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等离子体对电子间相互作用的屏蔽效应研究

李向富 朱晓禄 蒋刚

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等离子体对电子间相互作用的屏蔽效应研究

李向富, 朱晓禄, 蒋刚

Plasma screening effect on electron-electron interactions

Li Xiang-Fu, Zhu Xiao-Lu, Jiang Gang
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  • 在计算等离子体环境中的原子结构时, 一般情况下只考虑等离子体对核-电子相互作用的屏蔽, 较少考虑其对电子-电子相互作用的屏蔽. 本文采用MCDHF (multi-configuration Dirac-Hartree-Fork)方法结合屏蔽势研究了电子-电子相互作用的等离子体屏蔽对原子结构参数的影响随电子密度、电子温度、核电荷数和束缚电子个数的变化规律. 结果表明, 对于类氦离子的基态和第一激发态, 等离子体对电子-电子相互作用的屏蔽引起的能量移动量、跃迁能移动量和跃迁几率移动量分别随着电子密度和电子温度的升高而不断增大和减小; 随着核电荷数的增大, 能量移动量逐渐增大并趋于稳定值, 跃迁能移动量和跃迁几率移动量逐渐减小并趋于0. 能量移动量随着束缚电子个数的增加而增大. 当满足电子密度(束缚电子个数)大于或者等于其临界值以及电子温度(核电荷数)小于或者等于其临界值任意一条件时, 等离子体对电子-电子相互作用的屏蔽效应不可忽略.
    In the calculation of atomic structures within the plasma environment, the plasma screening effect on nuclei - electron interactions is generally considered, but the plasma screening effect on electron - electron interactions is less considered. In this work, the MCDHF method combined with the screening potential is used to study plasma screening effect on the atomic structure parameters versus the electron density, electron temperature, nuclear charge and the number of bound electrons. For the ground states and the first excited states of helium-like ions, the energy shifts, transition energy shifts and transition probability shifts caused by the plasma screening effect on electron-electron interactions increase with the increase of electron densities and decrease with increasing the electron temperatures, respectively. With the increase of nuclear charge, the energy shifts increase gradually and tends to a stable value, while the transition energy shifts and transition probability shifts decrease gradually and tend to 0. The energy shifts increase with the increase of the number of bound electrons. The electron density, electron temperature, nuclear charge and number of bound electrons corresponding to the percentages of transition energy shifts and transition probability shifts caused by plasma screening on electron-electron interactions greater than or equal to 10%, are called as the critical electron density, critical electron temperature, critical nuclear charge and critical number of bound electrons, respectively. When one of the following four conditions is satisfied, the percentages of transition energy shifts and transition probability shifts caused by plasma screening on electron-electron interactions will be greater than or equal to 10%, and the plasma screening effect on electron - electron interactions can not be ignored. 1) The electron density is greater than or equal to the critical electron density, when the electron temperature is a fixed value. 2) The electron temperature is less than or equal to the critical electron temperature, when the electron density is a fixed value. 3) The nuclear charge is less than or equal to the critical nuclear charge, when the electron density and temperature are both fixed. 4) The number of bound electrons is greater than or equal to the critical number of bound electrons, when the electron density and temperature are both fixed.
      通信作者: 李向富, lixf808@163.com
    • 基金项目: 国家自然科学基金(批准号: 12265018)、甘肃省自然科学基金(批准号: 20JR10RA131)、甘肃省教育厅青年博士基金(批准号: 2022QB-162)和陇东学院博士基金(批准号: XYBY202005)资助的课题
      Corresponding author: Li Xiang-Fu, lixf808@163.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12265018), the Natural Science Foundation of Gansu Province, China (Grant No. 20JR10RA131), the Young Doctor Foundation of Education Department of Gansu Province, China (Grant No. 2022QB-162) and the Doctor Foundation of Longdong University, China (Grant No. XYBY202005)
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    Hu S X 2017 Phys. Rev. Lett. 119 065001Google Scholar

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    Papoulia A, Schiffmann S, Bieron J, Gaigalas G, Godefroid M, Harman Z, Jönsson P, Oreshkina N S, Pyykk P, Tupitsyn I I 2021 Phys. Rev. A 103 022815Google Scholar

