Quantum electrodynamical (QED) calculations of ionization energies of the $1sndD$ states are performed for the helium atom. We reproduce the previously known relativistic and QED effects up to order $m{\alpha }^5$ and extend the theory by calculating the complete $m{\alpha }^6$ correction. The total contribution of the $m{\alpha }^6$ effects is shown to be much smaller than previously estimated, due to a large cancellation between the radiative and nonradiative parts of this correction. As a result of our calculations, we confirm the previously reported deviations between measured transition energies and theoretical predictions for the $nD\text{−}2S$ and $nD\text{−}2P$ transitions. Possible reasons for this discrepancy are analyzed.

• Received 9 June 2020
• Accepted 23 June 2020

DOI:https://doi.org/10.1103/PhysRevA.102.012807