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W6+离子的电子碰撞电离研究

马莉莉 张世平 张芳军 李麦娟 蒋军 丁晓彬 颉录有 张登红 董晨钟

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W6+离子的电子碰撞电离研究

马莉莉, 张世平, 张芳军, 李麦娟, 蒋军, 丁晓彬, 颉录有, 张登红, 董晨钟

Theoretical investigation of electron-impact ionization of W6+ ion

Ma Li-Li, Zhang Shi-Ping, Zhang Fang-Jun, Li Mai-Juan, Jiang Jun, Ding Xiao-Bin, Xie Lu-You, Zhang Deng-Hong, Dong Chen-Zhong
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  • 采用细致能级扭曲波方法计算了W6+离子基态$ {\text{[Kr]4}}{{\text{d}}^{{10}}}{5}{{\text{s}}^{2}}{4}{{\text{f}}^{{14}}}{5}{{\text{p}}^{6}} $和亚稳态$ {\text{[Kr]4}}{{\text{d}}^{{10}}}{5}{{\text{s}}^{2}}{4}{{\text{f}}^{{14}}}{5}{{\text{p}}^{5}}{5}{{\text{d}}^{1}} $, $ {\text{[Kr]4}}{{\text{d}}^{{10}}}{5}{{\text{s}}^{2}}{4}{{\text{f}}^{{13}}}{5}{{\text{p}}^{6}}{5}{{\text{d}}^{1}} $, $ {\text{[Kr]4}}{{\text{d}}^{{10}}}{5}{{\text{s}}^{2}}{4}{{\text{f}}^{{14}}}{5}{{\text{p}}^{5}}{5}{{\text{f}}^{1}} $, $ {\text{[Kr]4}}{{\text{d}}^{{10}}}{5}{{\text{s}}^{2}}{4}{{\text{f}}^{{13}}}{5}{{\text{p}}^{6}}{5}{{\text{f}}^{1}} $的电子碰撞单电离(EISI)截面. 为了考虑亚稳态离子对电离的贡献, 本文采用了3种模型来确定母离子束中处于长寿命能级的比值. 与Pindzola和Griffin (1997 Phys. Rev. A 56 1654)的理论结果和Stenke等(1995 J. Phys. B: At. Mol. Opt. Phys. 28 2711)实验结果进行比较, 发现在考虑了亚稳态的贡献后本文结果与Stenke等的实验结果吻合得很好.
    Due to its unique characteristics, metal tungsten has been selected as the wall material for the tokamak magnetic confinement fusion device. The wall material directly interacts with the plasma for a long time, thus causing tungsten atoms and ions to be sputtered and ionized into different charge states, which then enter the tokamak device as plasma impurities. To ensure stable plasma combustion conditions, highly complex model is currently being used to evaluate the behavior of tungsten impurities and their influence on the tokamak plasma. This requires various high-precision atomic data for tungsten atoms and different ionized states of tungsten ions. Electron collision ionization, as a fundamental atomic physical process, is widely encountered in laboratory and astrophysical plasma environments. The parameters such as electron collision ionization cross-sections and rate coefficients are crucial for plasma radiation transport simulations and state diagnostics.Electron-impact single-ionization (EISI) cross sections of the ground state and metastable state for W6+ ions are calculated by using the level-to-level distorted-wave (LLDW) method. The contributions of direct ionization (DI) cross section and excited autoionization (EA) cross section to the total EISI cross section are primarily considered.Comparison of our calculation results with the experimental data from Stenke et al. (Stenke M, Aichele K, Harthiramani D, Hofmann G, Steidl M, Volpel R, Salzborn E 1995 J. Phys. B: At. Mol. Opt. Phys. 28 2711) reveals that the EISI cross section considering only the ground state is significantly smaller than the experimental result. Therefore, it is imperative to take into account the contribution from the metastable state. To determine the fraction of ions in long-lived energy levels within the parent ion beam, three models are employed.Our results, which include the contribution of metastable states, accord well with the experimental results of Stenke et al. Compared with the theoretical calculation result of Pindzola et al. our calculaiton provides a more comprehensive understanding of the electron-impact single-ionization process for W6+ ions. The comparison is illustrated in the attached figure.
      通信作者: 张登红, zhangdh@nwnu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 12364034)和甘肃省科技计划(批准号: 23YFFA0074)资助的课题.
      Corresponding author: Zhang Deng-Hong, zhangdh@nwnu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12364034) and the Science and Technology Project of Gansu Province, China (Grant No. 23YFFA0074).
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  • 图 1  W6+, W7+和W8+离子主要组态能级, 虚线分别表示W6+的单电离和双电离阈值

