Strain dependence of defect-induced tunneling states in KCl:Li+

The far-infrared absorption data of Kahan et al. on the pressure dependence of impurity-induced lattice modes in KCl: ${\mathrm{Li}}^{+}$ are analyzed in terms of a static three-dimensional potential that separates into a sum of three one-dimensional symmetric double-minimum potentials. Numerical calculations have been performed on two model potentials, a quartic well with a quadratic barrier (two parameters) and a harmonic well perturbed by a Gaussian barrier (three parameters). We show that both potentials can account for the strain dependence of the observed absorption lines and the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$-${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ isotope effect for the lowest frequency line. In each case the potential-barrier height is found to depend linearly on the lattice constant, while the off-center displacement (coordinate of minimum energy) is weakly linear in strain up to an abrupt collapse at the lattice constant for which the barrier disappears. The strain dependence of KCl: ${\mathrm{Li}}^{+}$ can be partitioned into three regimes of behavior: an off-center (tunneling) region, a very anharmonic transition region, and a harmonic region perturbed by an increasingly weak anharmonicity.