The fine structure and ionization energy of the $1s2s2p$ ${}^{4}P$ state of the helium negative ion ${\mathrm{He}}^{-}$ are calculated in Hylleraas coordinates, including relativistic and QED corrections up to $O({\alpha }^{4}m{c}^2)$, $O\mathbf{(}(\mu /M){\alpha }^{4}m{c}^2\mathbf{)}$, $O({\alpha }^{5}m{c}^2)$, and $O\mathbf{(}(\mu /M){\alpha }^{5}m{c}^2\mathbf{)}$. Higher order corrections are estimated for the ionization energy. A comparison is made with other calculations and experiments. We find that the present results for the fine structure splittings agree with experiment very well. However, the calculated ionization energy deviates from the experimental result by about 1 standard deviation. The estimated theoretical uncertainty in the ionization energy is much less than the experimental accuracy.

• Received 24 September 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.263007