    Fig. 1.  Energy levels of the main configurations of W6+ , W7+and W8+ ions. Dotted horizontal lines mark the thresholds for single and double ionization of W6+.

    图 2  W6+离子基态的DI截面, 其中蓝色、红色和绿色虚线分别表示5s, 5p和4f壳层对总DI截面的贡献, 黑色实线是总的DI截面

    Fig. 2.  DI cross sections for ground state W6+ ions. The blue, red and green dashed lines represent the contribution of the 5s, 5p and 4f subshell to the total DI cross section respectively, the black solid line is the total DI cross section.

    图 3  W6+离子基态$ {\text{[Kr]4}}{{\text{d}}^{{10}}}{5}{{\text{s}}^{2}}{4}{{\text{f}}^{{14}}}{5}{{\text{p}}^{6}} $激发到nl能级的EA截面占总EA截面的比例

    Fig. 3.  Ratios of the EA cross section from the ground state $ {\text{[Kr]4}}{{\text{d}}^{{10}}}{5}{{\text{s}}^{2}}{4}{{\text{f}}^{{14}}}{5}{{\text{p}}^{6}} $ of the W6+ to the nl state to the total EA cross section.

    图 4  W6+离子基态的EA截面, 其中绿色、黄色和红色阴影区域分别表示5s, 5p和4d壳层对总EA截面的贡献

    Fig. 4.  EA cross sections for ground state W6+ ions. The green, yellow and red shadow areas represent the contribution of the 5s, 5p and 4d subshell to the total EA cross section, respectively.

    图 5  W6+离子基态$ {\text{[Kr]4}}{{\text{d}}^{{10}}}{5}{{\text{s}}^{2}}{4}{{\text{f}}^{{14}}}{5}{{\text{p}}^{6}} $的总EISI截面, 其中黑色圆点为Stenke等[26]的实验结果, 黑色实线为目前LLDW计算结果, 红色实线为CADW结果[16]

    Fig. 5.  Total EISI cross section for ground state $ {\text{[Kr]4}}{{\text{d}}^{{10}}}{5}{{\text{s}}^{2}}{4}{{\text{f}}^{{14}}}{5}{{\text{p}}^{6}} $ of W6+ ions. Black solid circles are the experimental results of Stenke et al.[26], black solid line is the present LLDW total cross section, red solid line is CADW calculated result[16].

    图 6  亚稳态$ {4}{{\text{d}}^{{10}}}{5}{{\text{s}}^{2}}{4}{{\text{f}}^{{13}}}{5}{{\text{p}}^{6}}{5}{{\text{d}}^{1}} $(a), $ {\text{[Kr]4}}{{\text{d}}^{{10}}}{5}{{\text{s}}^{2}}{4}{{\text{f}}^{{14}}}{5}{{\text{p}}^{5}}{5}{{\text{d}}^1} $(b), $ {4}{{\text{d}}^{{10}}}{5}{{\text{s}}^{2}}{4}{{\text{f}}^{{14}}}{5}{{\text{p}}^{5}}{5}{{\text{f}}^{1}} $(c)和$ {4}{{\text{d}}^{{10}}}{5}{{\text{s}}^{2}}{4}{{\text{f}}^{{13}}}{5}{{\text{p}}^{6}}{5}{{\text{f}}^{1}} $(d)长寿命能级的EISI截面