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    马堃, 陈展斌, 黄时中 2019 物理学报 68 023102Google Scholar

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    Janev R K, Zhang S B, Wang J G 2016 Matter and Radiation at Extremes 1 237Google Scholar

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    Qi Y Y, Ning L N 2014 Phys. Plasmas 21 033301Google Scholar

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    Qi Y Y, Wu Y, Wang J G 2009 Phys. Plasmas 161 033507

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    Sahoo S, Ho Y K 2006 Phys. Plasmas 13 063301Google Scholar

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    Kang S, He J, Xu N, Chen C Y 2014 Commun. Theor. Phys. 62 881Google Scholar

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    Li H W, Kar S 2012 Phys. Plasmas 19 073303Google Scholar

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    Li Y Q, Wu J H, Hou Y, Yuan J M 2008 J. Phys. B: At. Mol. Opt. Phys. 41 145002Google Scholar

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    Li X D, Rosmej F B 2012 EPL 99 33001Google Scholar

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

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    White A J, Collins L A 2020 Phys. Rev. Lett. 125 055002Google Scholar

    [18]

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

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    Zhang S B, Wang J G, Janev R K 2010 Phys. Rev. Lett. 104 023203Google Scholar

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    李永强, 吴建华, 袁建民 2008 物理学报 57 4042Google Scholar

    Li Y Q, Wu J H, Yuan J M 2008 Acta Phys. Sin. 57 4042Google Scholar

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    Li B W, Dong C Z, Jiang J, Wang J G 2010 Plasma Sci. Technol. 12 372

    [22]

    Kar S, Ho Y K 2009 J. Phys. B: At. Mol. Opt. Phys. 42 044007Google Scholar

    [23]

    Mukherjee P K, Karwowski J, Diercksen Geerd H F 2002 Chem. Phys. Lett. 363 323Google Scholar

    [24]

    Chen C, Zhao G P, Qi Y Y, Liu L, Chen Z B, Wang J G 2022 Phys. Plasmas 29 072901Google Scholar

    [25]

    Chen Z B, Qi Y Y, Sun H Y, Zhao G P, Liu P F, Wang K 2020 J. Quant. Spectrosc. Radiat. Transfer 3 8

    [26]

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

    [27]

    Zhao G P, Liu L, Wang J G, Janev R K, Yan J 2018 Matter and Radiation at Extremes 3 300Google Scholar

    [28]

    Zhao G P, Liu L, Wang J G, Janev R K 2017 Phys. Plasmas 24 053509Google Scholar

    [29]

    Zhao G P, Liu L, Wang J G, Janev R K 2017 Phys. Plasmas 24 103504Google Scholar

    [30]

    Li W G, Cheng Y J, Wu J Y, Wu Y, Wang J G, Zhang S B 2021 Phys. Plasmas 28 012708Google Scholar

    [31]

    Murillo M S, Weisheit J C 1998 Phys. Rep. 302 1Google Scholar

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    Ichimaru S 1982 Rev. Mod. Phys. 54 1017Google Scholar

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

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    NIST https://www.nist.gov/pml/atomic-spectra-database

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    Jönsson P, Gaigalas G, Bieroń J, Fischer C F, Grant I P 2013 Comput. Phys. Commun. 184 2197Google Scholar

    [36]

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

    [37]

    Xie L Y, Wang J G, Janev R K, Qu Y Z, Dong C Z 2012 Eur. Phys. J. D 66 125Google Scholar

    [38]

    Chen Z B, Ma K, Hu H W, Wang K 2018 Phys. Plasmas 25 072120Google Scholar

    [39]

    Saha B, Fritzsche S 2006 Phys. Rev. E 73 036405Google Scholar

  • 图 1  当电子温度为50 eV时, $ {\rm{Al}}^{11+} $离子$ {\rm{1}}{{\rm{s}}^{\rm{2}}}{(^{\rm{1}}}{{{\rm{S}}}_{\rm{0}}}) $$ {\rm{1 s2 p}}{(^{\rm{1}}}{{{\rm{P}}}_{\rm{1}}}) $原子态的能量移动量以及$ {\rm{1}}{{\rm{s}}^{\rm{2}}}{(^{\rm{1}}}{{{\rm{S}}}_{\rm{0}}}) $$ {\rm{1 s2 p}}{(^{\rm{1}}}{{{\rm{P}}}_{\rm{1}}}) $的跃迁能移动量随电子密度的变化

