Influence of relativistic effects on photoionization process of hydrogen-like ions in plasma environment

Ge Di; Zhao Guo-Peng; Qi Yue-Ying; Chen Chen; Gao Jun-Wen; Hou Hong-Sheng

doi:10.7498/aps.73.20240016

Abstract

In this study, the photoionization cross sections of C⁵⁺, Al¹²⁺, and W⁷³⁺ ions in a Debye plasma environment are calculated in the dipole approximation. The main emphasis is placed on investigating the influence of relativistic effects on shape resonances, Cooper minima, and virtual state effects. The relativistic effects lead to fine-structure splittings, allowing the appearance of double-shape resonance peaks in the total cross-section. Because the width and energy position of resonance peak are affected by the near critical screening length, the increase of nuclear charge Z leads to the significant differences in the size, width, and position of the double-shape resonance peak. The energy position of Cooper minimum in the photoelectrons is related to the critical screening length corresponding to the final continuum state. Unlike the deeper minima observed in the total photoionization cross-sections for C⁵⁺ and Al¹²⁺ ions, for the higher nuclear charge of W⁷³⁺ ions, the significant fine-structure splitting arising from relativistic effects results in substantial differences in the positions of the Cooper minima in the partial cross-sections. Therefore, when superimposed on the total cross section, these minima appear shallower. The W⁷³⁺ ion has a higher nuclear charge, and the screening length related to the virtual state effect is completely different from that of C⁵⁺ ion and Al¹²⁺ ion. Moreover, for the same screening length, there is a significant difference in the virtual state enhancement amplitude between C⁵⁺ ion and Al¹²⁺ ion in the low energy region .

Keywords:

Authors and contacts

1.
College of Data Science, Jiaxing University, Jiaxing 314001, China
2.
School of Physics, Hangzhou Normal University, Hangzhou 311121, China

Corresponding author: Zhao Guo-Peng, guopengzhao@zjxu.edu.cn ; Qi Yue-Ying, yying_qi@zjxu.edu.cn ;

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12105119) and the Open Foundation for Key Laboratory of Clean Energy and Carbon Neutrality of Zhejiang Province, China (Grant No. 204022023006A).

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References

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Cited By

图 1 (a) C⁵⁺, (b) Al¹²⁺ 和 (c) W⁷³⁺ 离子初态为1s_1/2的总标度光电离截面随标度的光电子能量的变化关系, 不同颜色的曲线对应不同的标度屏蔽长度

Figure 1. Behavior of the total 1s_1/2 scaled photoionization cross sections of (a) C⁵⁺, (b) Al¹²⁺ and (c) W⁷³⁺ ion as a function of scaled photoelectron energy. The colors of the lines are for different scaled screening lengths.

DownLoad: Full-Size Img PowerPoint

图 2 W⁷³⁺ 离子初态为1s_1/2的跃迁　(a) 1s_1/2→εp_1/2, (b) 1s_1/2→εp_3/2贡献的标度的分截面和(c)总光电离截面随标度的光电子能量的变化关系, 不同颜色的曲线对应不同的标度的屏蔽长度

Figure 2. Behavior of scaled partial (a) 1s_1/2→εp_1/2, (b) 1s_1/2→εp_3/2 and (c) total 1s_1/2 photoionization cross sections of W⁷³⁺ ion as a function of scaled photoelectron energy. The colors of the lines are for different scaled screening lengths.

DownLoad: Full-Size Img PowerPoint

图 3 (a) C⁵⁺, (b) Al¹²⁺ 和 (c) W⁷³⁺ 离子初态为2s_1/2的总标度光电离截面随标度的光电子能量的变化关系, 不同颜色的曲线对应不同的标度的屏蔽长度

Figure 3. Behavior of the total 2s_1/2 scaled photoionization cross sections of (a) C⁵⁺, (b) Al¹²⁺ and (c) W⁷³⁺ ion as a function of scaled photoelectron energy. The colors of the lines are for different scaled screening lengths.

DownLoad: Full-Size Img PowerPoint

图 4 (a) C⁵⁺, (b) Al¹²⁺ 和 (c) W⁷³⁺ 离子初态为2s_1/2的总标度光电离截面随标度的光电子能量的变化关系, 不同颜色的曲线对应不同的标度的屏蔽长度

Figure 4. Behavior of the total 2s_1/2 scaled photoionization cross sections of (a) C⁵⁺, (b) Al¹²⁺ and (c) W⁷³⁺ ion as a function of scaled photoelectron energy. The colors of the lines are for different scaled screening lengths

DownLoad: Full-Size Img PowerPoint

图 5 W⁷³⁺ 离子跃迁　(a) 2s_1/2→εp_1/2和 (b) 2s_1/2→εp_3/2贡献的分标度截面随标度的光电子能量的变化关系. 不同颜色的曲线对应不同的标度的屏蔽长度

Figure 5. Behavior of partial (a) 2s_1/2→εp_1/2 and (b) 2s_1/2→εp_3/2 scaled photoionization cross sections of W⁷³⁺ ion as a function of scaled photoelectron energy. The colors of the lines are for different scaled screening lengths.

