Stochastic model for classical bath variables and its influence on line-shape expressions

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Abstract
A stochastic theory of hyperfine spectra is presented in which the coupled nucleus-ion system is treated quantum mechanically, and the interaction between the ionic spin and its surroundings is taken into account via effective fluctuating fields. The theory treats in detail a larger subsystem than the one considered by Clauser and Blume, and it is shown that the Clauser-Blume results can be obtained from the more general result given here, when the rate of fluctuations in the surrounding bath is much faster than the frequencies of the radiating system. A perturbative calculation also enables us to establish a connection between the stochastic- and the many-body-theory results for the line shape. The theory is worked out for Mössbauer line shape but can be applied easily to other related problems in atomic and nuclear spectroscopy. Application of the results derived here to analyze specific experimental situations will be dealt with elsewhere.