On radiative and non-radiative decay times in the weak coupling limit

A modified exponential energy gap law for nonradiative decay has been derived for 4f-4f transitions where only a few phonons participate in the transition. Its preexponential factor varies by only a factor of 10 for different host materials and is purely electronic in nature. The modified law is the usual law (giving a factor of 105 variation) modified by using an energy gap which is effectively two (maximum) phonon energies smaller than the energy difference between the initial and the final electronic state. A general relation between the radiative and nonradiative decay rates has been constructed. For 4f-4f transitions this relation enables one to predict the nonradiative decay rate from a knowledge of the radiative decay rate to within one order of magnitude accuracy. The paper also contains a review of the theory of nonradiative and radiative decay in the presence of weak electron-phonon coupling and the Judd-Ofelt theory for forced electric dipole 4f-4f transitions.