Abstract
We report a calculation of relativistic corrections of order \(m\alpha ^7\) to the Bethe logarithm for the \(2^3S\) and \(2^3P\) states of helium-like ions. The calculation is required for improving the accuracy of theoretical energies of helium-like ions and for checking the evaluation of the \(m\alpha ^7\) effects in helium performed in Patkóš et al. (Phys Rev A 103:042809, 2021), where a significant discrepancy with experimental results was found. The large-Z limit of the relativistic Bethe logarithm is determined numerically, in excellent agreement with the analytical results obtained from the hydrogen theory.
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Data Availability Statement
The datasets generated during the current study (numerical values of the functions \(P_{Li}(k)\) and values of the asymptotic expansion constants) are available from the corresponding author on request. This manuscript has no associated data or the data will not be deposited.
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Acknowledgements
The work was supported by the Russian Science Foundation (Grant No. 20-62-46006). K.P. acknowledges support from the National Science Center (Poland) Grant No. 2017/27/B/ST2/02459. Computations were performed partly in the computer cluster “Tornado” of St. Petersburg Polytechnic University.
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VAY performed the numerical part of the calculation. VP and KP performed the derivation of formulas and the analytical part of the calculation.
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Yerokhin, V.A., Patkóš, V. & Pachucki, K. Relativistic Bethe logarithm for triplet states of helium-like ions. Eur. Phys. J. D 76, 142 (2022). https://doi.org/10.1140/epjd/s10053-022-00474-8
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DOI: https://doi.org/10.1140/epjd/s10053-022-00474-8