III}$ absorption edge, and resonant enhancements have been found on quadrupolar ordering superlattice spots. [@Nakao01] Only one peak appeared as a function of photon energy, which was assigned to the $E_1$ process. In the $E_1$ process, $5d$ states of Ce in the intermediate state are to be modulated in accordance with the superlattice spots. Since the lattice distortion seems extremely small and the $5d$ states are less extending than the $4p$ states in transition-metal compounds, it is highly possible that the modulation is mainly caused by the Coulomb interaction between the $5d$ states and the orbital ordering $4f$ states. In our previous papers,[@Nagao; @Igarashi] we demonstrated this scenario by calculating the RXS spectra on the basis of the effective Hamiltonian of Shiina et al.[@Shiina; @Sakai; @Shiba] Without the help of lattice distortion, we obtained sufficient intensities of the spectra, and reproduced well the temperature and magnetic field dependences. This situation contrasts with those in transition-metal compounds.

![ (a) Sketch of the crystal structure of DyB$_2$C$_2$ ($P4/mbm$: $a=5.341$ ${\rm \AA}$, $c=3.547$ ${\rm \AA}$ at $30$ K). Gray large circles are Dy atoms. Solid and open small circles are B and C atoms, respectively. (b) Local coordinate frames attached to each sublattice. 