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等离子体环境中相对论效应对类氢离子光电离过程的影响

戈迪 赵国鹏 祁月盈 陈晨 高俊文 侯红生

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等离子体环境中相对论效应对类氢离子光电离过程的影响

戈迪, 赵国鹏, 祁月盈, 陈晨, 高俊文, 侯红生

Influence of relativistic effects on photoionization process of hydrogen-like ions in plasma environment

Ge Di, Zhao Guo-Peng, Qi Yue-Ying, Chen Chen, Gao Jun-Wen, Hou Hong-Sheng
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  • 本文在偶极近似下计算了Debye等离子体环境中C5+, Al12+ 和W73+ 离子的光电离截面, 重点研究了相对论效应对势形共振、Cooper极小和虚态效应的影响. 研究结果表明, 相对论效应随核电荷数的增大而增大, 使得精细结构劈裂越来越显著, 在光电离截面中出现了双共振结构的现象, 并且共振峰的大小、宽度和位置的差异都随着核电荷数的增加而越来越大; 分截面出现Cooper极小位置的差异也越来越大, 在总截面中叠加的极小值越来越浅; 出现虚态效应的等离子体屏蔽长度以及低能区光电离截面虚态增强的截面值也存在明显差异.
    In this study, the photoionization cross sections of C5+, Al12+, and W73+ ions in a Debye plasma environment are calculated in the dipole approximation. The main emphasis is placed on investigating the influence of relativistic effects on shape resonances, Cooper minima, and virtual state effects. The relativistic effects lead to fine-structure splittings, allowing the appearance of double-shape resonance peaks in the total cross-section. Because the width and energy position of resonance peak are affected by the near critical screening length, the increase of nuclear charge Z leads to the significant differences in the size, width, and position of the double-shape resonance peak. The energy position of Cooper minimum in the photoelectrons is related to the critical screening length corresponding to the final continuum state. Unlike the deeper minima observed in the total photoionization cross-sections for C5+ and Al12+ ions, for the higher nuclear charge of W73+ ions, the significant fine-structure splitting arising from relativistic effects results in substantial differences in the positions of the Cooper minima in the partial cross-sections. Therefore, when superimposed on the total cross section, these minima appear shallower. The W73+ ion has a higher nuclear charge, and the screening length related to the virtual state effect is completely different from that of C5+ ion and Al12+ ion. Moreover, for the same screening length, there is a significant difference in the virtual state enhancement amplitude between C5+ ion and Al12+ ion in the low energy region .
      通信作者: 赵国鹏, guopengzhao@zjxu.edu.cn ; 祁月盈, yying_qi@zjxu.edu.cn
    • 基金项目: 国家自然科学基金 (批准号: 12105119)和浙江省清洁能源与碳中和重点实验室开放基金(批准号: 204022023006A)资助的课题.
      Corresponding author: Zhao Guo-Peng, guopengzhao@zjxu.edu.cn ; Qi Yue-Ying, yying_qi@zjxu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12105119) and the Open Foundation for Key Laboratory of Clean Energy and Carbon Neutrality of Zhejiang Province, China (Grant No. 204022023006A).
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    Qi Y Y, Wang J G, Janev R K 2009 Phys. Rev. A 80 063404Google Scholar

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    Shore B W 1975 J. Phys. B 8 2023Google Scholar

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    Qi Y Y, Wang J G, Janev R K 2011 Eur. Phys. J. D 63 327Google Scholar

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    Cooper J W 1962 Phys. Rev. 128 681Google Scholar

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    Yin R Y, Pratt R H 1987 Phys. Rev. A 35 1149Google Scholar

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    Combet-Farnoux F 1972 Proceedings of the International Conference on Inner Shell Ionization Phenomena (Vol. 2) (Atlanta: University of Georgia Press) p1130

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    Lin C Y, Ho Y K 2010 Phys. Rev. A 81 033405Google Scholar

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    Lin C Y, Ho Y K 2010 Phys. Plasmas 17 093302Google Scholar

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    Lin C Y, Ho Y K 2011 Phys. Scr. T 144 014051Google Scholar

