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在稳态近似下, 通过构建三能级体系碰撞辐射模型, 解析研究了电四极(E2)跃迁对等离子体中离子能级布居的影响. 研究发现, 随着原子序数增加, E2跃迁速率逐渐增强, E2跃迁在低电子密度条件下对离子能级布居的影响愈发显著. 进一步地, 以电子束离子阱中类铁钼(Z = 42)和铀(Z = 92)等离子体为例, 数值求解了包含不同退激通道的离子能级布居. 在此基础上, 分析了考虑E2退激通道导致的能级布居变化对基组态磁偶极(M1)跃迁线强比的影响, 并指出在利用高离化态离子M1跃迁线强比进行等离子体电子密度诊断时E2退激发通道的重要性.The effects of electric-quadrupole (E2) transitions on ion energy-level populations in plasma are studied by constructing the collisional radiative model of a three-level atomic system in the steady-state approximation. It is found that the influence is non-negligible at the low electron density, and becomes larger when the E2 transition rate grows with atomic number increasing. Furthermore, we investigate the E2-transition effects on the populations of levels in the ground configuration for Fe-like Mo16+ and U66+ ions in an electron-beam ion-trap plasma. The level populations are obtained by solving the large-scale rate equation numerically. On this basis, we discuss the influence of the E2 transition on the line intensity ratio of the magnetic dipole (M1) lines. In addition, we point out the significance of the E2 transitions on the intensity ratio of the M1 lines that can be used to diagnose the electron density of plasma.
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Keywords:
- CR model /
- plasma diagnostics /
- atomic data and spectra
[1] Silwal R, Takacs E, Dreiling J M, Gillaspy J D, Ralchenko Y 2017 Atoms 5 30
Google Scholar
[2] Nakamura N, Numadate N, Kono Y, Murakami I, Kato D, Sakaue H A, Hara H 2021 Astrophys. J. 921 115
Google Scholar
[3] 黄文忠, 张覃鑫, 何绍堂, 谷渝秋, 尤永录, 江文勉 1995 物理学报 44 1783
Google Scholar
Huang W Z, Zhang Q X, He S T, Gu Y Q, You Y L, Jiang W M 1995 Acta Phys. Sin. 44 1783
Google Scholar
[4] Feldman U, Doron R, Klapisch M, Bar-Shalom A 2001 Phys. Scr. 63 284
Google Scholar
[5] Doron R, Feldman U 2001 Phys. Scr. 64 319
Google Scholar
[6] Ralchenko Y 2007 J. Phys. B:At. , Mol. Opt. Phys. 40 F175
Google Scholar
[7] Ralchenko Y, Draganic I N, Osin D, Gillaspy J D, Reader J 2011 Phys. Rev. A 83 032517
Google Scholar
[8] Ding X B, Liu J X, Koike F, Murakami I, Kato D, Sakaue H A, Nakamura N, Dong C Z 2016 Phys. Lett. A 380 874
Google Scholar
[9] He Z C, Meng J, Li Y J, Jia F S, Khan N, Niu B, Huang L Y, Hu Z M, Li J G, Wang J G, Zou Y M, Wei B R, Yao K 2022 J. Quant. Spectrosc. Radiat. Transf. 288 108276
Google Scholar
[10] Jonauskas V, Masys S, Kyniene A, Gaigalas G 2013 J. Quant. Spectrosc. Radiat. Transf. 127 64
Google Scholar
[11] Lu Q, Yan C L, Meng J, Xu G Q, Yang Y, Chen C Y, Xiao J, Li J G, Wang J G, Zou Y 2021 Phys. Rev. A 103 022808
Google Scholar
[12] Lu Q, He J, Tian H, Li M, Yang Y, Yao K, Chen C, Xiao J, Li J G, Tu B, Zou Y 2019 Phys. Rev. A 99 042510
Google Scholar
[13] Li W, Shi Z, Yang Y, Xiao J, Brage T, Hutton R, Zou Y 2015 Phys. Rev. A 91 062501
Google Scholar
