Théorique, numérique
Spectroscopy experiments on hydrogen molecular ions (H2+ or its isotope HD+), the simplest molecules in nature, have reached a record 12-digit accuracy, creating a strong motivation to improve the theory. This would allow a more precise determination of the proton-electron mass ratio mp/me, and contribute to setting constraints on new interactions beyond the Standard Model. Another system of interest (also 3-body) is the negative hydrogen ion H-. A new measurement of its photodetachment threshold is in progress, making it desirable to improve theoretical predictions. Moreover, this is useful for the GBAR project, an experiment aiming to measure the gravitational behavior of antimatter that involves the Hbar+ ion, i.e. the antimatter counterpart if H-. The internship will be devoted to improving the theoretical value of the H- electron affinity. In this case, sufficient precision can be achieved by considering the leading orders of the QED expansion. The aim of the PhD is to advance further the theoretical accuracy in the hydrogen molecular ions (in particular their hyperfine structure) through the evaluation of higher-order QED diagrams. This involves both analytical and numerical work: one first needs to express the energy correction in a suitable form, then the numerical calculation is performed using very precise wavefunctions obtained by numerical resolution of the Schrödinger equation.