Isotope Splitting of theF-Center In-Gap Mode in KI and KBr

High-resolution measurements at the F-center in-gap mode in KI and KBr have revealed a threefold structure in the absorption spectrum with lines at 82.62 ±{} 0.02, 81.98 ±{} 0.02, 81.19 ±{} 0.05 cm^-1 and at 99.60 ±{} 0.03, 99.07 ±{} 0.04, 98.50 ±{} 0.05 cm^-1, respectively. This structure is interpreted as due to the presence of two stable isotopes, K³⁹ and K⁴¹, in the crystal. In a three-dimensional-model calculation which uses as parameters changes in the force constants between the defect and the first nearest neighbors ($A01$) and changes in the force constant between the first and fourth nearest neighbors ($A14$), we found that the in-gap mode frequencies are extremely sensitive to the value of the latter. The position and splitting in the absorption lines can be explained in the calculation by using A01=-0.50, A14=-0.060 for KI and A01=-0.50, $A14=+0.002$ for KBr. Stress experiments on the strongest lines in KI are in agreement with our model. Extending the calculation to Cl^- and Br^- centers in KI, it is shown that the measured isotope splitting for Cl³⁵, Cl³⁷ and Br⁷⁹, Br⁸¹ centers can be explained by taking into account not only changes in $A01$ but also changes in $A14$.