Electronic Interactions in the4f65dConfiguration ofEu2+in Crystals

The electronic coupling in the $4f^{6}5d$ configuration of ${\mathrm{Eu}}^{2+}$ in crystals has been studied. The complete $f-d$ Coulomb matrix within $f^6\left({}_{}{}^7{}_{}{}^{}F_J^{}{}_{}{}^{}\right){}_{}{}^2{}_{}{}^{}e_g^{}{}_{}{}^{}$ has been obtained and the Hamiltonian diagonalized for various values of the spin-orbit and Coulomb parameters. The magneto-optical spectra in the first band and the $g$ values of the 4130-Å resonance line of Ca${\mathrm{F}}_2$: ${\mathrm{Eu}}^{2+}$ are quite well explained by using $f-d$ Coulomb interaction about one-half that of the free ion. Even this reduced interaction is by no means negligible and it is shown qualitatively that the same Coulomb $f-d$ parameters are appropriate for Eu${\mathrm{F}}_2$ as well as Ca${\mathrm{F}}_2$: ${\mathrm{Eu}}^{2+}$. It is argued that the reduction from the free-ion case is a physically significant result caused by the crystal environment of the ion, and is not merely the result of some neglected configuration interactions.