Formulation of radiative and nonradiative transitions of a polyatomic system within the crude adiabatic approximation

The theory of radiative and nonradiative transition rates has been formulated within the 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 are obtained using the Fermi Golden rule and Boltzmann distribution of occupancy of the vibrational states in equilibrium at temperature, T, of the excited electronic state. The radiative transition rates are found to be the same as that in the proper adiabatic approximation. Using this Hamiltonian, [Formula presented], the nonradiative transition rate has been calculated for a system with a single normal coordinate, q. An auxiliary function, U, has been defined to describe the temperature dependence of nonradiative transition rate. At low temperatures, the maximum rate is obtained when the Huang-Rhys parameter and the energy gap are nearly equal. The dependence of U on z for small s-values has been studied to verify the energy gap law observed for multiphonon relaxation between excited states of rare earth ions. © 2022 The Author(s)