    Fig. 6.  EISI cross sections for the metastable levels in the configuration $ {4}{{\text{d}}^{{10}}}{5}{{\text{s}}^{2}}{4}{{\text{f}}^{{13}}}{5}{{\text{p}}^{6}}{5}{{\text{d}}^{1}} $(a), $ {\text{[Kr]4}}{{\text{d}}^{{10}}}{5}{{\text{s}}^{2}}{4}{{\text{f}}^{{14}}}{5}{{\text{p}}^{5}}{5}{{\text{d}}^1} $(b), $ {4}{{\text{d}}^{{10}}}{5}{{\text{s}}^{2}}{4}{{\text{f}}^{{14}}}{5}{{\text{p}}^{5}}{5}{{\text{f}}^{1}} $(c)和$ {4}{{\text{d}}^{{10}}}{5}{{\text{s}}^{2}}{4}{{\text{f}}^{{13}}}{5}{{\text{p}}^{6}}{5}{{\text{f}}^{1}} $ (d).

    图 7  W6+离子的拟合截面与实验[14]的比较, 其中红色、绿色和蓝色虚线分别表示模型1、模型2和模型3的结果; 黑色实线为基态$ 4{{\text{f}}^{14}}5{{\text{p}}^6} $的EISI截面

    Fig. 7.  Comparison of our W6+ ions fitting EISI with experiment[14]. Red, green and blue solid line respresent the results of the Model 1, Model 2 and Model 3, respectively. The black solid line is the EISI cross section of ground state $ 4{{\text{f}}^{14}}5{{\text{p}}^6} $.

    图 8  W6+离子基态$ {\text{[Kr]4}}{{\text{d}}^{{10}}}{5}{{\text{s}}^{2}}{4}{{\text{f}}^{{14}}}{5}{{\text{p}}^{6}} $的EISI截面, 其中黑色圆点为LLDW方法计算的结果, 红色实线为(24)式拟合的结果

    Fig. 8.  Electron-impact ionization cross sections for W6+ ions ground state $ {\text{[Kr]4}}{{\text{d}}^{{10}}}{5}{{\text{s}}^{2}}{4}{{\text{f}}^{{14}}}{5}{{\text{p}}^{6}} $. Black dots are the results for calculated using the LLDW method, red dashed line is the results for the fitting results by Eq. (24).

    表 1  W6+离子基态$ {5}{{\text{p}}^{6}} $和激发态$ {5}{{\text{p}}^{5}}{5}{{\text{d}}^{1}} $外壳层电离阈值

    Table 1.  Threshold energies for the ionization of electrons in the outer subshells of W6+ ion ground state $ {5}{{\text{p}}^{6}} $ and excited state $ {5}{{\text{p}}^{5}}{5}{{\text{d}}^{1}} $.

    Configuration Method 5d 4f 5p 5s 4d
    5p6 FAC 118.28 120.19 166.43 334.88
    MCDF[28] 119.0 120.6 166.8 335.9
    NIST[29] 122.01$ \pm $0.06 122.11$ \pm $0.06
    5p55d1 FAC 81.85 120.45 122.14 164.24
    MCDF[28] 81.95 120.9 122.4 164.2
    下载: 导出CSV

    表 2  W6+离子的长寿命能级(大于10–5 s)和寿命($ a \pm b \equiv a \times {10^{ \pm b}} $)

    Table 2.  Long-lived levels (exceeding 10–5 s) and its lifetimes ($ a \pm b \equiv a \times {10^{ \pm b}} $) of the W6+ ion.

