Influence of Local Phonon Damping on Mössbauer Spectra

The contribution of localized-mode phonon emission and absorption to the M\"ossbauer emission process is evaluated in the presence of damping. Net-zero-phonon processes, in which the number of localized phonons (of a given type) emitted is the same as the number absorbed, are shown to contribute to the intensity in the vicinity of the unshifted gamma-ray energy. This contribution is shown to be distributed over a minimum width Γ+2γ where Γ is the gamma-ray natural width, and γ, the width of the localized phonon, is larger than Γ. The complete M\"ossbauer spectrum including all multiphonon contributions can be obtained in our approximation by using the continuous spectrum of nonlocalized phonons plus a Lorentz-broadened peak associated with each localized phonon. Optical absorption at impurities in solids may have linewidths Γ> the phonon widths γ, thus permitting local phonon enhancement of the zero-phonon transitions in impurity absorption or emission.