Effects of electric quadrupole transitions on ion energy-level populations of in electron beam ion trap plasma

Meng Ju; He Zhen-Cen; Yan Jun; Wu Ze-Qing; Yao Ke; Li Ji-Guang; Wu Yong; Wang Jian-Guo

doi:10.7498/aps.71.20220489

Abstract

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.

Keywords:

Authors and contacts

1.
National Key Laboratory of Computational Physics, Institute of Applied Physics and ComputationalMathematics, Beijing 100088, China
2.
Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), Fudan University, Shanghai 200433, China
3.
HEDPS, Center for Applied Physics and Technology, and College of Engineering, Peking University, Beijing 100871, China

Corresponding author: Yao Ke, keyao@fudan.edu.cn ; Li Ji-Guang, li_jiguang@iapcm.ac.cn ;

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11874090, 11874008, 11734013, 11934004, 11404180, 11604052 and 11774037) and the National Key Research and Development Program of China (Grant Nos. 2017YFA0403200, 2017YFA0402300).

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References

[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

Cited By

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

图 5 类铁钼离子(a)和铀离子(b)的密度敏感线, 图中的数字(9/7, ···)对应于跃迁标号, 与表1一致

Figure 5. Density-sensitive line radios for Mo¹⁶⁺(a) and U⁶⁶⁺(b). The numbers (9/7, ···) correspond to the transitions in Table 1.

DownLoad: Full-Size Img PowerPoint

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- uration	Key	Level	E_RMBPT/ eV	E_NIST/ 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

DownLoad: CSV

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
Z	Line	Upper	Lower	ΔE/eV	RMBPT	NIST^[20,21]	gf	A/s^–1
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

DownLoad: CSV

[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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