Many-body perturbation theory for spin-forbidden two-photon spectroscopy off-element compounds and its application toEu2+inCaF2

Predictions of the two-photon transition intensities for ${\mathrm{Eu}}^{2+}$ in ${\mathrm{CaF}}_2$ generally give poor agreement with experiment because the low-lying excited states make a straightforward application of perturbation theory unreliable. In this work we explicitly include the effective Coulomb interaction and the crystal-field interaction for the excited configuration in the zeroth-order Hamiltonian, and treat the spin-orbit interaction as a perturbation. We obtain a good agreement with measured multiplet to multiplet two-photon absorption intensities. The linewidths of the two-photon absorption peaks, which vary dramatically, are explained by selection rules for nonradiative relaxation.