Mössbauer Spectra in a Fluctuating Environment II. Randomly Varying Electric Field Gradients

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.