Resonance Scattering of Phonons by Molecular Impurity Centers

The scattering of phonons at polyatomic (molecular) impurity centers cannot be handled by the regular Lifshitz method because of the additional degrees of freedom. A method is presented which makes it possible to eliminate the molecular coordinates by means of a molecular Green's function. This Green's function defines an effective disturbance in the lattice system with singular poles at the molecular frequencies. Thus the low rank $t$ matrix of the scattering formalism, defining the scattering amplitude, has sharp resonances near the molecular frequencies. The abstract scattering formalism is applied to a simple example which exhibits the influence of librational modes of a molecule with strong internal bindings on phonon scattering. The $t$ matrix for the chosen model is diagonalized by complete group theoretical reduction and reveals the structure of the molecular resonances explicitly. It is found that the resonance is very sharp if the molecular frequency is much smaller than the Debye frequency, and decreases for higher frequencies.