We study the resonant x-ray emission spectroscopy (RXES) and the magnetic c
ircular dichroism (MCD) at the L-2,L-3 absorption edges rare-earth elements
, especially gadolinium ion. To this end, an atomic model is adopted and th
e multiplet coupling effect is taken into account. Using the formula of the
coherent second order optical process which consists of the excitation pro
cess from the 2p core state to the empty 5d state and of the radiative deca
y from the 3d core state to the 2p core hole, we calculate RXES-MCD spectra
. By inspection, we have confirmed that the enhancement of the 2p-5d dipole
matrix element proposed for MCD of x-ray absorption spectroscopy. In addit
ion, characteristic features of the spectra observed in gadolinium metallic
compounds are reproduced by our calculations.