Photodetachment energy of negative hydrogen ions

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$\mathrm{.}$06447(68)$\mathrm{c}\mathrm{m}$^{-1} for the detachment to the hydrogen ground-state hyperfine level $(F=\mathit{0})$, which is 220 times more precise than the best experimental determination to date, 6082$\mathrm{.}$99(15)$\mathrm{c}\mathrm{m}$^{-1}, as reported by Lykke $etal.$ 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$\mathrm{.}$70676(68)$\mathrm{c}\mathrm{m}$^{-1} for ^{2}$\mathrm{H}$^{-}(F=1/2) and 6087$\mathrm{.}$87924(68)$\mathrm{c}\mathrm{m}$^{-1} for ^{3}$\mathrm{H}$(F=0).