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

Single-channel quantum defect theory (QDT) is used to approximate the Born- Oppenheimer electronic wavefunction of Rydberg diatomic states. The develop ment is based on an extension of quantum-mechanical and semiclassical appro aches for the estimation of molecular transition dipole matrix elements as a function of internuclear distance R. The theory is tested by a calculatio n of the singlet and tripler transition moments of the H-2 molecule involvi ng Rydberg states with n = 2-4; l = 0-2. For small and moderate internuclea r distance the agreement with ab initio data is found to be generally good, and in some cases identical results are obtained. The disagreement is attr ibuted to a breakdown of the one-channel QDT representation of the interact ing electronic states for large R values. The predicted moments for i (3)Pi (g-e) (3)Sigma(u)(+) and j (3)Delta(g-c) (3)Pi(u) transitions remove existi ng discrepancies between theoretical and accurate experimental lifetimes fo r i 3 Pi(g)(-)(upsilon = 0, N = 1) and j (3)Delta(g)(-)(upsilon = 1, N = 3) states.