    Fig. 1.  Energy shifts of $ {\rm{1}}{{\rm{s}}^{\rm{2}}}{(^{\rm{1}}}{{{\rm{S}}}_{\rm{0}}}) $ and $ {\rm{1 s2 p}}{(^{\rm{1}}}{{{\rm{P}}}_{\rm{1}}}) $ atomic states, and the transition energy shifts of $ {\rm{1}}{{\rm{s}}^{\rm{2}}}{(^{\rm{1}}}{{{\rm{S}}}_{\rm{0}}}) $$ {\rm{1 s2 p}}{(^{\rm{1}}}{{{\rm{P}}}_{\rm{1}}}) $ transition for $ {\rm{Al}}^{11+} $ ions vary with electron densities, when the electron temperature is equal to 50 eV

    图 2  当电子密度为$ 5.0\times10^{24}\;{\rm{cm}}^{-3} $时, $ {\rm{Al}}^{11+} $离子$ {\rm{1}}{{\rm{s}}^{\rm{2}}}{(^{\rm{1}}}{{{\rm{S}}}_{\rm{0}}}) $$ {\rm{1 s2 p}}{(^{\rm{1}}}{{{\rm{P}}}_{\rm{1}}}) $原子态的能量移动量以及$ {\rm{1}}{{\rm{s}}^{\rm{2}}}{(^{\rm{1}}}{{{\rm{S}}}_{\rm{0}}}) $$ {\rm{1 s2 p}}{(^{\rm{1}}}{{{\rm{P}}}_{\rm{1}}}) $的跃迁能移动量随电子温度的变化

    Fig. 2.  Energy shifts of $ {\rm{1}}{{\rm{s}}^{\rm{2}}}{(^{\rm{1}}}{{{\rm{S}}}_{\rm{0}}}) $ and $ {\rm{1 s2 p}}{(^{\rm{1}}}{{{\rm{P}}}_{\rm{1}}}) $ atomic states, and the transition energy shifts of $ {\rm{1}}{{\rm{s}}^{\rm{2}}}{(^{\rm{1}}}{{{\rm{S}}}_{\rm{0}}}) $$ {\rm{1 s2 p}}{(^{\rm{1}}}{{{\rm{P}}}_{\rm{1}}}) $ transition for $ {\rm{Al}}^{11+} $ ions vary with electron temperatures, when the electron density is equal to $ 5.0 \times 10^{24}\;{\rm{cm}}^{-3} $

    图 3  当电子密度和温度分别为$ 5.0\times10^{23}\;{\rm{cm}}^{-3} $和50 eV时, 类氦离子(Z = 6, 10, 13, 18, 22, 26, 31) $ {\rm{1}}{{\rm{s}}^{\rm{2}}}{(^{\rm{1}}}{{{\rm{S}}}_{\rm{0}}}) $$ {\rm{1 s2 p}}{(^{\rm{1}}}{{{\rm{P}}}_{\rm{1}}}) $原子态的能量移动量以及$ {\rm{1}}{{\rm{s}}^{\rm{2}}}{(^{\rm{1}}}{{{\rm{S}}}_{\rm{0}}}) $$ {\rm{1 s2 p}}{(^{\rm{1}}}{{{\rm{P}}}_{\rm{1}}}) $的跃迁能移动量随核电荷数Z的变化

