Fine and hyperfine structures of pionic helium atoms

doi:10.1088/1674-1056/ac6db9

中国物理B ›› 2023, Vol. 32 ›› Issue (2): 23601-023601.doi: 10.1088/1674-1056/ac6db9

Fine and hyperfine structures of pionic helium atoms

Zhi-Da Bai(白志达)^1,2, Zhen-Xiang Zhong(钟振祥)^1,†, Zong-Chao Yan(严宗朝)^3,1, and Ting-Yun Shi(史庭云)¹

1 State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China;
2 University of Chinese Academy of Sciences, Beijing 100049, China;
3 Department of Physics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3, Canada

收稿日期:2022-01-31 修回日期:2022-04-14 接受日期:2022-05-07 出版日期:2023-01-10 发布日期:2023-01-31
通讯作者: Zhen-Xiang Zhong E-mail:zxzhong@wipm.ac.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11974382 and 11474316). ZCY acknowledges the support from NSERC and SHARCnet of Canada.

Fine and hyperfine structures of pionic helium atoms

Zhi-Da Bai(白志达)^1,2, Zhen-Xiang Zhong(钟振祥)^1,†, Zong-Chao Yan(严宗朝)^3,1, and Ting-Yun Shi(史庭云)¹

1 State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China;
2 University of Chinese Academy of Sciences, Beijing 100049, China;
3 Department of Physics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3, Canada

Received:2022-01-31 Revised:2022-04-14 Accepted:2022-05-07 Online:2023-01-10 Published:2023-01-31
Contact: Zhen-Xiang Zhong E-mail:zxzhong@wipm.ac.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11974382 and 11474316). ZCY acknowledges the support from NSERC and SHARCnet of Canada.

摘要/Abstract

摘要： The fine and hyperfine structures of pionic helium metastable states is calculated within the formalism of the Breit-Pauli Hamiltonian by using the variationally generated wave functions in Hylleraas coordinates. Our results not only verify the existing values of Hori ${\it et al.}$ [${Phys. Rev. A} {\bf 89}$, 042515 (2014)] for the fine structure of $\pi^4$He$^+$, but also determine the hyperfine structure of $\pi^3$He$^+$.

关键词: exotic atom, pionic helium, fine structure, hyperfine structure

Abstract: The fine and hyperfine structures of pionic helium metastable states is calculated within the formalism of the Breit-Pauli Hamiltonian by using the variationally generated wave functions in Hylleraas coordinates. Our results not only verify the existing values of Hori ${\it et al.}$ [${Phys. Rev. A} {\bf 89}$, 042515 (2014)] for the fine structure of $\pi^4$He$^+$, but also determine the hyperfine structure of $\pi^3$He$^+$.

Key words: exotic atom, pionic helium, fine structure, hyperfine structure

中图分类号: (Exotic atoms and molecules (containing mesons, antiprotons and other unusual particles))

36.10.-k

31.15.aj (Relativistic corrections, spin-orbit effects, fine structure; hyperfine structure) 31.15.ac (High-precision calculations for few-electron (or few-body) atomic systems)

Zhi-Da Bai(白志达), Zhen-Xiang Zhong(钟振祥), Zong-Chao Yan(严宗朝), and Ting-Yun Shi(史庭云). Fine and hyperfine structures of pionic helium atoms[J]. 中国物理B, 2023, 32(2): 23601-023601.

Zhi-Da Bai(白志达), Zhen-Xiang Zhong(钟振祥), Zong-Chao Yan(严宗朝), and Ting-Yun Shi(史庭云). Fine and hyperfine structures of pionic helium atoms[J]. Chin. Phys. B, 2023, 32(2): 23601-023601.

参考文献

[1] Hori M, Sótér A and Korobov V I 2014 Phys. Rev. A 89 042515
[2] Hori M, Aghai-Khozani H, Sótér A, Dax A and Barna D 2020 Nature 581 37
[3] Hori M, Aghai-Khozani H, Sótér A, Dax A and Barna D 2021 Few-Body Syst. 62 1
[4] Hori M, Aghai-Khozani H, Sótér A, Dax A and Barna D 2021 SciPost Phys. Proc. 5 26
[5] Korobov V I, Bakalov D and Monkhorst H J 1999 Phys. Rev. A 59 R919
[6] Beringer J, Arguin J F, Barnett R M, et al. 2012 Phys. Rev. D 86 010001
[7] Mohr P J, Taylor B N and Newell D B 2012 Rev. Mod. Phys. 84 1527
[8] Eides M I, Grotch H and Shelyut V A 2001 Phys. Rep. 342 63
[9] Feshbach H 1962 Ann. Phys. 19 287
[10] Hahn Y, O'Malley T F and Spruch L 1962 Phys. Rev. A 128 932
[11] Hu M, Yao S, Wang Y, Li W, Gu Y and Zhong Z 2016 Chem. Phys. Lett. 654 114
[12] Drake G W F 2020 J. Phys. B 53 223001
[13] Altick P L and Moore E N 1965 Phys. Rev. Lett. 15 100
[14] Perkins J F 1969 Phys. Rev. 178 89
[15] Cassar M M and Drake G W F 2004 J. Phys. B 37 2485
[16] Zhong Z, Tong X, Yan Z and Shi T 2015 Chin. Phys. B 24 053102
[17] Korobov V I 2003 Phys. Rev. A 67 062501
[18] Yan Z, Zhang J and Li Y 2003 Phys. Rev. A 67 062504
[19] Drake G W F and Yan Z 1994 Chem. Phys. Lett. 229 486
[20] Bethe H A and Salpeter E E 2012 Quantum mechanics of one-and two-electron atoms (Springer Science & Business Media)
[21] Berestetskii V B, Lifshitz E M and Pitaevskii L P 1982 Quantum Electrodynamics (Butterworth-Heinemann)
[22] Korobov V I and Zhong Z X 2009 Phys. Rev. A 80 042506
[23] Pask T, Barna D, Dax A, Hayano R S, Hori M, Horváth D, Juhász B, Malbrunot C, Marton J, Ono N, Suzuki K, Zmeskal J and Widmann E 2008 J. Phys. B 41 081008
[24] Pask T, Barna D, Dax A, Hayano R S, Hori M, Horváth, Friedreich S, Juhász B, Massiczek O, Ono N, Sótér A and Widmann E 2009 Phys. Lett. B 678 55
[25] Ho Y K 1983 Phys. Rep. 99 1
[26] Bai Z D, Zhong Z X, Yan Z C and Shi T Y 2021 Chin. Phys. B 30 023101

