Mössbauer Spectra in a Fluctuating Environment

The Mössbauer line shape in the presence of time-dependent electric field gradients and magnetic fields is considered. Two specific soluble stochastic models are treated: (1) a static electric field gradient with a randomly fluctuating magnetic field which takes on values $+h$ and $-h$, each directed along the axis of the field gradient, and (2) as in (1), but with the fluctuating magnetic field perpendicular to the axis of the field gradient. Example (2) is more complex than (1), since the fluctuating field is in this case capable of inducing transitions between the nuclear levels, while in (1) this is not possible. Specific calculations for the two cases illustrate the differences between them.