    Configuration Index Level J Energy/eV Lifetimes/s Configuration Index Level J Energy/eV Lifetimes/s
    5p6 0 $ 5{{\mathrm{p}}}_{+}^{4} $ 0 0 30 $ 5{{\mathrm{p}}}_{+}^{3}5{{\mathrm{f}}}_{+}^{1} $ 4 78.81 8.70×10–1
    4f135d1 1 $ 4{{\mathrm{f}}}_{+}^{7}5{{\mathrm{d}}}_{-}^{1} $ 2 36.18 2.63×10–1 31 $ 5{{\mathrm{p}}}_{+}^{3}5{{\mathrm{f}}}_{+}^{1} $ 2 79.10 4.12×10–1
    2 $ 4{{\mathrm{f}}}_{+}^{7}5{{\mathrm{d}}}_{-}^{1} $ 3 37.44 2.11×10–1 32 $ 5{{\mathrm{p}}}_{-}^{1}5{{\mathrm{f}}}_{-}^{1} $ 3 89.54 7.15×10–5
    3 $ 4{{\mathrm{f}}}_{+}^{7}5{{\mathrm{d}}}_{-}^{1} $ 4 37.72 3.38×10–1 33 $ 5{{\mathrm{p}}}_{-}^{1}5{{\mathrm{f}}}_{+}^{1} $ 3 89.61 7.18×10–5
    4 $ 4{{\mathrm{f}}}_{+}^{7}5{{\mathrm{d}}}_{+}^{1} $ 6 37.98 6.19×10–2 34 $ 5{{\mathrm{p}}}_{-}^{1}5{{\mathrm{f}}}_{+}^{1} $ 4 89.70 7.00×10–5
    5 $ 4{{\mathrm{f}}}_{+}^{7}5{{\mathrm{d}}}_{+}^{1} $ 2 38.29 2.59×10–2 35 $ 5{{\mathrm{p}}}_{-}^{1}5{{\mathrm{f}}}_{+}^{1} $ 2 90.00 6.78×10–5
    6 $ 4{{\mathrm{f}}}_{+}^{7}5{{\mathrm{d}}}_{+}^{1} $ 4 38.78 1.26×10–2 4f135f1 36 $ 4{{\mathrm{f}}}_{+}^{7}5{{\mathrm{f}}}_{+}^{1} $ 1 75.70 1.23×10+2
    7 $ 4{{\mathrm{f}}}_{+}^{7}5{{\mathrm{d}}}_{+}^{1} $ 3 38.94 2.03×10–2 37 $ 4{{\mathrm{f}}}_{+}^{7}5{{\mathrm{f}}}_{-}^{1} $ 2 75.72 1.48×10+1
    8 $ 4{{\mathrm{f}}}_{+}^{7}5{{\mathrm{d}}}_{+}^{1} $ 5 39.10 2.75×10–2 38 $ 4{{\mathrm{f}}}_{+}^{7}5{{\mathrm{f}}}_{-}^{1} $ 6 75.77 1.92×10+4
    9 $ 4{{\mathrm{f}}}_{+}^{7}5{{\mathrm{d}}}_{+}^{1} $ 4 39.22 1.10×10–2 39 $ 4{{\mathrm{f}}}_{+}^{7}5{{\mathrm{f}}}_{+}^{1} $ 3 75.91 4.47×10+1
    10 $ 4{{\mathrm{f}}}_{-}^{5}5{{\mathrm{d}}}_{+}^{1} $ 0 39.41 8.02×10–2 40 $ 4{{\mathrm{f}}}_{+}^{7}5{{\mathrm{f}}}_{-}^{1} $ 3 76.12 4.60×10+2
    11 $ 4{{\mathrm{f}}}_{-}^{5}5{{\mathrm{d}}}_{-}^{1} $ 2 39.53 5.97×10–3 41 $ 4{{\mathrm{f}}}_{+}^{7}5{{\mathrm{f}}}_{-}^{1} $ 4 76.13 6.76×10+1
    12 $ 4{{\mathrm{f}}}_{-}^{5}5{{\mathrm{d}}}_{-}^{1} $ 3 40.23 5.14×10–2 42 $ 4{{\mathrm{f}}}_{+}^{7}5{{\mathrm{f}}}_{-}^{1} $ 5 76.17 2.11×10+1
    13 $ 4{{\mathrm{f}}}_{-}^{5}5{{\mathrm{d}}}_{+}^{1} $ 5 40.52 4.06×10–3 43 $ 4{{\mathrm{f}}}_{+}^{7}5{{\mathrm{f}}}_{+}^{1} $ 2 76.18 2.97
    14 $ 4{{\mathrm{f}}}_{-}^{5}5{{\mathrm{d}}}_{+}^{1} $ 2 40.79 4.96×10–3 44 $ 4{{\mathrm{f}}}_{+}^{7}5{{\mathrm{f}}}_{+}^{1} $ 5 76.20 2.95×10+1
