site $j$. The $| \psi_0 \rangle$ represents the ground state with energy $E_0$, while $|\Lambda\rangle$ represents the intermediate state with energy $E_{\Lambda}$. The $\Gamma$ describes the life-time broadening width of the core hole.

![\[fig.geom\] Geometry of the RXS experiment. Photon with polarization $\sigma$ or $\pi$ is scattered into the state of polarization $\sigma'$ or $\pi'$ at the Bragg angle $\theta$. The azimuthal angle $\psi$ describes the rotation of the sample around the scattering vector ${\textbf G}$. ](Fig.1.eps){width="6.50cm"}

Energy profiles
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In localized models, the ground state and the intermediate state at each site are well specified by the eigenfunctions of the angular momentum operator, $|J,m\rangle$. The CEF and the intersite interaction usually lift the degeneracy in the ground state. Thus the ground state at site $j$ may be expressed as $|\psi_0\rangle_j = \sum_m c_j(m)|J,m\rangle$. On the other hand, in the intermediate state, we can neglect the CEF and the intersite interaction in a good approximation, since their energies are much smaller than the intra-atomic Coulomb interaction and the spin-orbit interaction (SOI) which give rise to the multiplet structure. Thus the intermediate state preserves the rotational symmetry. Under the assumption, as derived in Appendix, we obtain a general expression of the 