Magnetic shielding in the atomic hydrogen anion

The atomic hydrogen anion ${\mathrm{H}}^{\ensuremath{-}}$ 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 ${\mathrm{H}}^{\ensuremath{-}}$ in a Penning trap, we study the magnetic shielding of ${\mathrm{H}}^{\ensuremath{-}}$ using the nonrelativistic quantum electrodynamics theory, by accurately calculating the nonrelativistic shielding, as well as finite nuclear mass, relativistic, and partially QED corrections. We find that the finite nuclear mass correction is quite significant in ${\mathrm{H}}^{\ensuremath{-}}$ 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.