$\alpha^4$ Ry corrections to singlet states of helium

Abstract

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