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等离子体屏蔽效应对Ar16+基态和激发态能级的影响

马堃 陈展斌 黄时中

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等离子体屏蔽效应对Ar16+基态和激发态能级的影响

马堃, 陈展斌, 黄时中

Influence of plasma shielding effect on ground state and excited state energies of Ar16+

Ma Kun, Chen Zhan-Bin, Huang Shi-Zhong
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  • 基于Rayleigh-Ritz变分原理, 发展了一套处理弱耦合等离子体环境中多电子原子(离子)非相对论能量及其相对论修正的解析方法. 通过考虑电子间交换相互作用以及内外壳层电子的屏蔽效应, 计算了Ar16+基态1s2 1S、单激发态1sns 1,3S (n = 2—5), 1snp 1,3P (n = 2—5) 和双激发态2snp 1P (n = 2—5)非相对论能量及其相对论修正值(包括质量修正、单体和双体达尔文修正以及自旋-自旋接触相互作用项), 讨论了等离子体屏蔽效应对能级的影响. 结果表明: 相对论质量修正和第一类达尔文修正占主导, 比其他相对论修正项高出三个数量级. 此外, 等离子体屏蔽效应具有明显的态选择性, 屏蔽效应对外壳层电子的影响大于内壳层电子, 随着等离子体屏蔽参数的增加, 外壳层电子轨道向外延展, 激发态越高, 延展程度越大.
    A systematical knowledge of the atomic properties in plasma is of great interest for various research areas, such as the explanation of the X-ray radiation from universe, plasma diagnostics, extreme ultraviolet (EUV) and X-ray sources and so on. Among these researches, the detailed information about how the plasma influences the atomic energy level and transition spectrum are crucial for understanding the X-ray emission mechanism and the state of plasma. An analytic calculation method of treating the non-relativistic energy and its relativistic corrections for the multi-electron atoms embedded in weakly coupled plasma is developed based on the Rayleigh-Ritz variation method. The systematical investigations are performed for the ground state 1s2 1S, single excited states 1sns 1,2S (n = 2−5), 1snp 1,3P (n = 2−5) and double excited state 2s2p 1P of Ar16+ ion in weak coupled plasma. The analytic formulas for calculating the non-relativistic energy and its relativistic correction energy are derived, which include mass correction, one and two-body Darwin correction, spin-spin contact interaction and orbit-orbit interaction. All the angular integration spin sums involved in the problem are worked out explicitly by using the irreducible theory. The influence of plasma on non-relativistic energy and relativistic correction energy are discussed. The results show that the mass correction and the one-body Darwin correction are the main ones among the terms of relativistic correction, and are three orders of magnitude greater than the other relativistic terms. The plasma shielding effect mainly affects the non-relativistic energy, and has little effect on the relativistic correction. At the same time, it has a more significant selectivity for the electronic configuration. Further research shows that the influence of plasma on the energy of the outer shell electron is greater than that of the inner shell electron. With the increase of the plasma shielding parameters, the outer shell electron extends outward, and the higher the excited state, the greater the degree of extension is. This work should be useful for astrophysical applications where such a plasma environment exists.
      通信作者: 马堃, makun@hsu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11804112, 11504421)、安徽省自然科学基金(批准号: 1808085QA22)、安徽省高校优秀青年人才支持计划重点项目(批准号: gxyqZD2016301)和安徽省高校自然科学研究项目(批准号: KJHS2015B01)资助的课题.
      Corresponding author: Ma Kun, makun@hsu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11804112, 11504421), the Natural Science Foundation of Anhui Province, China (Grant No. 1808085QA22), the Key Project for Young Talents in College of Anhui Province, China (Grant No. gxyqZD2016301), and the Natural Science Foundation of the Higher Education Institutions of Anhui Province, China (Grant No. KJHS2015B01).
    [1]

    Debye P, Hückel E 1923 Z. Phys. 24 185

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

    [3]

    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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    Ray D 2000 Phys. Rev. E 62 4126Google Scholar

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    Wu Z Q, Han G X, Yan J, Pang J Q 2002 J. Phys. B 35 2305Google Scholar

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

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    Saha B, Fritzsche S 2007 J. Phys. B 40 259Google Scholar

