Roles of the Van Vleck Orbit-Lattice Interaction in anS-State Ion

Abstract

Using the Van Vleck orbit-lattice interaction, we show that the phonon-induced shift of a spectral line is proportional to the Debye-Waller factor. Based on this result, we propose a convenient method of measuring the Debye temperature. We show also that the orbit-lattice interaction is not the mechanism to account for the discrepancy between the theoretical and experimental $g$ values of the ground state. Within our approximation, we have found the phonon-induced ground-state splitting of ${\mathrm{Gd}}^{3+}$ in Ca${\mathrm{F}}_2$ at $T=293\mathrm{}$ °K to be 3.6×${10}^{-3\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$ with a correct sign. This is smaller than the experimental value by a factor of 40, and is smaller than the theoretical estimate by a factor of 4.