CALCULATION OF NONRADIATIVE ELECTRON TRANSITION RATES IN A LATTICE-LOCALIZED-ELECTRON SYSTEM

We outline a method for the calculation of (nonradiative) electron transition rates between pure electronic states (for an impurity or defect electron trapped in a crystalline lattice) which employs functions that may be directly correlated with the radiative spectral functions obtained from the interaction of the electron with an externally applied electromagnetic field. In order to handle a possibly strong electron-lattice distortion Vd we have introduced a canonical transformation [expiR](Ho+Vd)[exp(-iR)]toHo+Vd our unperturbed Hamiltonian, to insure the use of pure electronic states with our transition-inducing perturbation Vu. We have chosen Cr3+ and V3+ in corundum as a physical example for the theory, since their d electrons appear experimentally to exhibit a strong Vd type of coupling to the 194-cm-1 Eu mode of the Al2O3 lattice. Particular emphasis has been given to the temperature dependence of the T24→E2 and T24→A24 transition rates for Cr3+. © 1969 The American Physical Society.