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

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 Gd³⁺ in CaF₂ at $T=293$ ^∘{}K to be 3.6×{}10^-3 cm^-1 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.