| Popis: |
The theory of radiative and nonradiative transition rates has been formulated within the framework of crude adiabatic approximation for an optical ion in a solid. The basis set consists of products of electronic wavefunctions at the equilibrium nuclear configuration in the ground electronic state, and the vibronic wavefunction associated with electronic states. The radiative and nonradiative transition rates for relaxation from the excited electronic state to a lower (ground) electronic state are obtained using the Fermi Golden rule and Boltzmann distribution of occupancy of the vibrational states in equilibrium at temperature, , of the excited electronic state. The radiative transition rates are found to be the same as that in the proper adiabatic approximation. The perturbing Hamiltonian that drives the nonradiative transition turns out to be the same as in a typical crystal field Hamiltonian, . Using this Hamiltonian, the nonradiative transition rate has been calculated for a system with a single configuration or normal coordinate, . An auxiliary function, , has been defined to describe the temperature dependence of nonradiative transition rate. At low temperatures, the maximum rate is obtained for where and represent the Huang-Rhys parameter and the energy gap between the two associated electronic states in terms of vibrational energy quantum, respectively. This is in keeping with the classical Arrhenius theory which predicts a peak at when the system relaxes thermally from the excited to the ground electronic state over an energy barrier. The dependence of on for small s-values has been studied to verify the energy gap law observed for multiphonon relaxation between excited states of rare earth ions. For most cases of interest, the temperature dependence of the nonradiative transition rates exhibits a characteristic temperature at which these rates start increasing rapidly with increasing temperature-this is usually observed for most luminescent materials. Other theoretical advantages for using the crude adiabatic theory will be pointed out during the presentation. |
