Magnetic shielding in the atomic hydrogen anion

TL;DR

This paper accurately calculates the magnetic shielding of the hydrogen anion H$^-$, including various corrections, to facilitate precise comparisons of antiproton and proton magnetic moments in experimental setups.

Contribution

It provides the first high-precision calculation of H$^-$ magnetic shielding, incorporating finite nuclear mass, relativistic, and QED corrections.

Findings

Finite nuclear mass correction is significant, about 0.1% of total shielding.

Relativistic correction is less than the nuclear mass correction, less than 0.05%.

Final shielding constant has nine parts-per-trillion accuracy.

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.