Vibronic Structure and Optical Properties of theM(C2h)Center in MgF2

The optical properties of the $M\left(C_{2h}\right)$ center in Mg${\mathrm{F}}_2$ are analyzed in terms of an effective one-phonon density of states, using a combination of convolution integration and moment analysis. A satisfactory fit to the experimental absorption spectrum at $T=0\mathrm{}$ is obtained for this intermediate coupling case, including particularly the sharp structure seen in the one-phonon region. Good agreement between theory and experiment is also found for the no-phonon line and broad-band parameters in absorption as functions of temperature. A calculated luminescence spectrum, derived from that for absorption by using a simple model to estimate the quadratic coupling, compares well with the observed emission band at $T=0\mathrm{}$.