α4Rcorrections to singlet states of helium

Abstract

Corrections of order ${\alpha }^4\mathcal{R}$ are calculated for the singlet states $1{}^{1}S_0$ and $2{}^{1}S_0$ of the helium atom. The result for the $1{}^{1}S_0$ state is in slight disagreement with that of Korobov and Yelkhovsky [Phys. Rev. Lett. 87, 193003 (2001)]. The results obtained lead to a significant improvement of the transition frequencies between low-lying levels of the helium atom. In particular theoretical predictions for the $2{}^{1}S_0\text{−}1{}^{1}S_0$ transition are found to be in disagreement with experimental values.