DownLoad: Full-Size Img PowerPoint

图 6 (a) C⁵⁺, (b) Al¹²⁺ 和 (c) W⁷³⁺ 离子初态为2p_1/2的总标度光电离截面随标度的光电子能量的变化关系, 不同颜色的曲线对应不同的标度的屏蔽长度

Figure 6. Behavior of the total 2p_1/2 scaled photoionization cross sections of (a) C⁵⁺, (b) Al¹²⁺ and (c) W⁷³⁺ ion as a function of scaled photoelectron energy. The colors of the lines are for different scaled screening lengths.

DownLoad: Full-Size Img PowerPoint

图 7 (a) C⁵⁺, (b) Al¹²⁺ 和 (c) W⁷³⁺ 离子初态为2p_3/2的总标度光电离截面随标度的光电子能量的变化关系, 不同颜色的曲线对应不同的标度的屏蔽长度

Figure 7. Behavior of the total 2p_3/2 scaled photoionization cross sections of (a) C⁵⁺, (b) Al¹²⁺ and (c) W⁷³⁺ ion as a function of scaled photoelectron energy. The colors of the lines are for different scaled screening lengths.

DownLoad: Full-Size Img PowerPoint

图 8 Al¹²⁺ 离子跃迁　(a) 2p_3/2→εs_1/2, (b) 2p_3/2→εd_3/2和(c) 2p_3/2→εd_5/2贡献的分标度截面随标度的光电子能量的变化关系. 不同颜色的曲线对应不同的标度的屏蔽长度

Figure 8. Behavior of partial (a) 2p_3/2→εs_1/2, (b) 2p_3/2→εd_3/2, and (c) 2p_3/2→εd_5/2 scaled photoionization cross sections of Al¹²⁺ ion as a function of scaled photoelectron energy. The colors of the lines are for different scaled screening lengths.

DownLoad: Full-Size Img PowerPoint

表 1 C⁵⁺, Al¹²⁺ 和 W⁷³⁺离子$ n \leqslant 3 $的临界标度屏蔽长度$ \delta _{nlj}^{\text{c}} $

Table 1. Values of critical scaled screening lengths $ \delta _{nlj}^{\text{c}} $ for C⁵⁺, Al¹²⁺, and W⁷³⁺ ions for $ n \leqslant 3 $.

n		s_1/2	p_1/2	p_3/2	d_3/2	d_5/2
1	C⁵⁺	0.8397
	Al¹²⁺	0.8389
	W⁷³⁺	0.8035
2	C⁵⁺	3.2222	4.5391	4.5406
	Al¹²⁺	3.2167	4.5324	4.5395
	W⁷³⁺	2.9810	4.2398	4.4945
3	C⁵⁺	7.1681	8.8690	8.8714	10.9464	10.9472
	Al¹²⁺	7.1573	8.8570	8.8680	10.9425	10.9460
	W⁷³⁺	6.6887	8.3325	8.7293	10.7822	10.8983

