The fine and hyperfine structures of the low-n 3????????u Rydberg states of H2 revisited

The experimental fine and hyperfine structures of low np pi(3)Pi???????(u) Rydberg states with n =2-4 measured in the 1970's for various vibration-rotation levels by Lichten and collaborators, and by Miller and Freund, are reanalysed in the framework of molecular frame-transformation multichannel quantum defect theory MQDT. Instead of the level by level treatment in terms of an effective Hamiltonian as was carried out at the time, a global theory is applied to all levels at once. It is found that the essence of the observed level patterns is well represented by MQDT in terms of a substantially reduced number of dynamical parameters - quantum defects - although the experimental accuracy of the experiments is not yet quite reached. Possible reasons for the remaining discrepancies are given. Since quantum defect theory MQDT, a formalism derived from scattering theory, is still rather little used in the domain of modern ultra-high precision spectroscopy, the occasion is taken here to review some of its key elements. [Graphics]