QED calculation of ionization energies of $1snd$ states in helium

Abstract

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 cancelation between the radiative and non-radiative 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 $nD$--$2S$ and $nD$--$2P$ transitions. Possible reasons for this discrepancy are analyzed.