Sidebands in the Infrared Spectrum ofUCenters in Alkali Halides

A description of the sidebands in the infrared spectrum of crystals containing $U$ centers is presented, together with numerical calculations for the case of $U$ centers in KBr. The sidebands are assumed to arise from the second-order dipole moment and the cubic anharmonicity. Symmetry considerations and the assumption of short-range second-order dipole moment and third-order anharmonic interactions are utilized, and the resulting formulas are evaluated numerically for specific examples within the framework of nearest-neighbor-coupling interactions together with altered harmonic force constants between the defects and their nearest neighbors. It is found within this framework that either the second-order dipole or the cubic an-harmonic coupling mechanism can give reasonable agreement with experiment, but that it is always necessary to have a strong decrease in the central force constant between the impurity and its nearest neighbors, as compared with the nearest-neighbor force constant in a pure crystal. This has as its consequence the prediction of a localized mode in the gap between the acoustical and optical frequency branches.