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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 School of Physics and Technology, Wuhan University, Wuhan 430072, China;
2 College of Physics and Electronic Science, Hubei Normal University, Huangshi 435002, China |
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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.
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Received: 30 May 2021
Revised: 18 July 2021
Accepted manuscript online: 07 August 2021
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PACS:
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03.65.Ge
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(Solutions of wave equations: bound states)
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31.15.-p
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(Calculations and mathematical techniques in atomic and molecular physics)
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| Fund: 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. |
Corresponding Authors:
Sanjiang Yang, Haoxue Qiao
E-mail: s.yang@whu.edu.cn;qhx@whu.edu.cn
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Cite this article:
Chengdong Zhou(周成栋), Yuewu Yu(余岳武), Sanjiang Yang(杨三江), and Haoxue Qiao(乔豪学) Geometric quantities of lower doubly excited bound states of helium 2022 Chin. Phys. B 31 030301
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