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    Belkhiri M, Fontes C J, Poirier M 2015 Phys. Rev. A 92 032501Google Scholar

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    Fernley J A, Taylor K T, Seaton M J 1987 J. Phys. B 20 6457Google Scholar

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    Peach G, Saraph H E, Seaton M J 1988 J. Phys. B 21 3669Google Scholar

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    Fernley J A, Taylor K T, Seaton M J 1987 J. Phys. B 20 6457Google Scholar

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    Kaspi S, Brandt W N, Netzer H, Sambruna R, Chartas G, Garmire G P, Nousek J A 2000 Astrophys. J. Lett. 535 L17Google Scholar

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    Saha B, Bhattacharyya S, Mukherjee T K, Mukherjee P K 2003 Int. J. Quantum Chem. 92 413Google Scholar

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    Costa A M, Martins M C, Parente F, Santos J P, Indelicato P 2001 Atom. Data Nucl. Dat. 79 223Google Scholar

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    Goryaev F F, Vainshtein L A, Urnov A M 2017 Atom. Data Nucl. Dat. 113 117Google Scholar

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    Saha J K, Bhattacharyya S, Mukherjee T K, Mukherjee P K 2010 J. Quant. Spectrosc. Radiat. Transfer 111 675Google Scholar

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  • 图 1  A16+ 1s2 1S, 1s2s 1,3S, 1s2p 1,3P和2s2p 1P 的相对论修正能量随参数u的变化

    Fig. 1.  Relativistic corrections against parameter u for 1s2 1S, 1s2s 1,3S, 1s2p 1,3P and 2s2p 1P of Ar16+.

    图 2  等离子能级偏移与参数u之间的关系

    Fig. 2.  Plasma energy shifts against parameter u.

    图 3  内外壳层电子径向波函数模方

    Fig. 3.  Module of radial wave functions for inner and outer shell electron.

    表 1  相对论修正对C4+基态1s2 1S能级的影响(单位: a.u.)

    Table 1.  Effects of relativistic correction on ground state 1s2 1S energies level in C4+ (unit: a.u.).

    u${\alpha _{1{\rm{s}}}}$ENREMCED1ΔERSETRef.[20]Ref.[25,26]
    05.6875−32.3477−0.06965080.0587822−0.01087−32.35857−32.4176−32.3612
    0.15.68614−31.1633−0.06958430.0587401−0.01084−31.17414−31.2324−31.177
    0.25.68218−30.0095−0.06939050.0586174−0.01077−30.02027−30.079−30.0237
    0.35.67577−28.8854−0.06907810.0584193−0.01066−28.89606−28.9557
    0.45.66706−27.7899−0.06865490.0581507−0.01050−27.80040−27.8614
    0.55.65616−26.7223−0.06812820.0578158−0.01031−26.73261−26.7963−26.7395
    0.65.64318−25.6817−0.0675050.0574187−0.01009−25.69179−25.7576
    0.75.62821−24.6674−0.06679160.0569630−0.00983−24.67723−24.7457
    0.85.61134−23.6788−0.06599420.0564522−0.00954−23.68834−23.7006−23.7594
    0.95.59263−22.7151−0.06511860.0558895−0.00923−22.72433−22.7986
    1.05.57215−21.7758−0.06417010.0552778−0.00889−21.78469−21.8629
    下载: 导出CSV

    表 2  Ar16+ 1sns, 1snp和2s2p组态变分参数

    Table 2.  Variation parameters of 1sns, 1snp and 2snp configurations in Ar16+.

    2S+1n1sns 2S+1S1snp 2S+1P2snp 2S+1P
    ${\alpha _{1{\rm{s}}}}$${\alpha _{n{\rm{s}}}}$ENR${\alpha _{1{\rm{s}}}}$${\alpha _{n{\rm{p}}}}$ENR${\alpha _{2{\rm{s}}}}$${\alpha _{n{\rm{p}}}}$ENR
    1117.6875−312.848
    217.932417.3433−198.38418.010716.9176−197.96917.411317.8229−77.601
    317.981517.2194−178.1418.000816.9725−178.01817.942817.2934−56.8575
    417.992417.1623−171.06818.000116.9852−171.01717.976617.2143−49.655
    517.996117.129−167.7991816.9901−167.77317.988217.1692−46.3425
    3218.013717.1931−199.19617.957717.266−198.504
    318.003117.1286−178.35517.9917.1509−178.162
    418.001217.0962−171.15517.996117.1079−171.076
    518.000617.0768−167.84317.998117.0845−167.803
    下载: 导出CSV

    表 3  Ar16+基态1s2 1S相对论性能量(单位: a.u.)