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    Xie L Y, Wang J G, Janev R K 2014 Phys. Plasmas 21 063304Google Scholar

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    Zheng X, Chi H C, Lin S T, Jiang G, Qiao C, Huang K N 2019 Indian J. Phys. 93 267Google Scholar

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    Shukla P K, Eliasson B 2008 Phys. Lett. A 372 2897Google Scholar

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    Qi Y Y, Wang J G, Janev R K 2017 Phys. Plasmas 24 062110Google Scholar

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    Das M 2014 Phys. Plasmas 21 012709Google Scholar

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    Chen Z B, Wang K 2020 J. Quant. Spectrosc. Radiat. Transfer 245 106847Google Scholar

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    Sharma R, Goyal A 2022 Indian J. Phys. 96 1829Google Scholar

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    Zeng J, Li Y, Gao C, Yuan J 2020 A& A 634 A117Google Scholar

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    Zeng J, Li Y, Yuan J 2021 J. Quant. Spectrosc. Radiat. Transfer 272 107777Google Scholar

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    Li X, Rosmej F B 2020 Phys. Lett. A 384 126478Google Scholar

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    Dawra D, Dimri M, Singh A K, Jha A K S, Pandey R K, Sharma R, Mohan M 2021 Phys. Plasmas 28 112706Google Scholar

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    Singh D, Varshni Y P 1983 Phys. Rev. A 28 2606Google Scholar

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    Stanton L G, Murillo M S 2015 Phys. Rev. E 91 033104Google Scholar

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    Chen Z B, Qi Y Y, Sun H Y, Zhao G P, Liu P F, Wang K 2020 J. Quant. Spectrosc. Radiat. Transfer 253 107170Google Scholar

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    Zhao G P, Chen C, Liu L, Chen Z B, Qi Y Y, Wang J G 2022 Phys. Plasmas 29 053301Google Scholar

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    Baimbetov F B, Nurekenov Kh T, Ramazanov T S 1995 Phys. Lett. A 202 211Google Scholar

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    Das N, Das B, Ghoshal A 2022 Phys. Plasmas 29 073505Google Scholar

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    Chen Z B, Hu H W, Ma K, Liu X B, Guo X L, Li S, Zhu B H, Huang L, Wang K 2018 Phys. Plasmas 25 032108Google Scholar

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    Xie H H, Jiao L G, Liu A, Ho Y K 2021 Int. J. Quantum Chem.   121 e26653Google Scholar

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    Wu J Y, Wu Y, Qi Y Y, Wang J G, Janev R K, Zhang S B 2019 Phys. Rev. A 99 012705Google Scholar

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    Wu J Y, Qi Y Y, Cheng Y J, Wu Y, Wang J G, Janev R K, Zhang S B 2020 Phys. Plasmas 27 043301Google Scholar

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    Zhao G P, Qi Y Y, Liu L, Wang J G, Janev R K 2019 Phys. Plasmas 26 063509Google Scholar

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    Chen C, Zhao G P, Chen Z B, Qi Y Y, Liu L, Wu Y, Wang J G 2023 Phys. Plasmas 30 123503Google Scholar

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    Qi Y Y, Ning L N, Wang J G, Qu Y Z 2013 Phys. Plasmas 20 123301Google Scholar

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    Qi Y Y, Ye D D, Wang J G, Qu Y Z 2015 Chin. Phys. B 24 033403Google Scholar

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    Hoarty D J, Allan P, James S F, Brown C R D, Hobbs L M R, Hill M P, Harris J W O, Morton J, Brookes M G, Shepherd R, Dunn J, Chen H, Marley E V, Beiersdorfer P, Chung H K, Lee R W, Brown G, Emig J 2013 Phys. Rev. Lett. 110 265003Google Scholar

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    Gormezano C, Sips A C C, Luce T C, Ide S, Becoulet A 2007 Nucl. Fusion 47 S285Google Scholar

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    Dyall K G, Grant I P, Johnson C T, Parpia F A, Plummer E P 1989 Comput. Phys. Commun. 55 425Google Scholar

