Stochastic Theory of Line Shape: Off-Diagonal Effects in Fine and Hyperfine Structure

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Abstract
An extension of the stochastic model of relaxation effects is used to derive a theory of the line shape of fine and hyperfine structure. The theory is developed for Mössbauer spectra, but can be readily applied in related fields such as perturbed angular correlations, electron and nuclear spin resonance, and optical spectroscopy. Previous stochastic-model theories of hyperfine spectra have used a semiclassical fluctuating-field approach which inherently restricts the hyperfine Hamiltonian to matrix elements which are diagonal with respect to the electronic states. In the present theory, these restrictions are removed by using a quantum-mechanical treatment of the combined electronic-nuclear system, wherein the relaxation enters as random instantaneous transitions between electronic states. This allows inclusion of the effects of off-diagonal electronic hyperfine matrix elements (e.g., the pseudoquadrupole interaction). A model for the relaxation is presented which allows all the transition rates to be specified independently, as is necessary to treat finite temperatures. Two examples are used to illustrate the the theory and to compare it with other theories.