AI 中文总结
研究类氦和类锂离子中电子间相互作用的高阶量子电动力学贡献，基于狄拉克-库仑格林函数，通过减去虚假贡献提高积分收敛性，给出兰姆位移贡献的改进数值，计算有限核尺寸修正，降低理论预测不确定性，为相关计算提供改进方法。
AI 中文摘要
我们对类氦和类锂离子中电子间相互作用的高阶量子电动力学贡献进行了理论研究，通过在单光子交换图的光子线上插入一个虚电子-正电子回路。我们的方法基于狄拉克-库仑格林函数，考虑了虚电子对与原子核电场在精细结构常数α与原子序数Z的所有阶次的相互作用。我们表明，通过从被积函数中明确减去非规范不变的虚假贡献，可以显著提高相关积分的数值收敛性。我们给出了在广泛的核电荷数Z范围内，对兰姆位移贡献的改进数值。我们的计算与阿尔捷米耶夫等人之前对类氦离子的结果吻合良好，但在类锂情况下发现了差异。此外，我们计算了该图的有限核尺寸修正，对于重离子，其可使图的尺寸减小超过5%。改进的量子电动力学计算不仅降低了少电子离子中电子间相互作用理论预测的不确定性，而且这些方法未来还可用于改进密切相关的单电子双回路量子电动力学图的计算。
英文摘要
We present a theoretical study of the higher-order QED contribution to the interelectronic interaction in He- and Li-like ions, where a virtual electron-positron loop is inserted into the photon line of the one-photon exchange diagram. Our approach is based on the Dirac-Coulomb Green's function and accounts for the interaction of the virtual $e^+e^-$ pair with the electric field of the nucleus to all orders in $αZ$, with $α$ being the fine-structure constant and $Z$ the atomic charge number. We show that the numerical convergence of the involved integrals can be significantly improved by explicitly subtracting the non-gauge-invariant spurious contributions from the integrands. We present improved numerical values for this contribution to the Lamb shift over a wide range of nuclear charge numbers $Z$. Our calculations agree well with previous results by Artemyev and co-workers [Phys. Rev. A 56, 3529 (1997); Phys. Rev. A 60, 45 (1999)] for He-like ions, but we find a discrepancy in the Li-like case. Moreover, we calculate the finite nuclear size correction to this diagram, which can reduce its size by more than 5% for heavy ions. The improved QED calculations not only decrease the uncertainty of theoretical predictions for the interelectronic interaction in few-electron ions but the methods could also be used in the future to improve calculations of closely related one-electron two-loop QED diagrams.