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    Grant I P 1974 J. Phys. B: At. Mol. Phys. 7 1458

    [41]

    Jönsson P, He X, Froese Fischer C, Grant I P 2007 Comput. Phys. Commun. 177 597Google Scholar

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    Tews M G, Perger W F 2001 Comput. Phys. Commun. 141 205Google Scholar

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    Perger W F, Halabuka Z, Trautmann D 1993 Comput. Phys. Commun. 76 250Google Scholar

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    Landau L D, Lifshitz E M 1958 Quantum Mechanics: Non-Relativistic Theory (London: Pergamon

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    Bilycki M, Stachov A, Karwowski J, Mukherjee P K 2007 Chem. Phys. 331 346Google Scholar

  • 图 1  (a) C5+, (b) Al12+ 和 (c) W73+ 离子初态为1s1/2的总标度光电离截面随标度的光电子能量的变化关系, 不同颜色的曲线对应不同的标度屏蔽长度

    Fig. 1.  Behavior of the total 1s1/2 scaled photoionization cross sections of (a) C5+, (b) Al12+ and (c) W73+ ion as a function of scaled photoelectron energy. The colors of the lines are for different scaled screening lengths.

    图 2  W73+ 离子初态为1s1/2的跃迁 (a) 1s1/2→εp1/2, (b) 1s1/2→εp3/2贡献的标度的分截面和(c)总光电离截面随标度的光电子能量的变化关系, 不同颜色的曲线对应不同的标度的屏蔽长度

    Fig. 2.  Behavior of scaled partial (a) 1s1/2→εp1/2, (b) 1s1/2→εp3/2 and (c) total 1s1/2 photoionization cross sections of W73+ ion as a function of scaled photoelectron energy. The colors of the lines are for different scaled screening lengths.

    图 3  (a) C5+, (b) Al12+ 和 (c) W73+ 离子初态为2s1/2的总标度光电离截面随标度的光电子能量的变化关系, 不同颜色的曲线对应不同的标度的屏蔽长度

    Fig. 3.  Behavior of the total 2s1/2 scaled photoionization cross sections of (a) C5+, (b) Al12+ and (c) W73+ ion as a function of scaled photoelectron energy. The colors of the lines are for different scaled screening lengths.

    图 4  (a) C5+, (b) Al12+ 和 (c) W73+ 离子初态为2s1/2的总标度光电离截面随标度的光电子能量的变化关系, 不同颜色的曲线对应不同的标度的屏蔽长度

    Fig. 4.  Behavior of the total 2s1/2 scaled photoionization cross sections of (a) C5+, (b) Al12+ and (c) W73+ ion as a function of scaled photoelectron energy. The colors of the lines are for different scaled screening lengths

    图 5  W73+ 离子跃迁 (a) 2s1/2→εp1/2和 (b) 2s1/2→εp3/2贡献的分标度截面随标度的光电子能量的变化关系. 不同颜色的曲线对应不同的标度的屏蔽长度

    Fig. 5.  Behavior of partial (a) 2s1/2→εp1/2 and (b) 2s1/2→εp3/2 scaled photoionization cross sections of W73+ ion as a function of scaled photoelectron energy. The colors of the lines are for different scaled screening lengths.

    图 6  (a) C5+, (b) Al12+ 和 (c) W73+ 离子初态为2p1/2的总标度光电离截面随标度的光电子能量的变化关系, 不同颜色的曲线对应不同的标度的屏蔽长度

    Fig. 6.  Behavior of the total 2p1/2 scaled photoionization cross sections of (a) C5+, (b) Al12+ and (c) W73+ ion as a function of scaled photoelectron energy. The colors of the lines are for different scaled screening lengths.

    图 7  (a) C5+, (b) Al12+ 和 (c) W73+ 离子初态为2p3/2的总标度光电离截面随标度的光电子能量的变化关系, 不同颜色的曲线对应不同的标度的屏蔽长度

    Fig. 7.  Behavior of the total 2p3/2 scaled photoionization cross sections of (a) C5+, (b) Al12+ and (c) W73+ ion as a function of scaled photoelectron energy. The colors of the lines are for different scaled screening lengths.