[14] Han X Y, Gao X, Zeng D L, Jin R, Yan J, Li J M 2014 Phys. Rev. A 89 042514
Google Scholar
[15] Gu M F 2008 Can. J. Phys. 86 675
Google Scholar
[16] Ding X B, Yang J X, Zhu L F, Koike F, Murakami I, Kato D, Sakaue H A, Nakamura N, Dong C Z 2018 Phys. Lett. A 382 2321
Google Scholar
[17] Ding X, Zhang F, Yang Y, Zhang L, Koike F, Murakami I, Kato D, Sakaue H A, Nakamura N, Dong C 2020 Phys. Rev. A 101 042509
Google Scholar
[18] Lu Q, Yan C L, Fu N, Yang Y, Chen C Y, Xiao J, Wang K, Zou Y 2021 J. Quant. Spectrosc. Radiat. Transf. 262 107533
Google Scholar
[19] Qiu M L, Zhao R F, Guo X L, Zhao Z Z, Li W X, Du S Y, Xiao J, Yao K, Chen C Y, Hutton R, Zou Y 2014 J. Phys. B:At. , Mol. Opt. Phys. 47 175002
Google Scholar
[20] Gu M F, Holczer T, Behar E and Kahn S M 2006 Astrophys. J. 641 1227
Google Scholar
[21] Lindgren I 1974 J. Phys. B:At. , Mol. Opt. Phys. 7 2441
Google Scholar
[22] Kramida A, Ralchenko Y, Reader J, and NIST ASD Team 2021 NIST Atomic Spectra Database (ver. 5.9) [Online]. Available:https://physics.nist.gov/asd [2022, May 19]. National Institute of Standards and Technology, Gaithersburg, MD
[23] Sugar J and Musgrove A 1988 J. Phys. Chem. Ref. Data 17 155
Google Scholar
[24] Ralchenko Y, Gillaspy J D, Reader J, Osin D, Curry J J, Podpaly Y A 2013 Phys. Scr. T156
[25] Guo X L, Si R, Li S, Huang M, Hutton R, Wang Y S, Chen C Y, Zou Y M, Wang K, Yan J, Li C Y, Brage T 2016 Phys. Rev. A 93 012513
Google Scholar
[26] Ralchenko Y 2013 Plasma Fusion Res. 8 2503024
Google Scholar
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图 1 三能级原子体系能级图 (a) 模型I不包含E2跃迁; (b) 模型II包含E2跃迁示意图
Fig. 1. Energy levels of the three-level atomic system: (a) Model I without the E2 transition; (b) Model II with inclusion of the E2 transition.
图 2 类铁钼(Mo16+)离子(a)和铀(U66+)离子(b)基组态内的禁戒跃迁, 其中实线为M1跃迁, 虚线为E2跃迁, 图中的数字(0, 1, 2, ···)表示能级序号
Fig. 2. Energy-level diagram of the ground state configuration of Fe-like Mo16+ (a) and Fe-like U66+ (b) ions. Solid lines represent the M1 transitions and dashed lines represent the E2 transitions. The numbers (0, 1, 2, ···) correspond to the energy levels labels.
图 3 类铁钼离子(a)和铀离子(b)处于基组态3d8能级的离子布居对密度的依赖关系, 图中的数字(0, 1, 2, ···)对应于图1中类铁钼离子和铀离子的能级序号
Fig. 3. The electron-density dependence of the population distribution of energy levels belonging to 3d8 configuration of Fe-like Mo16+(a) and U66+(b) ions. The numbers (0, 1, 2, ···) correspond to the energy levels of Mo16+ and U66+ of Fig.1.
图 4 类铁钼离子(a)和铀离子(b)基组态内M1跃迁谱线强度对密度的依赖关系, 图中的(0 –1, ···)是相应跃迁, 数字表示该跃迁的下能级和上能级序号
Fig. 4. The electron-density dependence of the intensity ratios for the M1 transitions from the ground configuration of Mo16+(a) and U66+(b). The numbers (0 –1, ···) correspond to the lower and upper energy levels of the lines, respectively.
表 1 类铁钼离子和铀离子的基组态精细能级激发能
Table 1. Excitation energies of the lowest excited levels of Fe-like Mo16+, U66+ ions.
