Electronic spectra of impurities in crystals

Abstract

Perturbed matrix theory is applied to the calculation of the position, intensity, and polarization of the absorption band due to an impurity in a crystal. Many practical approximations are derived. Especial emphasis is laid on the role of the second moment, S, of the host's exciton band, a quantity experimentally determinable. The approximations are compared with the exact results of model calculations for which naphthalene was taken as host crystal. The theory is applied with success to the spectra of isotopically impure naphthalene (first singlet transition, S(0) = 1400cm-2 and benzene (3B1u, S(0) = 700cm-2 S(0) is the second moment of the exciton band at the transition origin, and is related to S by a Franck-Condon factor.