Please wait a minute...
Chin. Phys. B, 2023, Vol. 32(2): 023601    DOI: 10.1088/1674-1056/ac6db9
ATOMIC AND MOLECULAR PHYSICS Prev   Next  

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
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$^+$.
Keywords:  exotic atom      pionic helium      fine structure      hyperfine structure  
Received:  31 January 2022      Revised:  14 April 2022      Accepted manuscript online:  07 May 2022
PACS:  36.10.-k (Exotic atoms and molecules (containing mesons, antiprotons and other unusual particles))  
  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)  
Fund: 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.
Corresponding Authors:  Zhen-Xiang Zhong     E-mail:  zxzhong@wipm.ac.cn

Cite this article: 

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 2023 Chin. Phys. B 32 023601

[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
[1] Spin pumping by higher-order dipole-exchange spin-wave modes
Peng Wang(王鹏). Chin. Phys. B, 2023, 32(3): 037601.
[2] Hyperfine structures and the field effects of IBr molecule in its rovibronic ground state
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). Chin. Phys. B, 2021, 30(11): 113301.
[3] Low temperature Pmmm and C2/m phases in Sr2CuO3+δ high temperature superconductor
Hai-Bo Wang(王海波), Zhen-Lin Luo(罗震林), Yuan-Jun Yang(杨远俊), Qing-Qing Liu(刘清青), Si-Xia Hu(胡思侠), Meng-Meng Yang(杨蒙蒙), Chang-Qing Jin(靳常青), Chen Gao(高琛). Chin. Phys. B, 2019, 28(5): 056103.
[4] Velocity-selective spectroscopy measurements of Rydberg fine structure states in a hot vapor cell
Jun He(何军), Dongliang Pei(裴栋梁), Jieying Wang(王杰英), Junmin Wang(王军民). Chin. Phys. B, 2017, 26(11): 113202.
[5] Stark effect of the hyperfine structure of ICl in its rovibronic ground state: Towards further molecular cooling
Qing-Hui Wang(王庆辉), Xu-Ping Shao(邵旭萍), Xiao-Hua Yang(杨晓华). Chin. Phys. B, 2016, 25(1): 013301.
[6] Manipulating coupling state and magnetism of Mn-doped ZnO nanocrystals by changing the coordination environment of Mn via hydrogen annealing
Yan Cheng(程岩), Wen-Xian Li(李文献), Wei-Chang Hao(郝维昌), Huai-Zhe Xu(许怀哲), Zhong-Fei Xu(徐忠菲), Li-Rong Zheng(郑离荣), Jing Zhang(张静),Shi-Xue Dou(窦士学), Tian-Min Wang(王天民). Chin. Phys. B, 2016, 25(1): 017301.
[7] Structure and chemical valence study of Srn+1RunO3n+1 (n=1, 2, ∞) series
Zheng Long (郑龙), Zhu Xiao-Qin (朱小芹), Sui Yong-Xing (眭永兴), Xue Jian-Zhong (薛建忠), Liu Bo (刘波), Pei Ming-Xu (裴明旭). Chin. Phys. B, 2015, 24(5): 056101.
[8] Precision calculation of fine structure in helium and Li+
Zhang Pei-Pei (张佩佩), Zhong Zhen-Xiang (钟振祥), Yan Zong-Chao (严宗朝), Shi Ting-Yun (史庭云). Chin. Phys. B, 2015, 24(3): 033101.
[9] Spectrally selective optical pumping in Doppler-broadened cesium atoms
Zhang Jun-Hai (张军海), Zeng Xian-Jin (曾宪金), Li Qing-Meng (李庆萌), Huang Qiang (黄强), Sun Wei-Min (孙伟民). Chin. Phys. B, 2013, 22(5): 053202.
[10] The variation of Mn-dopant distribution state with x and its effect on the magnetic coupling mechanism in Zn1-xMnxO nanocrystals
Cheng Yan (程岩), Hao Wei-Chang (郝维昌), Li Wen-Xian (李文献), Xu Huai-Zhe (许怀哲), Chen Rui (陈蕊), Dou Shi-Xue (窦士学). Chin. Phys. B, 2013, 22(10): 107501.
[11] A theoretical study of the oxygen K-edge near-edge X-ray absorption ne structure of N2O/Ir(110)
Wu Tai-Quan(吴太权), Zhu Ping(朱萍), Wang Xin-Yan(王新燕), and Luo Hong-Lei (罗宏雷) . Chin. Phys. B, 2012, 21(7): 076801.
[12] Influence of reducing anneal on the ferromagnetism in single crystalline Co-doped ZnO thin films
Lu Zhong-Lin(路忠林), Zou Wen-Qin(邹文琴), Xu Ming-Xiang (徐明祥), and Zhang Feng-Ming(张凤鸣). Chin. Phys. B, 2010, 19(5): 056101.
[13] Transition energy and dipole oscillator strength for 1s22p-1s2nd of Cr2l+ ion
Wang Zhi-Wen(王治文), Liu Ying(刘影), Hu Mu-Hong(胡木宏), Li Xin-Ru(李新汝), and Wang Ya-Nan(王亚男). Chin. Phys. B, 2008, 17(8): 2909-2913.
[14] Determination of the sites of Fe atoms in Fe-substituted Mn12
Cao Hui-Bo(曹慧波), Chen Dong-Liang(陈栋梁), He Lun-Hua(何伦华), Zhang Jun-Rong(张俊荣), Wang Fang-Wei(王芳卫), Wu Zi-Yu(吴自玉), and Yan Qi-Wei(严启伟). Chin. Phys. B, 2007, 16(3): 784-787.
[15] Relativistic energy, fine structure and hyperfine structure of the low-lying excited states for Be-like system
Zhang Meng (张孟), Gou Bing-Cong (苟秉聪). Chin. Phys. B, 2005, 14(8): 1554-1558.
No Suggested Reading articles found!