Z Config-
urationKey Level ERMBPT/
eVENIST/
eV [22, 23]42 3d8 0 $ (3{\rm d}_+^4)_4 $ 0.000 0 42 3d8 1 $ ((3{\rm d}_-^3)_{3/2}(3{\rm d}_+^5)_{\rm 5/2})_3 $ 3.012 3.007 42 3d8 2 $ (3{\rm d}_{+}^{4})_{2} $ 3.358 3.351 42 3d8 3 $ ((3{\rm d}_{-}^3)_{3/2}(3{\rm d}_+^5)_{5/2})_2 $ 6.331 6.323 42 3d8 4 $ (3{\rm d}_+^4)_0 $ 8.478 8.474 42 3d8 5 $ ((3{\rm d}_{-}^3)_{3/2}(3{\rm d}_+^5)_{5/2})_{1} $ 8.721 8.717 42 3d8 6 $ (3{\rm d}_{-}^{2})_2 $ 9.680 9.666 42 3d8 7 $ ((3{\rm d}_{-}^3)_{3/2}(3{\rm d}_+^5)_{5/2})_4 $ 10.183 10.219 42 3d8 8 $ (3{\rm d}_{-}^2)_0 $ 21.972 21.906 92 3d8 0 $ (3{\rm d}_{+}^4)_4$ 0.000 92 3d8 1 $ (3{\rm d}_+^4)_2 $ 12.183 92 3d8 2 $ (3{\rm d}_+^4)_0 $ 40.048 92 3d8 3 $ ((3{\rm d}_{-}^3)_{3/2}(3{\rm d}_+^5)_{5/2})_3 $ 188.701 92 3d8 4 $((3{\rm d}_{-}^3)_{3/2}(3{\rm d}_+^5)_{5/2})_2$ 201.451 92 3d8 5 $ ((3{\rm d}_-^3)_3/2(3{\rm d}_+^5)_{5/2})_4 $ 207.021 92 3d8 6 $ ((3{\rm d}_-^3)_{3/2}(3{\rm d}_+^5)_{5/2})_1 $ 208.894 92 3d8 7 $ (3{\rm d_-^2})_2 $ 386.738 92 3d8 8 $ (3{\rm d}_{-}^2)_0 $ 419.338 
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表 2 类铁钼离子和铀离子的基组态M1跃迁的跃迁能ΔE、波长λ、跃迁速率A和振子强度gf
Table 2. Transition energies ΔE, wavelengths λ, transition rates A and oscillator strength gf for the M1 transitions in the ground configuration of Fe-like Mo16+ and U66+.
Z Line Upper Lower ΔE/eV λ/ nm gf A/s–1 RMBPT NIST[20,21] 42 1 8 5 13.3 93.56 94.01 5.80 × 10–7 4.42 × 103 42 2 7 0 10.2 121.76 121.33 6.65 × 10–7 3.33 × 102 42 3 7 1 7.17 172.89 171.91 2.86 × 10–7 70.9 42 4 6 1 6.67 185.93 186.19 1.62 × 10–6 6.26 × 102 42 5 6 2 6.32 196.10 196.33 5.21 × 10–9 1 42 6 5 2 5.36 231.18 231.05 4.08 × 10–7 1.70 × 102 42 7 6 3 3.35 370.16 370.92 2.60 × 10–6 2.53 × 102 42 8 3 1 3.32 373.56 373.83 2.40 × 10–6 2.30 × 102 42 9 1 0 3.01 411.66 412.37 6.28 × 10–6 3.53 × 102 42 10 3 2 2.97 417.04 417.19 1.87 × 10–6 1.43 × 102 42 11 5 3 2.39 518.72 517.87 1.03 × 10–6 84.9 42 12 6 5 0.959 1292.39 1306.47 2.70 × 10–7 1 42 13 2 1 0.346 3583.17 3604.19 3.93 × 10–7 0.408 42 14 5 4 0.243 5107.12 5102.22 1.42 × 10–7 0.121 92 1 7 1 3.75 × 102 3.31 3.93 × 10–8 4.79 × 104 92 2 8 6 2.10 × 102 5.89 7.32 × 10–5 1.41 × 108 92 3 5 0 2.07 × 102 5.99 1.01 × 10–4 2.09 × 107 92 4 7 3 1.98 × 102 6.26 2.68 × 10–4 9.12 × 107 92 5 6 1 1.97 × 102 6.30 6.79 × 10–5 3.80 × 107 92 6 4 1 1.89 × 102 6.55 1.47 × 10–4 4.56 × 107 92 7 3 0 1.89 × 102 6.57 3.39 × 10–4 7.48 × 107 92 8 7 4 1.85 × 102 6.69 9.07 × 10–5 2.70 × 107 92 9 7 6 1.78 × 102 6.97 8.10 × 10–6 2.22 × 106 92 10 3 1 1.77 × 102 7.02 3.01 × 10–5 5.81 × 106 92 11 6 2 1.69 × 102 7.34 4.86 × 10–5 2.00 × 107 92 12 5 3 18.3 67.68 6.64 × 10–6 1.07 × 104 92 13 4 3 12.7 97.24 7.80 × 10–6 1.10 × 104
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[1] Silwal R, Takacs E, Dreiling J M, Gillaspy J D, Ralchenko Y 2017 Atoms 5 30
Google Scholar
[2] Nakamura N, Numadate N, Kono Y, Murakami I, Kato D, Sakaue H A, Hara H 2021 Astrophys. J. 921 115