    Fig. 3.  Energy shifts of $ {\rm{1}}{{\rm{s}}^{\rm{2}}}{(^{\rm{1}}}{{{\rm{S}}}_{\rm{0}}}) $ and $ {\rm{1 s2 p}}{(^{\rm{1}}}{{{\rm{P}}}_{\rm{1}}}) $ atomic states, and the transition energy shifts of $ {\rm{1}}{{\rm{s}}^{\rm{2}}}{(^{\rm{1}}}{{{\rm{S}}}_{\rm{0}}}) $$ {\rm{1 s2 p}}{(^{\rm{1}}}{{{\rm{P}}}_{\rm{1}}}) $ transition for He-like ions (Z = 6, 10, 13, 18, 22, 26, 31) vary with nuclear charge Z, when the electron density and temperature are $ 5.0\times10^{23}\;{\rm{cm}}^{-3} $ and 50 eV respectively

    表 1  电子温度为50 eV时, ${\rm{C}}^{4+}$离子$1 {\rm{s}}^2(^1 {\rm{S}}_0)$原子态的能量随电子密度的变化

    Table 1.  Energies of ${\rm{1 s}}^2(^1 {\rm{S}}_0)$ atomic state for ${\rm{C}}^{4+}$ ions vary with electron densities, when the electron temperature is 50 eV

    电子密度/$\;{\rm{cm}}^{-3}$ 德拜屏蔽强度 模型A 模型B
    $E_ {\rm{DB}}$ $E_ {\rm{DB}}$[37] $E_ {\rm{SM}}$ $E_ {\rm{DB}}$ $E_ {\rm{DB}}$[37] $E_ {\rm{SM}}$
    9.87(19) 0.01 –32.3007 –32.2978 –32.3008 –32.3106 –32.3079 –32.3108
    3.95(20) 0.02 –32.1811 –32.1783 –32.1817 –32.2011 –32.1982 –32.2016
    2.47(21) 0.05 –31.8245 –31.8215 –31.8282 –31.8740 –31.8711 –31.8775
    9.87(21) 0.1 –31.2363 –31.2324 –31.2511 –31.3345 –31.3306 –31.3482
    1.54(22) 0.125 –30.9451 –30.9412 –30.9680 –31.0673 –31.0633 –31.0885
    3.95(22) 0.2 –30.0830 –30.0790 –30.1395 –30.2758 –30.2717 –30.3284
    6.17(22) 0.25 –29.5177 –29.5137 –29.6041 –29.7565 –29.7523 –29.8370
    8.88(22) 0.3 –28.9597 –28.9557 –29.0814 –29.2436 –29.2394 –29.3571
    1.58(23) 0.4 –27.8653 –27.8614 –28.0730 –28.2372 –28.2328 –28.4309
    2.47(23) 0.5 –26.7992 –26.7963 –27.1109 –27.2557 –27.2522 –27.5467
    3.55(23) 0.6 –25.7604 –25.7576 –26.1932 –26.2986 –26.2948 –26.7027
    注1: $E_ {\rm{DB}}$表示用德拜模型计算的能量 注2: $E_ {\rm{SM}}$表示用SM模型计算的能量
    下载: 导出CSV

    表 2  等离子体对电子-电子相互作用屏蔽引起$\rm{Al}^{11+}$离子$1 {\rm{s}}^2$($^1 {\rm{S}}_0$)—1s2p($^1 {\rm{P}}_1$)跃迁能移动量和跃迁几率移动量所占百分比随电子密度和温度的变化.

    Table 2.  The variation of percentages of the transition energy shifts and transition probability shifts of ${\rm{1 s}}^2$($^1 {\rm{S}}_0$)–1s2p($^1 {\rm{P}}_1$) transition for Al11+ ions caused by plasma screening on electron-electron interaction as a function of plasma electron density and temperature

    电子温度为50 eV 电子密度为$5.0\times 10^{24}\;{\rm{cm}}^{-3}$
    电子密度
    /$\;{\rm{cm}}^{-3}$
    ${\text{%}} \Delta E_ {\rm{TE} }$ ${\text{%} } \Delta A$ 温度/eV ${\text{%} }\Delta E_ {\rm{TE} }$ ${\text{%} } \Delta A$
    1.0(22) 7.53 7.84 10 8.72 10.30
    5.0(22) 7.51 7.59 20 8.68 10.20
    1.0(23) 7.52 7.63 30 8.60 9.99
    5.0(23) 7.60 7.80 40 8.50 9.73
    1.0(24) 7.70 8.00 50 8.39 9.48
    3.0(24) 8.08 8.77 60 8.29 9.24
    5.0(24) 8.39 9.48 70 8.19 9.04
    7.0(24) 8.66 10.17 80 8.11 8.88
    9.0(24) 8.91 10.86 90 8.04 8.74
    1.0(25) 9.04 11.27 100 7.98 8.62
    下载: 导出CSV

