Effects of static distortions on the properties of impurity resonances in the asymptotic limit of low frequencies

A previous study of defect-host coupling in low-frequency harmonic impurity resonance systems is extended to include effects of force-constant changes arising from static distortions. Numerical calculations based upon realistic host-crystal phonons and a defect model involving two force-constant-change parameters are carried out for NaI:${\mathrm{Cl}}^{-}$ in the asymptotic limit of zero frequency. Computed amplitude patterns near the defect reveal the presence of substantial defect-host coupling for all values of the force-constant changes consistent with the zero-frequency requirement. The calculated isotope shifts for Na${\mathrm{I}:}^{35-37}$ ${\mathrm{Cl}}^{-}$ turn out to be substantially lower than the measured value, suggesting that anharmonic effects play an important role in the isotope shift of this system.