Photodetachment energy of negative hydrogen ions

Abstract

We report a high-precision calculation of the photodetachment energy of the hydrogen anion \mathrm{H}^{-}. The nonrelativistic bound-state energy is obtained using an exact three-body approach, and supplemented by leading relativistic, quantum-electrodynamic, finite-nuclear-size, and hyperfine corrections. Our result is 6083$.$06447(68)\mathrm{cm}^{-1} for the detachment to the hydrogen ground-state hyperfine level \mathit{(F=0)}, which is 220 times more precise than the best experimental determination to date, 6082$.$99(15)\mathrm{cm}^{-1}, as reported by Lykke \mathit{et al.} Beyond their intrinsic interest, these results provide critical input for antihydrogen physics, where controlled photodetachment of \bar{\mathrm{H}}^{+} offers a path to producing ultracold antihydrogen (and its isotopes) for precision experiments. Corresponding calculations for the negative deuterium and tritium ions yield 6086$.$70676(68)\mathrm{cm}^{-1} for ^{2}\mathrm{H}^{-}(F=1/2) and 6087$.$87924(68)\mathrm{cm}^{-1} for ^{3}\mathrm{H}(F=0).