    表 3  当电子密度和温度分别为$4.0\times10^{23}\;{\rm{cm}}^{-3}$和50 eV时, 不同电荷态Al离子的基态能量移动量和其所占百分比

    Table 3.  Ground state energy shifts and their percentages of Al ions with different charge when the electron density and temperature are $4.0\times10^{23}\;{\rm{cm}}^{-3}$ and 50 eV respectively

    离子 束缚电子个数 原子态 E/atomic unit %∆E 束缚电子对个数 EEP/atomic unit
    ${\rm{Al}}^{11+}$ 2 ${\rm{1}}{{\rm{s}}^{\rm{2}}}{(^{\rm{1}}}{{{\rm{S}}}_{\rm{0}}})$ 0.556 3.83 1 0.556
    ${\rm{Al}}^{10+}$ 3 $\rm{1 s^22 s(^2 S_{1/2})}$ 1.590 7.47 3 0.530
    ${\rm{Al}}^{9+}$ 4 $\rm{1 s^22 s^2(^1 S_0)}$ 3.119 11.14 6 0.520
    ${\rm{Al}}^{8+}$ 5 $\rm{1 s^22 s^22 p(^2 P_{1/2})}$ 5.152 14.82 10 0.515
    ${\rm{Al}}^{7+}$ 6 $\rm{1 s^22 s^22 p^2(^3 P_0)}$ 7.662 18.48 15 0.511
    ${\rm{Al}}^{6+}$ 7 $\rm{1 s^22 s^22 p^3(^4 S_{3/2})}$ 10.635 22.11 21 0.506
    ${\rm{Al}}^{5+}$ 8 ${\rm{1}}{{\rm{s}}^{\rm{2}}}{\rm{2}}{{\rm{s}}^{\rm{2}}}{\rm{2}}{{\rm{p}}^{\rm{4}}}{(^{\rm{3}}}{{\rm{P}}_{\rm{2}}})$ 14.036 25.71 28 0.501
    ${\rm{Al}}^{4+}$ 9 ${\rm{1}}{{\rm{s}}^{\rm{2}}}{\rm{2}}{{\rm{s}}^{\rm{2}}}{\rm{2}}{{\rm{p}}^{\rm{5}}}{(^{\rm{2}}}{{\rm{P}}_{{\rm{3/2}}}})$ 17.948 29.38 36 0.499
    注1: %∆E表示等离子体对电子-电子相互作用的屏蔽而引起的能量移动量与其对核-电子相互作用的屏蔽而引起的能量移动量的百分比. 注2: ∆EEP表示总能量移动值对束缚电子对个数的平均值.
    下载: 导出CSV
  • [1]

    Dornheim T, Groth S, Bonitz M 2018 Phys. Rep. 744 1Google Scholar

    [2]

    Glenzer S H, Redmer R 2009 Rev. Mod. Phys. 81 1625Google Scholar

    [3]

    Das M, Sahoo B K, Pal S 2016 Phys. Rev. A 93 052513Google Scholar

    [4]

    李博文, 蒋军, 董晨钟, 王建国, 丁晓彬 2009 物理学报 58 5274Google Scholar

    Li B W, Jiang J, Dong C Z, Wang J G, Ding X B 2009 Acta Phys. Sin. 58 5274Google Scholar

    [5]

    Hu S X 2017 Phys. Rev. Lett. 119 065001Google Scholar

    [6]

    Papoulia A, Schiffmann S, Bieron J, Gaigalas G, Godefroid M, Harman Z, Jönsson P, Oreshkina N S, Pyykk P, Tupitsyn I I 2021 Phys. Rev. A 103 022815Google Scholar

    [7]

