Molecular hydrogen and its ion are the simplest of all molecules and as such are important systems for the development of molecular quantum mechanics. The rovibrational energy level structure of these one- and two-electron systems can be calculated extremely precisely by quantum-chemical methods which include the determination of relativistic and quantum-electrodynamic effects [1,2]. By comparison with the results of laser precision measurements of rovibrational intervals, fundamental constants or particle properties, such as the proton-to-electron mass ratio or the proton size, can be determined .
I will discuss the high-precision spectroscopy of molecular Rydberg states in combination with Rydberg-series extrapolation using multichannel quantum defect theory (MQDT) to determine vibrational, rotational, fine- and hyperfine-structure intervals of the molecular hydrogen ion . Choosing suitable valence states in the neutral molecules as intermediate levels allows us to excite Rydberg states that converge on selected rovibrational levels of the ions, and to overcome the limitations imposed by angular momentum selection rules or vanishing intensities in the direct spectroscopy of the ion.
For the excitation of Rydberg states, a resonant three-photon excitation scheme was employed, using pulsed vacuum-ultraviolet (VUV) and visible laser sources to reach the intermediate valence state and a cw near-infrared (NIR) laser source for the excitation to the Rydberg states. The use of a doubly skimmed, supersonic molecular beam emitted by a cryogenic pulsed valve enabled the reduction of the Doppler width of the NIR transitions to less than 3 MHz at 800 nm. In combination with an optical frequency comb used for the frequency calibration of the cw laser, the valence state - Rydberg state intervals are measured with a relative uncertainty of 4 × 10-10.
Additional studies of molecular Rydberg states at the first dissociation threshold of the molecular ions will be presented, that allowed the first observation of shape and Feshbach resonances of H+2
, HD+ and D+2
The observation of heavy Rydberg states (H+H-, H+D-, D+H-) that lead to a new measurement of the electron affinity of the hydrogen and deuterium atom will also be discussed.
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