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Abstract
We derive an expression for the M\"ossbauer line shape in the presence of an electric field gradient which jumps at random between the $x$, $y$, and $z$ axes. This Hamiltonian represents an idealized model for the effects on a nucleus of Jahn-Teller distortions, jump diffusion of vacancies, or electronic relaxation. A simplified calculation based on a model in which the field gradient jumps between positive and negative values along the $z$ axis is also given. In certain limiting circumstances the two calculations give similar results: The M\"ossbauer line shape consists of a single unsplit line for fast jumping, and of a quadrupole doublet for slow transitions. The results of the calculation agree with experiments of Pipkorn and Leider and of Chappert, Frankel, and Blum, as interpreted by Ham.
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