Google Scholar
[3] 黄文忠, 张覃鑫, 何绍堂, 谷渝秋, 尤永录, 江文勉 1995 物理学报 44 1783
Google Scholar
Huang W Z, Zhang Q X, He S T, Gu Y Q, You Y L, Jiang W M 1995 Acta Phys. Sin. 44 1783
Google Scholar
[4] Feldman U, Doron R, Klapisch M, Bar-Shalom A 2001 Phys. Scr. 63 284
Google Scholar
[5] Doron R, Feldman U 2001 Phys. Scr. 64 319
Google Scholar
[6] Ralchenko Y 2007 J. Phys. B:At. , Mol. Opt. Phys. 40 F175
Google Scholar
[7] Ralchenko Y, Draganic I N, Osin D, Gillaspy J D, Reader J 2011 Phys. Rev. A 83 032517
Google Scholar
[8] Ding X B, Liu J X, Koike F, Murakami I, Kato D, Sakaue H A, Nakamura N, Dong C Z 2016 Phys. Lett. A 380 874
Google Scholar
[9] He Z C, Meng J, Li Y J, Jia F S, Khan N, Niu B, Huang L Y, Hu Z M, Li J G, Wang J G, Zou Y M, Wei B R, Yao K 2022 J. Quant. Spectrosc. Radiat. Transf. 288 108276
Google Scholar
[10] Jonauskas V, Masys S, Kyniene A, Gaigalas G 2013 J. Quant. Spectrosc. Radiat. Transf. 127 64
Google Scholar
[11] Lu Q, Yan C L, Meng J, Xu G Q, Yang Y, Chen C Y, Xiao J, Li J G, Wang J G, Zou Y 2021 Phys. Rev. A 103 022808
Google Scholar
[12] Lu Q, He J, Tian H, Li M, Yang Y, Yao K, Chen C, Xiao J, Li J G, Tu B, Zou Y 2019 Phys. Rev. A 99 042510
Google Scholar
[13] Li W, Shi Z, Yang Y, Xiao J, Brage T, Hutton R, Zou Y 2015 Phys. Rev. A 91 062501
Google Scholar
[14] Han X Y, Gao X, Zeng D L, Jin R, Yan J, Li J M 2014 Phys. Rev. A 89 042514
Google Scholar
[15] Gu M F 2008 Can. J. Phys. 86 675
Google Scholar
[16] Ding X B, Yang J X, Zhu L F, Koike F, Murakami I, Kato D, Sakaue H A, Nakamura N, Dong C Z 2018 Phys. Lett. A 382 2321
Google Scholar
[17] Ding X, Zhang F, Yang Y, Zhang L, Koike F, Murakami I, Kato D, Sakaue H A, Nakamura N, Dong C 2020 Phys. Rev. A 101 042509
Google Scholar
[18] Lu Q, Yan C L, Fu N, Yang Y, Chen C Y, Xiao J, Wang K, Zou Y 2021 J. Quant. Spectrosc. Radiat. Transf. 262 107533
Google Scholar
[19] Qiu M L, Zhao R F, Guo X L, Zhao Z Z, Li W X, Du S Y, Xiao J, Yao K, Chen C Y, Hutton R, Zou Y 2014 J. Phys. B:At. , Mol. Opt. Phys. 47 175002
Google Scholar
[20] Gu M F, Holczer T, Behar E and Kahn S M 2006 Astrophys. J. 641 1227
Google Scholar
[21] Lindgren I 1974 J. Phys. B:At. , Mol. Opt. Phys. 7 2441
Google Scholar
[22] Kramida A, Ralchenko Y, Reader J, and NIST ASD Team 2021 NIST Atomic Spectra Database (ver. 5.9) [Online]. Available:https://physics.nist.gov/asd [2022, May 19]. National Institute of Standards and Technology, Gaithersburg, MD
[23] Sugar J and Musgrove A 1988 J. Phys. Chem. Ref. Data 17 155
Google Scholar
[24] Ralchenko Y, Gillaspy J D, Reader J, Osin D, Curry J J, Podpaly Y A 2013 Phys. Scr. T156
[25] Guo X L, Si R, Li S, Huang M, Hutton R, Wang Y S, Chen C Y, Zou Y M, Wang K, Yan J, Li C Y, Brage T 2016 Phys. Rev. A 93 012513
Google Scholar
[26] Ralchenko Y 2013 Plasma Fusion Res. 8 2503024
Google Scholar
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