    图 8  Al12+ 离子跃迁 (a) 2p3/2→εs1/2, (b) 2p3/2→εd3/2和(c) 2p3/2→εd5/2贡献的分标度截面随标度的光电子能量的变化关系. 不同颜色的曲线对应不同的标度的屏蔽长度

    Fig. 8.  Behavior of partial (a) 2p3/2→εs1/2, (b) 2p3/2→εd3/2, and (c) 2p3/2→εd5/2 scaled photoionization cross sections of Al12+ ion as a function of scaled photoelectron energy. The colors of the lines are for different scaled screening lengths.

    表 1  C5+, Al12+ 和 W73+离子$ n \leqslant 3 $的临界标度屏蔽长度$ \delta _{nlj}^{\text{c}} $

    Table 1.  Values of critical scaled screening lengths $ \delta _{nlj}^{\text{c}} $ for C5+, Al12+, and W73+ ions for $ n \leqslant 3 $.

    n s1/2 p1/2 p3/2 d3/2 d5/2
    1C5+0.8397
    Al12+0.8389
    W73+0.8035
    2C5+3.22224.53914.5406
    Al12+3.21674.53244.5395
    W73+2.98104.23984.4945
    3C5+7.16818.86908.871410.946410.9472
    Al12+7.15738.85708.868010.942510.9460
    W73+6.68878.33258.729310.782210.8983
    下载: 导出CSV
  • [1]

    Qi Y Y, Wang J G, Janev R K 2009 Phys. Rev. A 80 063404Google Scholar

    [2]

    Shore B W 1975 J. Phys. B 8 2023Google Scholar

    [3]

    Qi Y Y, Wang J G, Janev R K 2011 Eur. Phys. J. D 63 327Google Scholar

    [4]

    Cooper J W 1962 Phys. Rev. 128 681Google Scholar

    [5]

    Yin R Y, Pratt R H 1987 Phys. Rev. A 35 1149Google Scholar

    [6]

    Combet-Farnoux F 1972 Proceedings of the International Conference on Inner Shell Ionization Phenomena (Vol. 2) (Atlanta: University of Georgia Press) p1130

    [7]

    Lin C Y, Ho Y K 2010 Phys. Rev. A 81 033405Google Scholar

    [8]

    Lin C Y, Ho Y K 2010 Phys. Plasmas 17 093302Google Scholar

    [9]

    Lin C Y, Ho Y K 2011 Phys. Scr. T 144 014051Google Scholar

    [10]

    Xie L Y, Wang J G, Janev R K 2014 Phys. Plasmas 21 063304Google Scholar

    [11]

    Zheng X, Chi H C, Lin S T, Jiang G, Qiao C, Huang K N 2019 Indian J. Phys. 93 267Google Scholar

    [12]

    Shukla P K, Eliasson B 2008 Phys. Lett. A 372 2897Google Scholar

    [13]

    Qi Y Y, Wang J G, Janev R K 2017 Phys. Plasmas 24 062110Google Scholar

    [14]

    Das M 2014 Phys. Plasmas 21 012709Google Scholar

    [15]

    Chen Z B, Wang K 2020 J. Quant. Spectrosc. Radiat. Transfer 245 106847Google Scholar

    [16]

    Sharma R, Goyal A 2022 Indian J. Phys. 96 1829Google Scholar

    [17]

    Zeng J, Li Y, Gao C, Yuan J 2020 A& A 634 A117Google Scholar

    [18]

    Zeng J, Li Y, Yuan J 2021 J. Quant. Spectrosc. Radiat. Transfer 272 107777Google Scholar

    [19]

    Li X, Rosmej F B 2020 Phys. Lett. A 384 126478Google Scholar

    [20]

    Dawra D, Dimri M, Singh A K, Jha A K S, Pandey R K, Sharma R, Mohan M 2021 Phys. Plasmas 28 112706Google Scholar

    [21]

