may be mediated by the RKKY interaction, but the explicit form has not been derived yet. Note that the Ce-Ce interaction in CeB$_6$ has been extensively studied, describing well the phase diagram under the magnetic field. [@Shiina; @Sakai; @Shiba] But the molecular field may change little and even stabilize the quadrupole order. Therefore, we need not explicitly consider the molecular field by regarding the crystal field as including the effect. The charge anisotropy associated with the quadrupole order modulates the $5d$ states through the intra-atomic $5d$-$4f$ Coulomb interaction.

We calculate the RXS intensity within the $E_1$ transition. We take account of the above two processes, direct and indirect ones, of modulating the $5d$ states. Both processes give rise to the RXS intensities on the $(00\frac{\ell}{2})$ and on the $(h0\frac{\ell}{2})$ spots. Both give similar photon-energy dependences and the same azimuthal-angle dependence in agreement with the experiment. However, the mechanism of direct modulation of the $5d$ band gives rise to the intensities much larger than the mechanism of indirect modulation through the $5d$-$4f$ Coulomb interaction in a wide parameter range of the crystal field. This suggests that the RXS intensities are mainly controlled by the lattice distortion.

This paper is organized as 