Mainz 2026 – scientific programme
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A: Fachverband Atomphysik
A 8: Precision Spectroscopy of Atoms and Ions I (joint session A/Q)
A 8.2: Talk
Monday, March 2, 2026, 17:30–17:45, N 3
Precision calculation of the bound-electron g factor in molecular hydrogen ions — •Ossama Kullie1, Hugo Nogueira2, and Jean-Philippe Karr2,3 — 1Theoretical Physics at Institute for Physics, University of Kassel, Germany — 2Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, 4 place Jussieu, F-75005 Paris, France — 3Université Evry Paris-Saclay, Boulevard François Mitterrand, F-91000 Evry, France
In this work [1], we present calculations of the bound-electron g-factor for a wide range of rovibrational states in the ground electronic state (1sσ) of the molecular hydrogen ions H2+ and HD+. Relativistic and QED corrections of orders up to α5 are taken into account. All contributions are calculated in a nonrelativistic QED framework, except for relativistic corrections of order (Zα)4 and above, which are obtained by calculating the relativistic g-factor using a precise solution of the two-center Dirac equation with FEM [2]. A relative accuracy of ∼ 10−11 is achieved for the scalar g-factor component, with an improvement by more than three orders of magnitude over previous calculations. These results are useful for internal state identification and rovibraional spectroscopy of single molecular hydrogen ions in Penning traps, and open a new avenue towards precision tests of QED. Finally, a comparison with experimental result of high-precision Penning-trap spectroscopy of the ground-state spin structure of HD+ [2] is given. [1] Ossama Kullie, Hugo D. Nogueira and Jean-Philippe Karr, Phys. Rev. A 112, 052813 (2025). O. Kullie et. al., Phys. Rev. A 105, 052801 (2022). [3] Charlotte M. König et. al., Phys. Rev. Lett. (2025) under review.
Keywords: Atomic and molecular structure; relativistic Dirac equation; relativistic and quantum-electrodynamic effects; Molecules Gyromagnetic ratio; Schroedinger equation and Adiabatic approximation