### Speaker

### Description

Few-electron molecules are attractive systems for precision spectroscopy because their properties can be calculated with high accuracy by quantum-chemical methods.$^{1,2,3}$ The measurements serve to test theoretical predictions, ideally at the level where their accuracy is limited by the uncertainties of the fundamental constants or by unrecognized physical effects. I will report on precision measurements of energy intervals in cold samples of H$_2$. In particular, we determine the ionization energy with a precision ($\Delta\nu/\nu$) of 10$^{-10}$ from high-resolution Rydberg spectra$^{4,5,6}$ and derive the dissociation energy with an accuracy of 350 kHz, approaching the level where the size of the proton and the uncertainty in the proton-to-electron mass ratio would limit the accuracy of otherwise exact calculations. Comparison will be made to recent theoretical results in the context of a more-than-100-year-long series of experimental and theoretical determinations of the dissociation energy of H$_2$. I will also discuss the determination of an upper bound for a hypothetical global shift of the energy level structure of ortho-H$_2$ with respect to that of para-H$_2$.

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