ordering $4f$ states (open circles). Crosses represent the quadrupole moments $\langle \tilde{O}_{x^2-y^2} \rangle$ in the local coordinate frame for each sublattice. \[fig.parameter\]](fig.print.6.eps){width="8.0cm"}

Figure \[fig.parameter\](a) plots the peak intensity as a function of $|E_d|$ (at $\psi=-45^\circ$ in the $\sigma\to\sigma'$ channel). The intensity of the “main" peak increases with increasing values of $|E_d|$. It is nearly proportional to $|E_d|^2$.

Figure \[fig.azim1\] shows the azimuthal angle dependence of the main peak intensity for ${\textbf G}=(00\frac{5}{2})$, in good agreement with the experiment. The same dependence as eq. (\[eq.azim1\]) has been proposed on the basis of the symmetry of the scattering tensor.[@Matsumura] Note that the intensity ratio between the $\sigma\to\sigma'$ channel and the $\sigma\to\pi'$ channel is determined by a geometrical factor; the oscillation amplitude of intensity in the $\sigma\to\pi'$ channel is the factor $\sin^2\theta=0.312$ smaller than that in the $\sigma\to\sigma'$ channel.

![ Azimuthal angle dependence of the RXS intensity of the main peak on ${\textbf G}=(00\frac{5}{2})$, in comparison with the experiment at $T=20$ K.$^{17)}$ \[fig.azim1\]](fig.print.7.eps){width="8.0cm"}

The total amplitude is given by a combination of $\hat M(1,\omega)-\hat M(2,\omega)-\hat M(3,\omega)+\hat M(4,\omega)$. Thus, we have the final form, $$\frac{\hat M({\textbf G},\omega)}{\sqrt{N}} =
\left( \begin{array}{ccc}
 \frac{1}{2}(\xi(\omega)-\zeta(\omega)) & 0 & 0 \\
 0 & \frac{1}{2}(\zeta(\omega)-\xi(\omega)) & 0 \\
          0              & 