    Table 3.  Relativistic correction on ground state 1s2 1S energies level in Ar16+ (unit: a.u.).

    u${\alpha _{1{\rm{s}}}}$ENREMCED1ΔERSET
    017.6875−312.848−6.514885.30399−1.21089−314.05889
    0.117.6871−309.263−6.514255.30360−1.21065−310.47365
    0.217.6858−305.708−6.512385.30246−1.20992−306.91792
    0.317.6837−302.184−6.509295.30057−1.20872−303.39272
    0.417.6808−298.688−6.505015.29796−1.20705−299.89505
    0.517.6771−295.222−6.499575.29463−1.20494−296.42694
    0.617.6726−291.785−6.492995.29061−1.20238−292.98738
    0.717.6674−288.377−6.485305.28591−1.19939−289.57639
    0.817.6614−284.997−6.476525.28055−1.19597−286.19297
    0.917.6547−281.645−6.466685.27453−1.19215−282.83715
    1.017.6473−278.32−6.455805.26787−1.18793−279.50793
    下载: 导出CSV

    表 8  Ar16+基态2s2p 1P相对论性能量(单位: a.u.)

    Table 8.  Relativistic correction on excited state 2s2p 1P energies level in Ar16+ (unit: a.u.).

    u${\alpha _{2{\rm{s}}}}$${\alpha _{2{\rm{p}}}}$ENREMCED1ED2ESSCEOOΔERSET
    017.411317.8229−77.6010−0.594990.31621−8.39310 × 10−41.67862 × 10−3−0.0006009−0.27854−77.87954
    0.117.404317.8174−74.0566−0.594060.31583−8.38360 × 10−41.67672 × 10−3−6.00393 × 10−4−0.27800−74.33460
    0.217.383917.8014−70.6207−0.591390.31472−8.35602 × 10−41.67120 × 10−3−5.98927 × 10−4−0.27644−70.89714
    0.317.35117.7755−67.2898−0.587110.31294−8.31163 × 10−41.66233 × 10−3−5.96551 × 10−4−0.27393−67.56373
    0.417.306417.7402−64.0605−0.581320.31053−8.25157 × 10−41.65031 × 10−3−5.93313 × 10−4−0.27055−64.33105
    0.517.250817.6959−60.9298−0.574150.30754−8.17686 × 10−41.63537 × 10−3−5.89259 × 10−4−0.26637−61.19617
    0.617.184517.6429−57.8948−0.565690.30401−8.08845 × 10−41.61769 × 10−3−5.84432 × 10−4−0.26146−58.15626
    0.717.108117.5816−54.9531−0.556060.29998−7.98720 × 10−41.59744 × 10−3−5.78871 × 10−4−0.25586−55.20896
    0.817.021917.5122−52.1022−0.545340.29546−7.87391 × 10−41.57478 × 10−3−5.72611 × 10−4−0.24966−52.35186
    0.916.926217.4349−49.3398−0.533610.29051−7.74933 × 10−41.54987 × 10−3−5.65688 × 10−4−0.24289−49.58269
    1.016.821317.3499−46.6639−0.520980.28514−7.61414 × 10−41.52283 × 10−3−5.58134 × 10−4−0.23563−46.89953
    下载: 导出CSV

    表 4  Ar16+激发态1s2s 1S相对论性能量(单位: a.u.)

