QED calculations of energy levels of heliumlike ions with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>5</mml:mn><mml:mo>≤</mml:mo><mml:mi>Z</mml:mi><mml:mo>≤</mml:mo><mml:mn>30</mml:mn></mml:mrow></mml:math>
V. A. Yerokhin, Vojtěch Patkóš, Krzysztof Pachucki
Abstract
A calculation of two-electron QED effects to all orders in the nuclear binding strength parameter $Z\ensuremath{\alpha}$ is presented for the ground and $n=2$ excited states of heliumlike ions. After subtracting the first terms of the $Z\ensuremath{\alpha}$ expansion from the all-order results, we identify the higher-order QED effects of order $m{\ensuremath{\alpha}}^{7}$ and higher. Combining the higher-order remainder with the results complete through order $m{\ensuremath{\alpha}}^{6}$ from Yerokhin and Pachucki [Phys. Rev. A 81, 022507 (2010)], we obtain the most accurate theoretical predictions for the ground and nonmixing $n=2$ states of heliumlike ions with $Z=5\text{--}30$. For the mixing $2\phantom{\rule{0.16em}{0ex}}^{1}P_{1}$ and $2\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ 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 $Z>10$.