Influence of a Mass Defect on Resonance Absorption

Abstract

We theoretically calculate transition rates for three lattice phonons to excite the first vibrational level of a diatomic molecule in a linear lattice which contains an isotopic (no change in force constants) defect. We use Liebermann's method to couple lattice modes to internal molecular-vibrational modes, the exact lattice frequency distribution, and the Planck distribution for the phonon occupation numbers of the lattice states. The transition rates as a function of the mass defect for several molecular excitational energies have been obtained for the following cases: (1) molecule next to the defect, (2) defect molecule itself, and (3) molecule in a perfect lattice. The effects of a heavy- or light-mass defect are quite evident as the transition rate of the perfect molecule next to the defect is usually different from its perfect-lattice value. For certain molecular-vibrational frequencies we found that this perfect molecule could absorb energy only under the influence of the local mode and therefore could not absorb energy in a perfect lattice.