    Table 4.  Relativistic correction on excited state 1s2s 1S energies level in Ar16+ (unit: a.u.).

    u${\alpha _{1{\rm{s}}}}$${\alpha _{2{\rm{s}}}}$ENREMCED1ED2ESSCΔERSET
    017.932417.3433−198.384−3.930943.07620−7.249983 × 10−31.450003 × 10−2−0.84749−199.23149
    0.117.931917.3364−194.822−3.929823.07562−7.245793 × 10−31.44916 × 10−2−0.84695−195.66895
    0.217.930617.3164−191.335−3.926573.07394−7.233613 × 10−31.44672 × 10−2−0.84540−192.18040
    0.317.928517.284−187.921−3.921303.07121−7.213953 × 10−31.44279 × 10−2−0.84288−188.76388
    0.417.925617.2401−184.577−3.914153.06749−7.187233 × 10−31.43745 × 10−2−0.83947−185.41647
    0.517.921817.1852−181.301−3.905223.06284−7.153833 × 10−31.43077 × 10−2−0.83523−182.13623
    0.617.917317.1198−178.092−3.894623.05729−7.114063 × 10−31.42281 × 10−2−0.83022−178.92222
    0.717.91217.0445−174.947−3.882453.05090−7.068203 × 10−31.41364 × 10−2−0.82448−175.77148
    0.817.90616.9594−171.866−3.868803.04371−7.016463 × 10−31.40329 × 10−2−0.81807−172.68407
    0.917.899216.865−168.847−3.853773.03575−6.959053 × 10−31.39181 × 10−2−0.81106−169.65806
    1.017.891816.7615−165.889−3.837453.02706−6.896133 × 10−31.37923 × 10−2−0.80349−166.69249
    下载: 导出CSV

    表 5  Ar16+激发态1s2s 3S相对论性能量(单位: a.u.)

    Table 5.  Relativistic correction on excited state 1s2s 3S energies level in Ar16+ (unit: a.u.).

    u${\alpha _{1{\rm{s}}}}$${\alpha _{2{\rm{s}}}}$ENREMCED1ΔERSET
    018.013717.1931−199.196−3.977033.10590−0.87113−200.06713
    0.118.013317.1858−195.635−3.975943.10534−0.87060−196.50560
    0.218.012217.1646−192.149−3.972763.10370−0.86906−193.01806
    0.318.010417.1305−188.735−3.967613.10104−0.86657−189.60157
    0.418.007817.0841−185.392−3.960623.09742−0.86320−186.25520
    0.518.004617.0263−182.119−3.951893.09289−0.85900−182.97800
    0.618.000616.9574−178.912−3.941523.08748−0.85404−179.76604
    0.717.99616.878−175.77−3.929623.08124−0.84838−176.61838
    0.817.990716.7885−172.692−3.916273.07421−0.84206−173.53406
    0.917.984716.6891−169.676−3.901563.06643−0.83513−170.51113
    1.017.978116.5803−166.721−3.885573.05792−0.82765−167.54865
    下载: 导出CSV

    表 6  Ar16+激发态1s2p 1P相对论性能量(单位: a.u.)

    Table 6.  Relativistic correction on excited state 1s2p 1P energies level in Ar16+ (unit: a.u.).

    u${\alpha _{1{\rm{s}}}}$${\alpha _{2{\rm{p}}}}$ENREMCED1ED2ESSCEOOΔERSET
    018.010716.9176−197.969−3.581672.80005−2.073823 × 10−34.147643 × 10−3−0.0064010−0.78595−198.75495
    0.118.010316.9115−194.403−3.581232.79986−2.071283 × 10−34.142563 × 10−3−6.394563 × 10−3−0.78569−195.18869
    0.218.009116.8936−190.903−3.579942.79929−2.063883 × 10−34.127763 × 10−3−6.375753 × 10−3−0.78496−191.68796
    0.318.00716.8646−187.467−3.577822.79834−2.051933 × 10−34.103873 × 10−3−6.345353 × 10−3−0.78377−188.25077
    0.418.004216.8251−184.094−3.574902.79703−2.035733 × 10−34.071453 × 10−3−6.304033 × 10−3−0.78214−184.87614
    0.518.000716.7755−180.783−3.571212.79536−2.015513 × 10−34.031023 × 10−3−6.252373 × 10−3−0.78009−181.56309
    0.617.996316.7162−177.532−3.566772.79335−1.991533 × 10−33.983063 × 10−3−6.190923 × 10−3−0.77762−178.30962
    0.717.991316.6477−174.339−3.561612.79099−1.963993 × 10−33.927983 × 10−3−6.120133 × 10−3−0.77478−175.11378
    0.817.985516.57−171.203−3.555742.78830−1.933093 × 10−33.866193 × 10−3−6.040453 × 10−3−0.77155−171.97455
    0.917.97916.4835−168.124−3.549192.78527−1.899033 × 10−33.798063 × 10−3−5.952253 × 10−3−0.76797−168.89197
    1.017.971816.3883−165.101−3.541982.78193−1.861983 × 10−33.723953 × 10−3−5.855883 × 10−3−0.76404−165.86504
    下载: 导出CSV

    表 7  Ar16+基态1s2p 3P相对论性能量(单位: a.u.)

