LONGITUDINAL AND TRANSVERSE LOCALIZED VIBRATION MODES

In the presence of a finite concentration of impurities, each of which in isolation gives rise to triply degenerate localized vibration modes, a Lorentz field and macroscopic field are set up by the collective oscillations of the impurities vibrating in localized modes. These fields act back on the localized modes to shift their frequency, and to split the threefold degenerate modes into twofold degenerate transverse modes and a nondegenerate longitudinal mode. A theory of these effects is presented, and an estimate is made of the magnitude of the difference between the frequencies of the longitudinal and transverse localized modes. © 1969.