Precision spectroscopy of molecular hydrogen and its ion through molecular Rydberg states and MQDT-assisted extrapolation of Rydberg series

H₂⁺ and H₂ are the simplest of all ionic and neutral molecules and as such important systems for the development of molecular quantum mechanics.
The energy-level structure of H₂⁺ can be calculated extremely precisely and by comparison with the results of precise spectroscopic measurements, fundamental constants or particle properties, such as the proton-to-electron mass ratio or the proton size, may be determined.

Spin-rovibrational intervals in H₂⁺ are determined with sub-MHz accuracy from high-resolution measurements of Rydberg series of H₂ followed by Rydberg-series extrapolation using multichannel quantum defect theory.

For the excitation of Rydberg states, a resonant three-photon excitation scheme was employed, using pulsed VUV and VIS laser sources to reach the intermediate double-well GK state and a continuous-wave near-infrared laser source for the excitation to the Rydberg states. The valence state - Rydberg state intervals could be measured with a relative accuracy of 3E-10 using an optical frequency comb for the frequency calibration of the cw laser and employing a procedure to minimize systematic uncertainties. The measurements were used to determine the spin-rotational intervals of the first three rotational levels of para H₂⁺ and the fundamental vibrational interval.