0                    & 0
       \end{array}
\right).
\label{eq.final2}$$ Combining the geometrical factor in Table I to eq. (\[eq.final2\]), we obtain the scattering intensity. The spectral shape as a function of photon energy is found almost the same as that for the $(00\frac{\ell}{2})$ spot, so that we omit the corresponding figure. The azimuthal angle dependence is given by $$\begin{aligned}
 I_{\sigma\to\sigma'}({\textbf G},\omega) &\propto
    \frac{1}{4}|\xi(\omega)-\zeta(\omega)|^2
      (\cos^2\beta\cos^2\psi-\sin^2\psi)^2,
\nonumber \\
 I_{\sigma\to\pi'}({\textbf G},\omega) &\propto
    \frac{1}{4}|\xi(\omega)-\zeta(\omega)|^2 \nonumber\\
  &\times [\cos\theta\sin\beta(\cos\beta\cos\psi+\sin\psi)
\nonumber \\
& 
   -\sin\theta(1+\cos^2\beta)\sin\psi\cos\psi)]^2,
\label{eq.azim2}\end{aligned}$$ where $\beta$ is determined from $\tan\beta=(2hc)/(\ell a)$. Figure \[fig.azim2\] shows the azimuthal dependence of the peak intensity for the $(30\frac{3}{2})$ spot. A large non-resonant intensity has been observed in the $\sigma \rightarrow \sigma'$ channel, and the resonant behavior is not clear in the experiment.[@Tanaka; @Hirota] The non-resonant intensity may come from the Thomson scattering due to the lattice distortion. We hope that the resonant behavior discussed here is observed in the $\sigma \rightarrow \pi'$ channel, since the non-resonant intensity is expected to disappear in this channel.

![ Azimuthal angle dependence of the RXS intensity of the main peak on ${\textbf G}=(30\frac{3}{2})$. \[fig.azim2\]](fig.print.8.eps){width="8.0cm"}

Influence of quadrupole ordering 4f states
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The initial state is evaluated in § 2, where the $4f$ quadrupole moment is ordered. The 