Radiative properties of diatomic Rydberg states in quantum defect theory. Application to the hydrogen molecule

Abstract

Single-channel quantum defect theory (QDT) is used to approximate the Born-Oppenheimer electronic wavefunction of Rydberg diatomic states. The development is based on an extension of quantum-mechanical and semiclassical approaches for the estimation of molecular transition dipole matrix elements as a function of internuclear distance R. The theory is tested by a calculation of the singlet and triplet transition moments of the molecule involving Rydberg states with n = 2-4; l = 0-2. For small and moderate internuclear distance the agreement with ab initio data is found to be generally good, and in some cases identical results are obtained. The disagreement is attributed to a breakdown of the one-channel QDT representation of the interacting electronic states for large R values. The predicted moments for - and - transitions remove existing discrepancies between theoretical and accurate experimental lifetimes for and states.