Force-Constant Changes and the Crystal Impurity Problem

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Abstract
We study the crystal impurity problem for the case of nearest-neighbor force-constant changes around the defect site of body-centered and face-centered cubic crystals. We discuss general group-theoretical techniques for determining the dynamics of the system and also its response to an external optical probe. We provide closed-form expressions for all the necessary dynamical quantities, and show that their determination only requires knowledge of the pure-crystal density of states in cases where there are only central forces. We apply our results to the absorption spectra of xenon and of krypton in solid argon, to obtain good agreement with the observed data.