Isotope Effect in Crystal-Field Splitting

The Van Vleck orbit-lattice interaction attributed to the normal coordinates of the cubic molecular cluster transforming like ${\Gamma }_{4u}$ is used to calculate the ground-state splitting induced by the lattice vibrations. With the aid of the result obtained by Visscher, we have shown that the isotope shift in the crystal field splitting of the ground state follows the isotope-mass-difference-ratio relationship. We have also found that the temperature-dependent part of the isotope shift is due to the quantum corrections and should vanish in the classical limit.