    15 $ 4{{\mathrm{f}}}_{-}^{5}5{{\mathrm{d}}}_{+}^{1} $ 3 41.23 4.39×10–3 45 $ 4{{\mathrm{f}}}_{+}^{7}5{{\mathrm{f}}}_{+}^{1} $ 6 76.22 1.67×10+1
    16 $ 4{{\mathrm{f}}}_{-}^{5}5{{\mathrm{d}}}_{+}^{1} $ 4 41.37 4.69×10–3 46 $ 4{{\mathrm{f}}}_{+}^{7}5{{\mathrm{f}}}_{+}^{1} $ 4 76.26 6.77×10+1
    5p55d1 17 $ 5{{\mathrm{p}}}_{+}^{3}5{{\mathrm{d}}}_{-}^{1} $ 1 39.18 3.16×10+1 47 $ 4{{\mathrm{f}}}_{+}^{7}5{{\mathrm{f}}}_{+}^{1} $ 0 76.81 3.36×10–2
    18 $ 5{{\mathrm{p}}}_{+}^{3}5{{\mathrm{d}}}_{-}^{1} $ 3 40.64 5.40×10–1 48 $ 4{{\mathrm{f}}}_{-}^{5}5{{\mathrm{f}}}_{+}^{1} $ 1 77.73 1.31×10–2
    19 $ 5{{\mathrm{p}}}_{+}^{3}5{{\mathrm{d}}}_{-}^{1} $ 2 40.69 1.17×10–2 49 $ 4{{\mathrm{f}}}_{-}^{5}5{{\mathrm{f}}}_{-}^{1} $ 1 78.01 1.19×10–2
    20 $ 5{{\mathrm{p}}}_{+}^{3}5{{\mathrm{d}}}_{-}^{1} $ 4 40.88 3.15 50 $ 4{{\mathrm{f}}}_{-}^{5}5{{\mathrm{f}}}_{-}^{1} $ 5 78.03 1.10×10–2
    21 $ 5{{\mathrm{p}}}_{+}^{3}5{{\mathrm{d}}}_{-}^{1} $ 2 41.76 1.11×10–2 51 $ 4{{\mathrm{f}}}_{-}^{5}5{{\mathrm{f}}}_{+}^{1} $ 6 78.11 1.06×10–2
    22 $ 5{{\mathrm{p}}}_{+}^{3}5{{\mathrm{d}}}_{-}^{1} $ 3 43.18 7.07×10–3 52 $ 4{{\mathrm{f}}}_{-}^{5}5{{\mathrm{f}}}_{+}^{1} $ 2 78.16 1.11×10–2
    23 $ 5{{\mathrm{p}}}_{-}^{1}5{{\mathrm{d}}}_{-}^{1} $ 2 51.40 4.05×10–5 53 $ 4{{\mathrm{f}}}_{-}^{5}5{{\mathrm{f}}}_{+}^{1} $ 3 78.31 1.07×10–2
    24 $ 5{{\mathrm{p}}}_{-}^{1}5{{\mathrm{d}}}_{+}^{1} $ 2 52.83 4.30×10–5 54 $ 4{{\mathrm{f}}}_{-}^{5}5{{\mathrm{f}}}_{-}^{1} $ 3 78.40 1.10×10–2
    25 $ 5{{\mathrm{p}}}_{-}^{1}5{{\mathrm{d}}}_{+}^{1} $ 3 53.44 3.42×10–5 55 $ 4{{\mathrm{f}}}_{-}^{5}5{{\mathrm{f}}}_{-}^{1} $ 2 78.44 9.91×10–3
    5p55f1 26 $ 5{{\mathrm{p}}}_{+}^{3}5{{\mathrm{f}}}_{-}^{1} $ 2 77.81 2.43 56 $ 4{{\mathrm{f}}}_{-}^{5}5{{\mathrm{f}}}_{+}^{1} $ 4 78.47 1.07×10–2
    27 $ 5{{\mathrm{p}}}_{+}^{3}5{{\mathrm{f}}}_{-}^{1} $ 4 78.11 1.75×10+1 57 $ 4{{\mathrm{f}}}_{-}^{5}5{{\mathrm{f}}}_{-}^{1} $ 4 78.50 1.04×10–2
    28 $ 5{{\mathrm{p}}}_{+}^{3}5{{\mathrm{f}}}_{+}^{1} $ 3 78.31 1.13 58 $ 4{{\mathrm{f}}}_{-}^{5}5{{\mathrm{f}}}_{+}^{1} $ 5 78.50 1.06×10–2
    29 $ 5{{\mathrm{p}}}_{+}^{3}5{{\mathrm{f}}}_{-}^{1} $ 3 78.70 9.02×10–1 59 $ 4{{\mathrm{f}}}_{-}^{5}5{{\mathrm{f}}}_{-}^{1} $ 0 86.47 3.52×10–4
    下载: 导出CSV

