Method of Gaussian quadrature in the calculation of optical absorption and magnetic circular dichroism spectra of s2 ions in alkali halide crystals: application to KBr:In+

The problem of calculating the lineshape function for optical absorption and magnetic circular dichroism due to ionic impurities with the ns2 outer electron configuration, incorporated substitutionally in alkali halide crystals, has been reformulated. The complete energy matrix has been diagonalized directly. Integration over the interaction mode coordinates of Eg and T2g symmetry has been carried out numerically using Gaussian quadrature formulae; the interaction with the A1g mode has been taken into account by the usual convolution procedure. The method has been applied to KBr:In+. The calculated lineshape functions for optical absorption at temperatures ranging from 4 to 300 K and, for MCD at 5 K, are in good agreement with the experimentally determined lineshapes. Moreover, the theory accounts very well for the observed variation of the effective g tensor for the A band with temperature. The calculated values for the moments of the absorption and MCD lineshape functions are in reasonably satisfactory agreement with those deduced from the observed spectra.