    马堃, 陈展斌, 黄时中 2019 物理学报 68 023102Google Scholar

    Ma K, Chen Z B, Huang S Z 2019 Acta Phys. Sin. 68 023102Google Scholar

    [8]

    Janev R K, Zhang S B, Wang J G 2016 Matter and Radiation at Extremes 1 237Google Scholar

    [9]

    Qi Y Y, Ning L N 2014 Phys. Plasmas 21 033301Google Scholar

    [10]

    Qi Y Y, Wu Y, Wang J G 2009 Phys. Plasmas 161 033507

    [11]

    Sahoo S, Ho Y K 2006 Phys. Plasmas 13 063301Google Scholar

    [12]

    Kang S, He J, Xu N, Chen C Y 2014 Commun. Theor. Phys. 62 881Google Scholar

    [13]

    Li H W, Kar S 2012 Phys. Plasmas 19 073303Google Scholar

    [14]

    Li Y Q, Wu J H, Hou Y, Yuan J M 2008 J. Phys. B: At. Mol. Opt. Phys. 41 145002Google Scholar

    [15]

    Li X D, Rosmej F B 2012 EPL 99 33001Google Scholar

    [16]

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

    [17]

    White A J, Collins L A 2020 Phys. Rev. Lett. 125 055002Google Scholar

    [18]

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

    [19]

    Zhang S B, Wang J G, Janev R K 2010 Phys. Rev. Lett. 104 023203Google Scholar

    [20]

    李永强, 吴建华, 袁建民 2008 物理学报 57 4042Google Scholar

    Li Y Q, Wu J H, Yuan J M 2008 Acta Phys. Sin. 57 4042Google Scholar

    [21]

    Li B W, Dong C Z, Jiang J, Wang J G 2010 Plasma Sci. Technol. 12 372

    [22]

    Kar S, Ho Y K 2009 J. Phys. B: At. Mol. Opt. Phys. 42 044007Google Scholar

    [23]

    Mukherjee P K, Karwowski J, Diercksen Geerd H F 2002 Chem. Phys. Lett. 363 323Google Scholar

    [24]

    Chen C, Zhao G P, Qi Y Y, Liu L, Chen Z B, Wang J G 2022 Phys. Plasmas 29 072901Google Scholar

    [25]

    Chen Z B, Qi Y Y, Sun H Y, Zhao G P, Liu P F, Wang K 2020 J. Quant. Spectrosc. Radiat. Transfer 3 8

    [26]

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

    [27]

    Zhao G P, Liu L, Wang J G, Janev R K, Yan J 2018 Matter and Radiation at Extremes 3 300Google Scholar

    [28]

    Zhao G P, Liu L, Wang J G, Janev R K 2017 Phys. Plasmas 24 053509Google Scholar

    [29]

    Zhao G P, Liu L, Wang J G, Janev R K 2017 Phys. Plasmas 24 103504Google Scholar

    [30]

    Li W G, Cheng Y J, Wu J Y, Wu Y, Wang J G, Zhang S B 2021 Phys. Plasmas 28 012708Google Scholar

    [31]

    Murillo M S, Weisheit J C 1998 Phys. Rep. 302 1Google Scholar

    [32]

    Ichimaru S 1982 Rev. Mod. Phys. 54 1017Google Scholar

    [33]

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

    [34]

    NIST https://www.nist.gov/pml/atomic-spectra-database

    [35]

    Jönsson P, Gaigalas G, Bieroń J, Fischer C F, Grant I P 2013 Comput. Phys. Commun. 184 2197Google Scholar

    [36]

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

    [37]

    Xie L Y, Wang J G, Janev R K, Qu Y Z, Dong C Z 2012 Eur. Phys. J. D 66 125Google Scholar

    [38]

    Chen Z B, Ma K, Hu H W, Wang K 2018 Phys. Plasmas 25 072120Google Scholar

    [39]

    Saha B, Fritzsche S 2006 Phys. Rev. E 73 036405Google Scholar

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出版历程
  • 收稿日期:  2022-12-08
  • 修回日期:  2023-01-20
  • 上网日期:  2023-02-09
  • 刊出日期:  2023-04-05

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