    表 3  模型1和模型2中不同亚稳态W6+离子的比值

    Table 3.  Fractions of the various metastable W6+ ions in Model 1 and Model 2.

    Configurations Energy range
    (Model 1)/eV
    Energy range
    (Model 2)/eV
    [0, 118] [118, 1000] [0, 118] [118, 1000]
    5p6 0 0.35 0 0.31
    4f135d1 0.40 0.10 0.35 0.10
    5p55d1 0.40 0.11 0.35 0.12
    5p55f1 0.10 0.22 0.15 0.23
    4f135f1 0.10 0.22 0.15 0.24
    下载: 导出CSV

    表 4  模型3中W6+离子60个长寿命能级的比值λi     

    Table 4.  Fractions $ {\lambda _i} $ of 60 long-lived levels for for W6+ ions the Model 3.

    Level indexEnergy range/eVLevel indexEnergy range/eV
    [0, 118][118, 1000][0, 118][118, 1000]
    000.31000300.008000.02300
    10.044680.00625310.008000.02300
    20.044680.00625320.008000.02300
    30.044680.00625330.008000.02300
    40.044680.00625340.008000.02300
    50.044690.00625350.008000.02300
    60.044690.00625360.003330.01000
    70.044690.00625370.003330.01000
    80.044690.00625380.003330.01000
    90.044690.00625390.003330.01000
    100.044690.00625400.003330.01000
    110.044690.00625410.003330.01000
    120.044690.00625420.003330.01000
    130.044690.00625430.003330.01000
    140.044690.00625440.003330.01000
    150.044690.00625450.003330.01000
    160.044690.00625460.003330.01000
    170.138800.01333470.003330.01000
    180.138900.01333480.003330.01000
    190.138900.01333490.003330.01000
    200.138900.01333500.003330.01000
    210.138900.01333510.003330.01000
    220.138900.01333520.003340.01000
    230.138900.01334530.003340.01000
    240.138900.01334540.003340.01000
    250.138900.01334550.003340.01000
    260.008000.02300560.003340.01000
    270.008000.02300570.003340.01000
    280.008000.02300580.003340.01000
    290.008000.02300590.003340.01000
    下载: 导出CSV
  • [1]

    Demura A V, Kadomtsev M B, Lisitsa V S, Shurygin V A 2015 High Energy Density Physics 15 49Google Scholar

    [2]

    Biedermann C, Radtke R, Seidel R, Pütterich T 2009 Phys. Scr. T134 014026Google Scholar

    [3]

    Colgan J, Pindzola M S 2012 Eur. Phys. J. D 66 284Google Scholar

    [4]

    Wirth B D, Nordlund K, Whyte D G, Xu D 2011 MRS Bull. 36 216Google Scholar

    [5]

    Preval S P, Badnell N R, O’Mullane M G 2019 J. Phys. B: At. Mol. Opt. Phys. 52 025201Google Scholar

    [6]

    Kramida A E, Reader J 2006 Atomic Data and Nuclear Data Tables 92 457Google Scholar

    [7]

    Pütterich T, Neu R, Dux R, Whiteford A D, O’Mullane M G, Summers H P 2010 Nucl. Fusion 50 025012Google Scholar

    [8]

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出版历程
  • 收稿日期:  2024-03-21
  • 修回日期:  2024-04-24
  • 上网日期:  2024-05-09
  • 刊出日期:  2024-06-20

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