Mössbauer spectra in the presence of spin-phonon relaxation effects: Symmetry restrictions

The problem of evaluating the Mössbauer line shape in the presence of ion-phonon interactions has been considered. By means of a perturbation procedure it is shown how a limited number of matrix elements of the relaxation operator are relevant. Moreover, the restrictions imposed by the symmetry are also taken into account. In the case of ${\mathrm{Fe}}^{3+}$ in $C_3$ symmetry one has to diagonalize a 288×288 matrix. By taking into account the results obtained in this paper we have reduced the problem of deriving the line shape of the Mössbauer spectrum to that of diagonalizing three matrices of dimensions 16, 16, and 15.