Moments of absorption- and emission-band shapes of impurities in solids

General expressions are reviewed and explicitly presented for determining all quantum-mechanical moments of absorption- and emission-band shapes that originate from electronic transitions in a defect whose vibrational interaction contains, in the Condon and adiabatic approximations, terms both linear and quadratic in a single configuration coordinate. The zeroth through fourth absorption and emission moments are presented, the fourth moments for the first time. The band shapes, proportional to transition probabilities, have moments that differ from those of experimentally measured absorption coefficients and emission rates.