Theoretical energies of low-lying states of light helium-like ions

A rigorous quantum electrodynamical calculation is presented for energy levels of the $1\hspace{0.5em}{}^{1}S$, $2\hspace{0.5em}{}^{1}S$, $2\hspace{0.5em}{}^{3}S$, $2\hspace{0.5em}{}^1{P}_1$, and $2\hspace{0.5em}{}^3{P}_{0,1,2}$ states of helium-like ions with the nuclear charge $Z=3,\dots ,12$. The calculational approach accounts for all relativistic, quantum electrodynamical, and recoil effects up to orders $m{\alpha }^6$ and $m^2/M{\alpha }^5$, thus advancing the previously reported theory of light helium-like ions by one order in $\alpha$.

Figure 1

The higher order remainder function $G(Z)$ from Eq. (35) inferred from the all-order numerical results of Ref. [8] for the two-electron QED correction, in comparison with the $Z=0$ limit obtained by fitting the $1/Z$ expansion of the $m{\alpha }^6$ correction calculated in this work (denoted by the cross on the $y$ axis). The all-order results for $Z$ smaller than 30 (in some cases, 20) were left out since their numerical accuracy turns out to be not high enough.