Projects

Theory of hydrogen molecular ions

We work on improving the theoretical description hydrogen molecular ions such as H$_2^+$, HD$^+$ and their isotopologues. The topics under study include:

• The energy levels and rovibrational spectrum
• The hyperfine structure
• The bound-electron g-factor
• Transition probabilities and systematic shifts in high-resolution spectroscopy

This works relies on the following theoretical tools:

• High-precision numerical resolution of the three-body Schrödinger equation by variational methods
• Systematic expansion of relativistic and QED corrections following the NonRelativistic QED (NRQED) approach

An alternative approach, which could be well suited for certain QED contributions such as the one-loop self-energy, is also under study. It consists in a fully relativistic calculation utilizing a very precise numerical resolution of the Dirac equation for the bound electron.

Fundamental constants and BSM physics

By combining QED predictions with experimental measurements of rovibrational transition frequencies in hydrogen molecular ions, one can improve knowledge of fundamental constants such as the proton-to-electron mass ratio, the Rydberg constant and nuclear charge radii. We contribute to this aim by analysing existing spectroscopic data, but also by performing simulations in order to select the most promising transitions to be studied experimentally in the future.

The comparison between theory and experiment can also be used to constrain hypothetical “new physics” interactions. In this context, one interest of molecular sytems is that they are sensitive to interactions between nuclei. A self-consistent approach to constrain light new physics from spectroscopic data was built in a collaboration between atomic/molecular physicists and high-energy physicists. Work is ongoing to develop it further.