Photodetachment energy of negative hydrogen ions

TL;DR

This work delivers a high-precision calculation of the photodetachment energy for the hydrogen anion H$^{-}$ by solving the nonrelativistic three-body bound-state problem with explicit electron correlation and augmenting it with leading relativistic, QED, finite-nuclear-size, and hyperfine corrections. The authors extend the methodology to the deuterium and tritium negative ions, using a three-body (helium-like) framework with explicit mass-polarization and recoil terms, and they compute the Bethe logarithm with a dedicated many-body approach. The resulting photodetachment energies are $E_{ ext{PD}}=6083.06447(68) ext{ cm}^{-1}$ for $^{1} ext{H}^{-}$, and $6086.70679(68)$ and $6087.87924(68) ext{ cm}^{-1}$ for $^{2} ext{H}^{-}$ and $^{3} ext{H}^{-}$, respectively, with uncertainties at the level of $3.1 imes10^{-9}$ a.u. This sets a new benchmark for light-atom photodetachment thresholds, supports antihydrogen production schemes by providing precise laser detuning references, and points to future improvements through the remaining higher-order corrections in the QED/relativistic series.

Abstract

We report a high-precision calculation of the photodetachment energy of the hydrogen anion H$^{-}$, also known as the electron affinity of the hydrogen atom. 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 $6083.06447(68)$ cm$^{-1}$ for the detachment to the hydrogen ground-state hyperfine level $(F=0)$, which is 220 times more precise than the best experimental determination to date, $6082.99(15)$ cm$^{-1}$, as reported by Lykke et al. Beyond their intrinsic interest, these results provide critical input for antihydrogen physics, where controlled photodetachment of $\bar{H}^{+}$ offers a path to producing ultracold antihydrogen (and its isotopes) for precision experiments. We further determine the photodetachment thresholds for $^{2}$H$^{-}$ and $^{3}$H$^{-}$ into the ground hyperfine states of the corresponding hydrogenic atoms, yielding $6086.70679(68)$ cm$^{-1}$ for $^{2}$H$(F=1/2)$ and $6087.87924(68)$ cm$^{-1}$ for $^{3}$H$(F=0)$.

Figures (2)

• Figure 1: Comparison of experimental data (cross markers) and theoretical predictions (filled circles) of the ${}^1\mathrm{H}^{-}$ photodetachment energy (in $\mathrm{cm}^{-1}$). The horizontal red line extends our value for comparison. The HF correction was added to Drake's value (see Table \ref{['tab:Final-PD-comparison']}).
• Figure 2: Comparison of experimental data (cross markers) and our theoretical prediction (filled circles) of the $^{2}\mathrm{H}^{-}$ photodetachment energy ($\mathrm{cm}^{-1}$). The horizontal red line extends our value for comparison.