localized wavefunction of core states, the assumption seems quite reasonable. Accordingly, the RXS intensity observed in the experiment may be expressed for the scattering vector ${\textbf G}$ ($={\textbf k}'-{\textbf k}$) as $$I(\mbox{\boldmath{$\epsilon$}}',\mbox{\boldmath{$\epsilon$}}
  ,{\textbf G},\omega) \propto 
   \left|\frac{1}{\sqrt{N}}\sum_{j} {\textrm e}^{-i{\textbf G}\cdot
{\textbf r}_j} 
    M_j(\mbox{\boldmath{$\epsilon$}}',\mbox{\boldmath{$\epsilon$}},\omega)
  \right|^2 ,
\label{eq.rxs.intensity}$$ where $M_j(\mbox{\boldmath{$\epsilon$}}',\mbox{\boldmath{$\epsilon$}},\omega)$ represents the RXS amplitude at site $j$ with $N$ being the number of sites. For the $E$1 transition, it is expressed as[@Blume85; @Blume88; @Hannon88; @Hill96] $$M_j(\mbox{\boldmath{$\epsilon$}}',\mbox{\boldmath{$\epsilon$}},\omega) 
 =\sum_{\alpha',\alpha}{\bf \epsilon}'_{\alpha}{\bf \epsilon}_{\alpha'} 
  \sum_{\Lambda} 
  \frac{\langle\psi_0|x_{\alpha, j} |\Lambda\rangle
  \langle \Lambda|x_{\alpha', j}|\psi_0\rangle}
       {\hbar\omega-(E_{\Lambda}-E_0)+i\Gamma}, 
\label{eq.rxs.amplitude}$$ where the dipole operators $x_{\alpha, j}$’s are defined as $x_{1, j}=x_{j}$, $x_{2, j}=y_{j}$, and $x_{3, j}=z_{j}$ in the coordinate frame fixed to the crystal axes with the origin located at the center of 