interaction. We consider only the $j_p=3/2$ states ($L_{\rm III}$ edge). We describe the photoexcited $5d$ electron in the band by introducing a local Green’s function, $$G^{5d}_{m^d}(\hbar\omega)
   = \int_{\epsilon_F}^{\infty} 
   \frac{\rho^{5d}_{m^d}(\epsilon)}{\hbar\omega-\epsilon+i\delta}
   {\rm d}{\epsilon},
\label{eq.5dgreen}$$ where $\rho^{5d}_{m^d}(\epsilon)$ is the $m^d$ component of the $d$ DOS defined in §2. The Fermi energy $\epsilon_F$ is set to be zero so that the $5d$ band is almost empty.

Finite RXS intensities on superlattice spots arise from modulating the $5d$ states with wave vectors of superlattice spots. There are two origins to giving rise to such modulation. One is a direct influence from the buckling of sheets of B and C atoms, which is represented by the second term of eq. (\[eq.crystal\]). Another is the charge anisotropy of the $4f$ states in the quadrupole ordering phase. We discuss both origins separately. In the actual calculation, we specify the local coordinate frames with $\phi_1=28^{\circ}$, $\phi_2=180^{\circ}-28^{\circ}$, $\phi_3=90^{\circ}+28^{\circ}$, $\phi_4=90^{\circ}+152^{\circ}$ for four sublattices in accordance with the experiment.[@Yamauchi]

Direct influence of lattice distortion
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Let the $E_1$ transition take place at a particular site (called as “origin"). The excited $5d$ electron is attracted by the core hole potential at the origin. What is more important is that the $5d$ electron is 