QED calculations of energy levels of helium-like ions with $5\le Z\le 30$

Abstract

A calculation of two-electron QED effects to all orders in the nuclear binding strength parameter $Z\alpha$ is presented for the ground and $n=2$ excited states of helium-like ions. After subtracting the first terms of the $Z\alpha$ expansion from the all-order results, we identify the higher-order QED effects of order $m{\alpha }^7$ and higher. Combining the higher-order remainder with the results complete through order $m{\alpha }^6$ from [V. A. Yerokhin and K. Pachucki, Phys. Rev. A 81, 022507 (2010)], we obtain the most accurate theoretical predictions for the ground and non-mixing $n=2$ states of helium-like ions with $Z=5-30$. For the mixing $2^1{P}_1$ and $2^3{P}_1$ states, we extend the previous calculation by evaluating the higher-order mixing correction and show that it defines the uncertainty of theoretical calculations in the $LS$ coupling for $Z>10$.

References in corpus (6)

• Complete ${\alpha }^{7}m$ Lamb shift of helium triplet states
• Calculations of QED effects with the Dirac Green function
• Nonradiative ${\alpha }^{7}m$ QED effects in Lamb shift of helium triplet states
• Self-energy screening effects in the $g$ factor of Li-like ions
• QED calculation of the $2p$ fine structure in Li-like ions
• Two-photon exchange corrections to the $g$ factor of Li-like ions

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