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

Abstract

The experimental fine and hyperfine structures of low $np{\pi }^3{\mathrm{\Pi }}_u$ 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.

GRAPHICAL ABSTRACT

Keywords:

• Quantum defect theory
• spin-orbit/spin-spin interaction
• Rydberg states
• molecular hydrogen

Acknowledgements

The author wishes to thank Dr. Max Beyer (Amsterdam) for his helpful remarks on the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author.