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arXiv · 2508.16228

Magnetic shielding in the atomic hydrogen anion

Tymon Kilich·Krzysztof Pachucki
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Abstract

The atomic hydrogen anion H$^-$ is the lightest stable anion and its bound states and resonances are well studied in the literature. Due to the planned comparison of the bare antiproton to H$^-$ in a Penning trap, we study the magnetic shielding of H$^-$ using the nonrelativistic quantum electrodynamics theory, by accurately calculating the non-relativistic shielding, as well as finite nuclear mass, relativistic, and partially QED corrections. We find that the finite nuclear mass correction is quite significant in H$^-$ contributing about $0.1\%$ of the total shielding, which is more than twice as much as the relativistic correction. Our final result for the shielding constant has a nine-parts-per-trillion accuracy and paves the way for direct comparison of the antiproton-to-proton magnetic moments.

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Tymon Kilich, Krzysztof Pachucki. 2025-08-22. Magnetic shielding in the atomic hydrogen anion. https://doi.org/10.1103/fhnl-9mk9

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