    Singh D, Varshni Y P 1983 Phys. Rev. A 28 2606Google Scholar

    [22]

    Stanton L G, Murillo M S 2015 Phys. Rev. E 91 033104Google Scholar

    [23]

    Zhao G P, Xie L Y, Liu L, Wang J G, Janev R K 2018 Phys. Plasmas 25 083302Google Scholar

    [24]

    Chen Z B, Qi Y Y, Sun H Y, Zhao G P, Liu P F, Wang K 2020 J. Quant. Spectrosc. Radiat. Transfer 253 107170Google Scholar

    [25]

    Zhao G P, Chen C, Liu L, Chen Z B, Qi Y Y, Wang J G 2022 Phys. Plasmas 29 053301Google Scholar

    [26]

    Baimbetov F B, Nurekenov Kh T, Ramazanov T S 1995 Phys. Lett. A 202 211Google Scholar

    [27]

    Das N, Das B, Ghoshal A 2022 Phys. Plasmas 29 073505Google Scholar

    [28]

    Chen Z B 2023 Few-Body Syst. 64 74Google Scholar

    [29]

    Chen Z B, Hu H W, Ma K, Liu X B, Guo X L, Li S, Zhu B H, Huang L, Wang K 2018 Phys. Plasmas 25 032108Google Scholar

    [30]

    Xie H H, Jiao L G, Liu A, Ho Y K 2021 Int. J. Quantum Chem.   121 e26653Google Scholar

    [31]

    Wu J Y, Wu Y, Qi Y Y, Wang J G, Janev R K, Zhang S B 2019 Phys. Rev. A 99 012705Google Scholar

    [32]

    Wu J Y, Qi Y Y, Cheng Y J, Wu Y, Wang J G, Janev R K, Zhang S B 2020 Phys. Plasmas 27 043301Google Scholar

    [33]

    Zhao G P, Qi Y Y, Liu L, Wang J G, Janev R K 2019 Phys. Plasmas 26 063509Google Scholar

    [34]

    Chen C, Zhao G P, Chen Z B, Qi Y Y, Liu L, Wu Y, Wang J G 2023 Phys. Plasmas 30 123503Google Scholar

    [35]

    Qi Y Y, Ning L N, Wang J G, Qu Y Z 2013 Phys. Plasmas 20 123301Google Scholar

    [36]

    Qi Y Y, Ye D D, Wang J G, Qu Y Z 2015 Chin. Phys. B 24 033403Google Scholar

    [37]

    Hoarty D J, Allan P, James S F, Brown C R D, Hobbs L M R, Hill M P, Harris J W O, Morton J, Brookes M G, Shepherd R, Dunn J, Chen H, Marley E V, Beiersdorfer P, Chung H K, Lee R W, Brown G, Emig J 2013 Phys. Rev. Lett. 110 265003Google Scholar

    [38]

    Gormezano C, Sips A C C, Luce T C, Ide S, Becoulet A 2007 Nucl. Fusion 47 S285Google Scholar

    [39]

    Dyall K G, Grant I P, Johnson C T, Parpia F A, Plummer E P 1989 Comput. Phys. Commun. 55 425Google Scholar

    [40]

    Grant I P 1974 J. Phys. B: At. Mol. Phys. 7 1458

    [41]

    Jönsson P, He X, Froese Fischer C, Grant I P 2007 Comput. Phys. Commun. 177 597Google Scholar

    [42]

    Tews M G, Perger W F 2001 Comput. Phys. Commun. 141 205Google Scholar

    [43]

    Perger W F, Halabuka Z, Trautmann D 1993 Comput. Phys. Commun. 76 250Google Scholar

    [44]

    Landau L D, Lifshitz E M 1958 Quantum Mechanics: Non-Relativistic Theory (London: Pergamon

    [45]

    Bilycki M, Stachov A, Karwowski J, Mukherjee P K 2007 Chem. Phys. 331 346Google Scholar

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出版历程
  • 收稿日期:  2024-01-03
  • 修回日期:  2024-01-20
  • 上网日期:  2024-02-26
  • 刊出日期:  2024-04-20

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