Fine and hyperfine structures of pionic helium atoms

Fine and hyperfine structures of pionic helium atoms

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Peng Wang(王鹏). Spin pumping by higher-order dipole-exchange spin-wave modes[J]. 中国物理B, 2023, 32(3): 37601-037601.
[2]	Defu Wang(王得富), Xuping Shao(邵旭萍), Yunxia Huang(黄云霞), Chuanliang Li(李传亮), and Xiaohua Yang(杨晓华). Hyperfine structures and the field effects of IBr molecule in its rovibronic ground state[J]. 中国物理B, 2021, 30(11): 113301-113301.
[3]	王海波, 罗震林, 杨远俊, 刘清青, 胡思侠, 杨蒙蒙, 靳常青, 高琛. Low temperature Pmmm and C2/m phases in Sr₂CuO_3+δ high temperature superconductor[J]. 中国物理B, 2019, 28(5): 56103-056103.
[4]	何军, 裴栋梁, 王杰英, 王军民. Velocity-selective spectroscopy measurements of Rydberg fine structure states in a hot vapor cell[J]. 中国物理B, 2017, 26(11): 113202-113202.
[5]	王庆辉, 邵旭萍, 杨晓华. Stark effect of the hyperfine structure of ICl in its rovibronic ground state: Towards further molecular cooling[J]. 中国物理B, 2016, 25(1): 13301-013301.
[6]	程岩, 李文献, 郝维昌, 许怀哲, 徐忠菲, 郑离荣, 张静, 窦士学, 王天民. Manipulating coupling state and magnetism of Mn-doped ZnO nanocrystals by changing the coordination environment of Mn via hydrogen annealing[J]. 中国物理B, 2016, 25(1): 17301-017301.
[7]	郑龙, 朱小芹, 眭永兴, 薛建忠, 刘波, 裴明旭. Structure and chemical valence study of Sr_n+1Ru_nO_3n+1 (n=1, 2, ∞) series[J]. 中国物理B, 2015, 24(5): 56101-056101.
[8]	张佩佩, 钟振祥, 严宗朝, 史庭云. Precision calculation of fine structure in helium and Li⁺[J]. 中国物理B, 2015, 24(3): 33101-033101.
[9]	张军海, 曾宪金, 李庆萌, 黄强, 孙伟民. Spectrally selective optical pumping in Doppler-broadened cesium atoms[J]. 中国物理B, 2013, 22(5): 53202-053202.
[10]	程岩, 郝维昌, 李文献, 许怀哲, 陈蕊, 窦士学. The variation of Mn-dopant distribution state with x and its effect on the magnetic coupling mechanism in Zn_1-xMn_xO nanocrystals[J]. 中国物理B, 2013, 22(10): 107501-107501.
[11]	吴太权, 朱萍, 王新燕, 罗宏雷. A theoretical study of the oxygen K-edge near-edge X-ray absorption ne structure of N₂O/Ir(110)[J]. 中国物理B, 2012, 21(7): 76801-076801.
[12]	路忠林, 邹文琴, 徐明祥, 张凤鸣. Influence of reducing anneal on the ferromagnetism in single crystalline Co-doped ZnO thin films[J]. 中国物理B, 2010, 19(5): 56101-056101.
[13]	王治文, 刘影, 胡木宏, 李新汝, 王亚男. Transition energy and dipole oscillator strength for 1s²2p-1s²nd of Cr^2l+ ion[J]. 中国物理B, 2008, 17(8): 2909-2913.
[14]	曹慧波, 陈栋梁, 何伦华, 张俊荣, 王芳卫, 吴自玉, 严启伟. Determination of the sites of Fe atoms in Fe-substituted Mn₁₂[J]. 中国物理B, 2007, 16(3): 784-787.
[15]	张孟, 苟秉聪. Relativistic energy, fine structure and hyperfine structure of the low-lying excited states for Be-like system[J]. 中国物理B, 2005, 14(8): 1554-1558.