The leading relativistic and QED corrections to the ground state energy of the three-body system (epe) are calculated numerically using a Hylleraas correlated basis set. The accuracy of the nonrelativistic variational ground state wave function is discussed with respect to the convergence properties at the increase of the basis dimension and to the variance of the energy expectation value. Recent progress in the numerical procedure used to calculate expectation values for products of various physical operators is presented. It is shown that the nonrelativistic ground state energy can be calculated with an accuracy below the level width. The corrections to this energy include the lowest order Breit interaction, the vacuum polarization potential, one and two photon exchange contributions, the annihilation interaction, and spin-spin contact terms. The relativistic effects and the residual interactions considered here decrease the one electron binding energy from the nonrelativistic value of 0.012 005 070 232 980 10(3) a.u. to 0.011 981 051 246(2) a.u..
Relativistic and QED corrections to the $2pσ_{u}(\upsilon = 1)$ vibrational state of the $H^{+}_{2}$ molecular ion
对最近发现的第一振动$2pσ_u$态进行了相对论和QED修正。这个态具有极小的非相对论结合能$E_B=1.085045252(1)\times10^{-9}$ a. u。它的波函数在$R\approx100$ a. u处具有最大值。并延伸到数百个。结果表明，这种状态不会消失，如果高阶相对论和QED的修正，包括Casimir--Polder效应，考虑。
Application of the correlated B-spline basis functions to the leading relativistic and QED corrections of helium
B样条函数在计算原子物理中有着广泛的应用。与传统的B样条基（两个B样条的简单乘积）不同，最近发展的关联B样条基函数（C-BSBF）显式地包含了电子间坐标$r_{12}$，大大提高了极化率的计算精度[S. J. Yang \textit{et al} .，Phys. Rev. A \textbf{95}，062505（2017）]和bethe logarithm [ S. J. Yang \textit{et al} .，Phys. Rev. A \textbf{100}，042509（2019）]中的氦单重态。在这里，我们报告的扩展C-BSBF领先的相对论和QED校正计算的$1\,^1S$，$2\,^1S$，$2\,^3S$和$3\,^3S$态的氦的能级。用整体算符法计算了相对论动力学项$p_{1}^{4}$、接触势$δ^{3}(r_{1})$、$δ^{3}(r_{12})$和Araki-Sucher修正$\langle 1/r_{12}^{3} \rangle$，其中涉及的$r_{12}^n$和$r_{12}^n\ln r_{12}$是用Laplace展开式推广计算的.计算得到的基态能量分别为$δE_{rel}/α^{2}=-$ 1.951 754 7（2）和$δE_{QED}/α^{3}=$ 57.288 165（2），与以前的结果一致，这为利用C-BSBF计算高阶相对论效应和…
Non-adiabatic, Relativistic, and Leading-order QED Corrections for Rovibrational Intervals of $^4$He$_2^+$ ($X\ ^2Σ_\mathrm{u}^+$)
计算了$^4$ He $_2^+$分子离子在其$X\ ^2Σ_\text{u}^+$基态电子态的振转间隔，包括非绝热、相对论和首阶量子电动力学修正.对基态和基振动的转动激发序列进行了理论和实验的一致性分析。计算得到的最低能量转动间隔为$70.937\ 69(10)$ cm $^{-1}$，与最近报道的实验值$70.937\ 589(23)(60)_\text{sys}$ cm $^{-1}$ [L. Semeria，P. Jansen，G. M. Camenisch，F. Mellini，H. Schmutz和F. Merkt，Phys. Rev. Lett. 124，213001（2020）]。
