Magnetic shielding in the atomic hydrogen anion

TL;DR

This work delivers a highly accurate NRQED calculation of the nuclear magnetic shielding for the hydrogen anion $^1$H$^-$, incorporating finite nuclear mass, relativistic, and leading QED corrections to achieve a nine-part-per-trillion precision. The authors employ a Korobov exponential basis to solve the nonrelativistic problem and systematically evaluate first- and second-order matrix elements, including the $\sigma^{(2,1)}$ mass-correction and the split $\sigma^{(4,0)}$ relativistic contributions, supplemented by the logarithmic QED term $\sigma^{(5)}_{\rm log}$. The finite-mass correction is found to be about $0.1\%$ of the total shielding, exceeding the relativistic contribution, and the largest relativistic effect arises from $\sigma^{(4)}_{2A}$ due to singlet–triplet mixing; the final value is $\sigma = 24.243189(9) \times 10^{-6}$ with an uncertainty of 0.37 ppm. This result enables a direct comparison of proton and antiproton magnetic moments in planned Penning-trap experiments and provides a benchmark for first-principles testing of NRQED and related quantum-chemistry methods.

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.