Line broadening and line shift of long-lived states of nuclei in a lattice

Long-lived states of nuclei embedded in a lattice are continuously perturbed by the surrounding atoms. The perturbations can be considered as stochastic processes described by a stochastic variable. The first-order correlation function, from which the frequency spectrum radiated by the nuclei can be derived, depends, among other things, on the ensemble average of a particular function of the stochastic variable. This function depends on the actual perturbation mechanisms. Making use of the ergodic theorem allows for the calculation of this ensemble average and, hence, of the radiated frequency spectrum. The spectrum is shown to be Lorentzian and homogeneously broadened. Also a frequency shift with respect to the unperturbed frequency has been found. An order of magnitude of the broadening and shift is given.