    Table 7.  Relativistic correction on excited state 1s2p 3P energies level in Ar16+ (unit: a.u.).

    u${\alpha _{1{\rm{s}}}}$${\alpha _{2{\rm{p}}}}$ENREMCED1EOOΔERSET
    017.957717.266−198.504−3.547362.775396.7643 × 10−3−0.76521−199.26921
    0.117.957317.26−194.937−3.546942.775226.75783 × 10−3−0.76496−195.70196
    0.217.956217.2424−191.436−3.545712.774696.738923 × 10−3−0.76428−192.20028
    0.317.954317.2138−187.998−3.543692.773816.70833 × 10−3−0.76317−188.76117
    0.417.951717.1749−184.622−3.540912.772606.66673 × 10−3−0.76164−185.38364
    0.517.948317.1261−181.306−3.537392.771066.61473 × 10−3−0.75972−182.06572
    0.617.944317.0678−178.05−3.533152.769196.55273 × 10−3−0.75741−178.80741
    0.717.939617.0002−174.852−3.528222.767006.48123 × 10−3−0.75474−175.60674
    0.817.934216.9237−171.71−3.522622.764506.40083 × 10−3−0.75172−172.46172
    0.917.928116.8384−168.624−3.5163702.761706.31163 × 10−3−0.74836−169.37236
    1.017.921416.7445−165.593−3.5094902.758596.21423 × 10−3−0.74469−166.33769
    下载: 导出CSV
  • [1]

    Debye P, Hückel E 1923 Z. Phys. 24 185

    [2]

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

    [3]

    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

    [4]

    Ray D 2000 Phys. Rev. E 62 4126Google Scholar

    [5]

    Wu Z Q, Han G X, Yan J, Pang J Q 2002 J. Phys. B 35 2305Google Scholar

    [6]

    Das M 2014 Phys. Plasmas 21 012709Google Scholar

    [7]

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

    [8]

    Saha B, Fritzsche S 2007 J. Phys. B 40 259Google Scholar

    [9]

    Belkhiri M, Fontes C J, Poirier M 2015 Phys. Rev. A 92 032501Google Scholar

    [10]

    Fernley J A, Taylor K T, Seaton M J 1987 J. Phys. B 20 6457Google Scholar

    [11]

    Peach G, Saraph H E, Seaton M J 1988 J. Phys. B 21 3669Google Scholar

    [12]

    Fernley J A, Taylor K T, Seaton M J 1987 J. Phys. B 20 6457Google Scholar

    [13]

    Kaspi S, Brandt W N, Netzer H, Sambruna R, Chartas G, Garmire G P, Nousek J A 2000 Astrophys. J. Lett. 535 L17Google Scholar

    [14]

    Saha B, Bhattacharyya S, Mukherjee T K, Mukherjee P K 2003 Int. J. Quantum Chem. 92 413Google Scholar

    [15]

    Costa A M, Martins M C, Parente F, Santos J P, Indelicato P 2001 Atom. Data Nucl. Dat. 79 223Google Scholar

    [16]

    Goryaev F F, Vainshtein L A, Urnov A M 2017 Atom. Data Nucl. Dat. 113 117Google Scholar

    [17]

    Saha J K, Bhattacharyya S, Mukherjee T K, Mukherjee P K 2010 J. Quant. Spectrosc. Radiat. Transfer 111 675Google Scholar

    [18]

    Fang T K, Wu C S, Gao X, Chang T N 2017 Phys. Rev. A 96 052502Google Scholar

    [19]

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  • PDF下载量:  36
  • 被引次数: 0
出版历程
  • 收稿日期:  2018-10-27
  • 修回日期:  2018-12-10
  • 上网日期:  2019-01-01
  • 刊出日期:  2019-01-20

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