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High-Precision Penning Trap Spectroscopy of the Ground State Spin Structure of HD+

Charlotte M. König, Matthew Bohman*, Fabian Heiße, Jonathan Morgner, Tim Sailer, Bingsheng Tu†, Klaus Blaum, and Sven Sturm

Dimitar Bakalov

Hugo D. Nogueira and Jean-Philippe Karr‡

Ossama Kullie

Stephan Schiller

  • Theoretical Physics, Institute for Physics, Department of Mathematics and Natural Science, University of Kassel, Kassel, Germany

  • *Contact author: matthew.bohman@mpi-hd.mpg.de
  • †Present address: Institute for Modern Physics, Fudan University, Shanghai 200433, China.
  • ‡Also at Université Evry Paris-Saclay, Evry, 91000, France.
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Phys. Rev. Lett. 136, 143002 – Published 8 April, 2026

DOI: https://doi.org/10.1103/vrl8-bpmz

Abstract

We present high-precision spectroscopy of the ground state hyperfine structure of HD+ at 4 T. We determine the bound-electron g factor, ge,bound=−2.002 278 540 96(40), to a relative uncertainty of 2×10−10, the most precise determination of a bound-electron g factor of a molecular ion to date. The experimental value agrees with recently developed ab initio theory that now includes quantum-electrodynamical effects up to order α5 and has reduced the theoretical uncertainty by three orders of magnitude [O. Kullie et al., Precision calculation of the bound-electron g factor in molecular hydrogen ions, Phys. Rev. A 112, 052813 (2025)]. In addition, we extract the scalar spin-spin interaction coefficients E4=925 395.758(41)  kHz (electron-proton) and E5=142 287.821(22)  kHz (electron-deuteron), which show a moderate tension with another state-of-the-art theoretical prediction [M. Haidar et al., Higher-order corrections to the spin-orbit and spin-spin tensor interactions in HD+, Phys. Rev. A 106, 042815 (2022)].

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synopsis

Measuring an Electron’s Magnetism in a Molecule

Published 8 April, 2026

Precise spectroscopy of a simple molecular ion opens a new path toward stringent tests of quantum electrodynamics.

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Phys. Rev. Lett. 136, 143002– Published 8 April, 2026
  • Received 4 November 2025
  • Accepted 18 February 2026
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