  The dependence with energy of the resonant soft x-ray Bragg diffraction
intensity in DyB$_2$C$_2$ for the $(00{1/2})$ reflection at the Dy M$_{4,5}$
edges have been calculated by using an atomic multiplet hamiltonian including
the effect of crystal field and introducing an intra-atomic quadrupolar
interaction between the 3d core and 4f valence shell. These calculations are
compared with the experimental results (Mulders et al., J. Phys.: Condens.
Matter 18 (2006) 11195) in the antiferroquadrupolar and antiferromagnetic
phases of DyB$_2$C$_2$. We reproduce all the features appearing $(00{1/2})$
reflection energy profile in the antiferroquadrupolar ordered phase, and we
reproduce the behaviour of the resonant x-ray scattering intensity at different
energies in the vicinity of the Dy M$_5$ edge when the temperature is lowered
within the antiferromagnetic phase.
