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 ${\mathrm{cm}}^{-1\mathrm{}}$ and at 99.60 ± 0.03, 99.07 ± 0.04, 98.50 ± 0.05 ${\mathrm{cm}}^{-1\mathrm{}}$, respectively. This structure is interpreted as due to the presence of two stable isotopes, ${\mathrm{K}}^{39}$ and ${\mathrm{K}}^{41}$, 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 ($A01\mathrm{}$) and changes in the force constant between the first and fourth nearest neighbors ($A14\mathrm{}$), 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 $A01=-0.50\mathrm{}$, $A14=-0.060\mathrm{}$ for KI and $A01=-0.50\mathrm{}$, $A14=+0.002\mathrm{}$ for KBr. Stress experiments on the strongest lines in KI are in agreement with our model. Extending the calculation to ${\mathrm{Cl}}^{-}$ and ${\mathrm{Br}}^{-}$ centers in KI, it is shown that the measured isotope splitting for ${\mathrm{Cl}}^{35}$, ${\mathrm{Cl}}^{37}$ and ${\mathrm{Br}}^{79}$, ${\mathrm{Br}}^{81}$ centers can be explained by taking into account not only changes in $A01\mathrm{}$ but also changes in $A14\mathrm{}$.