中国物理B ›› 2022, Vol. 31 ›› Issue (3): 30301-030301.doi: 10.1088/1674-1056/ac1b88

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Geometric quantities of lower doubly excited bound states of helium

Chengdong Zhou(周成栋)1, Yuewu Yu(余岳武)1, Sanjiang Yang(杨三江)2,†, and Haoxue Qiao(乔豪学)1,‡   

  1. 1 School of Physics and Technology, Wuhan University, Wuhan 430072, China;
    2 College of Physics and Electronic Science, Hubei Normal University, Huangshi 435002, China
  • 收稿日期:2021-05-30 修回日期:2021-07-18 接受日期:2021-08-07 出版日期:2022-02-22 发布日期:2022-02-14
  • 通讯作者: Sanjiang Yang, Haoxue Qiao E-mail:s.yang@whu.edu.cn;qhx@whu.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 12074295). The authors thank Yongbo Tang for the meaningful discussion. The numerical calculations in this article were performed on the supercomputing system in the Supercomputing Center of Wuhan University.

Geometric quantities of lower doubly excited bound states of helium

Chengdong Zhou(周成栋)1, Yuewu Yu(余岳武)1, Sanjiang Yang(杨三江)2,†, and Haoxue Qiao(乔豪学)1,‡   

  1. 1 School of Physics and Technology, Wuhan University, Wuhan 430072, China;
    2 College of Physics and Electronic Science, Hubei Normal University, Huangshi 435002, China
  • Received:2021-05-30 Revised:2021-07-18 Accepted:2021-08-07 Online:2022-02-22 Published:2022-02-14
  • Contact: Sanjiang Yang, Haoxue Qiao E-mail:s.yang@whu.edu.cn;qhx@whu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 12074295). The authors thank Yongbo Tang for the meaningful discussion. The numerical calculations in this article were performed on the supercomputing system in the Supercomputing Center of Wuhan University.

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摘要： Expectation values of single electron and interelectronic geometric quantities such as $\langle r\rangle$, $\langle r_{12}\rangle$, $\langle r_<\rangle$, $\langle r_>\rangle$, $\langle \cos\theta_{12}\rangle$ and $\langle \theta_{12}\rangle$ are calculated for doubly excited $2{\rm p}n{\rm p}\,{}^1P^{\,\rm e}\,(3\leq n\leq5),\, 2{\rm p}n{\rm p}\,{}^3\!P^{\,\rm e}\,(2\leq n\leq5)$ and $2{\rm p}n{\rm d}\,{}^{1,3}D^{\,\rm o}\,(3\leq n\leq5)$ states of helium using Hylleraas-$B$-spline basis set. The energy levels converge to at least 10 significant digits in our calculations. The extrapolated values of geometric quantities except for $\langle \theta_{12}\rangle$ reach 10 significant digits as well; $\langle \theta_{12}\rangle$ reaches at least 7 significant digits using a multipole expansion approach. Our results provide a precise reference for future research.

关键词: doubly excited states, unnatural parity, Hylleraas-$B$-spline, geometric quantities

Abstract: Expectation values of single electron and interelectronic geometric quantities such as $\langle r\rangle$, $\langle r_{12}\rangle$, $\langle r_<\rangle$, $\langle r_>\rangle$, $\langle \cos\theta_{12}\rangle$ and $\langle \theta_{12}\rangle$ are calculated for doubly excited $2{\rm p}n{\rm p}\,{}^1P^{\,\rm e}\,(3\leq n\leq5),\, 2{\rm p}n{\rm p}\,{}^3\!P^{\,\rm e}\,(2\leq n\leq5)$ and $2{\rm p}n{\rm d}\,{}^{1,3}D^{\,\rm o}\,(3\leq n\leq5)$ states of helium using Hylleraas-$B$-spline basis set. The energy levels converge to at least 10 significant digits in our calculations. The extrapolated values of geometric quantities except for $\langle \theta_{12}\rangle$ reach 10 significant digits as well; $\langle \theta_{12}\rangle$ reaches at least 7 significant digits using a multipole expansion approach. Our results provide a precise reference for future research.

Key words: doubly excited states, unnatural parity, Hylleraas-$B$-spline, geometric quantities

中图分类号:  (Solutions of wave equations: bound states)

  • 03.65.Ge
31.15.-p (Calculations and mathematical techniques in atomic and molecular physics)