QED calculation of the $n=1$ and $n=2$ energy levels in He-like ions

We perform ab initio QED calculations of energy levels for the $n=1$ and $n=2$ states of He-like ions with the nuclear charge in the range $Z=12\text{–}100$. The complete set of two-electron QED corrections is evaluated to all orders in the parameter $\alpha Z$. Uncalculated contributions to energy levels come through orders ${\alpha }^3{\left(\alpha Z\right)}^2$, ${\alpha }^2{\left(\alpha Z\right)}^7$, and higher. A significant improvement in accuracy of theoretical predictions is achieved, especially in the high-$Z$ region.

Figure 1

The diagram of the one-photon exchange.

Figure 2

The diagrams of the two-photon exchange.

Figure 3

Self-energy screening and vacuum-polarization screening diagrams.

Figure 4

Comparison of our all-order numerical results for the second-order two-electron QED correction (square dots, solid line) with values for this correction within the $\alpha Z$ expansion [the contribution of order ${\alpha }^2{\left(\alpha Z\right)}^3$, dashed line] and with the related QED contribution by Drake [18] (dotted line), in units of ${\alpha }^2{\left(\alpha Z\right)}^3$.

Figure 5

Comparison of different evaluations for the total ionization energy of $n=1$ and 2 states of He-like ions. Plotted is the difference between the results obtained by us and by other authors, normalized by the factor ${\alpha }^2{\left(\alpha Z\right)}^4$. Error bars refer to the estimation of the uncertainty of the present evaluation, open diamonds denote the results by Drake [18], filled circles stand for those by Plante et al. [21], and filled triangles indicate the values by Cheng and Chen [24].