DownLoad: CSV

[1]	Qi Y Y, Wang J G, Janev R K 2009 Phys. Rev. A 80 063404 Google Scholar
[2]	Shore B W 1975 J. Phys. B 8 2023 Google Scholar
[3]	Qi Y Y, Wang J G, Janev R K 2011 Eur. Phys. J. D 63 327 Google Scholar
[4]	Cooper J W 1962 Phys. Rev. 128 681 Google Scholar
[5]	Yin R Y, Pratt R H 1987 Phys. Rev. A 35 1149 Google Scholar
[6]	Combet-Farnoux F 1972 Proceedings of the International Conference on Inner Shell Ionization Phenomena (Vol. 2) (Atlanta: University of Georgia Press) p1130
[7]	Lin C Y, Ho Y K 2010 Phys. Rev. A 81 033405 Google Scholar
[8]	Lin C Y, Ho Y K 2010 Phys. Plasmas 17 093302 Google Scholar
[9]	Lin C Y, Ho Y K 2011 Phys. Scr. T 144 014051 Google Scholar
[10]	Xie L Y, Wang J G, Janev R K 2014 Phys. Plasmas 21 063304 Google Scholar
[11]	Zheng X, Chi H C, Lin S T, Jiang G, Qiao C, Huang K N 2019 Indian J. Phys. 93 267 Google Scholar
[12]	Shukla P K, Eliasson B 2008 Phys. Lett. A 372 2897 Google Scholar
[13]	Qi Y Y, Wang J G, Janev R K 2017 Phys. Plasmas 24 062110 Google Scholar
[14]	Das M 2014 Phys. Plasmas 21 012709 Google Scholar
[15]	Chen Z B, Wang K 2020 J. Quant. Spectrosc. Radiat. Transfer 245 106847 Google Scholar
[16]	Sharma R, Goyal A 2022 Indian J. Phys. 96 1829 Google Scholar
[17]	Zeng J, Li Y, Gao C, Yuan J 2020 A& A 634 A117 Google Scholar
[18]	Zeng J, Li Y, Yuan J 2021 J. Quant. Spectrosc. Radiat. Transfer 272 107777 Google Scholar
[19]	Li X, Rosmej F B 2020 Phys. Lett. A 384 126478 Google Scholar
[20]	Dawra D, Dimri M, Singh A K, Jha A K S, Pandey R K, Sharma R, Mohan M 2021 Phys. Plasmas 28 112706 Google Scholar
[21]	Singh D, Varshni Y P 1983 Phys. Rev. A 28 2606 Google Scholar
[22]	Stanton L G, Murillo M S 2015 Phys. Rev. E 91 033104 Google Scholar
[23]	Zhao G P, Xie L Y, Liu L, Wang J G, Janev R K 2018 Phys. Plasmas 25 083302 Google Scholar
[24]	Chen Z B, Qi Y Y, Sun H Y, Zhao G P, Liu P F, Wang K 2020 J. Quant. Spectrosc. Radiat. Transfer 253 107170 Google Scholar
[25]	Zhao G P, Chen C, Liu L, Chen Z B, Qi Y Y, Wang J G 2022 Phys. Plasmas 29 053301 Google Scholar
[26]	Baimbetov F B, Nurekenov Kh T, Ramazanov T S 1995 Phys. Lett. A 202 211 Google Scholar
[27]	Das N, Das B, Ghoshal A 2022 Phys. Plasmas 29 073505 Google Scholar
[28]	Chen Z B 2023 Few-Body Syst. 64 74 Google Scholar
[29]	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 032108 Google Scholar
[30]	Xie H H, Jiao L G, Liu A, Ho Y K 2021 Int. J. Quantum Chem. 121 e26653 Google Scholar
[31]	Wu J Y, Wu Y, Qi Y Y, Wang J G, Janev R K, Zhang S B 2019 Phys. Rev. A 99 012705 Google Scholar
[32]	Wu J Y, Qi Y Y, Cheng Y J, Wu Y, Wang J G, Janev R K, Zhang S B 2020 Phys. Plasmas 27 043301 Google Scholar
[33]	Zhao G P, Qi Y Y, Liu L, Wang J G, Janev R K 2019 Phys. Plasmas 26 063509 Google Scholar
[34]	Chen C, Zhao G P, Chen Z B, Qi Y Y, Liu L, Wu Y, Wang J G 2023 Phys. Plasmas 30 123503 Google Scholar
[35]	Qi Y Y, Ning L N, Wang J G, Qu Y Z 2013 Phys. Plasmas 20 123301 Google Scholar
[36]	Qi Y Y, Ye D D, Wang J G, Qu Y Z 2015 Chin. Phys. B 24 033403 Google Scholar
[37]	Hoarty D J, Allan P, James S F, Brown C R D, Hobbs L M R, Hill M P, Harris J W O, Morton J, Brookes M G, Shepherd R, Dunn J, Chen H, Marley E V, Beiersdorfer P, Chung H K, Lee R W, Brown G, Emig J 2013 Phys. Rev. Lett. 110 265003 Google Scholar
[38]	Gormezano C, Sips A C C, Luce T C, Ide S, Becoulet A 2007 Nucl. Fusion 47 S285 Google Scholar
[39]	Dyall K G, Grant I P, Johnson C T, Parpia F A, Plummer E P 1989 Comput. Phys. Commun. 55 425 Google Scholar
[40]	Grant I P 1974 J. Phys. B: At. Mol. Phys. 7 1458
[41]	Jönsson P, He X, Froese Fischer C, Grant I P 2007 Comput. Phys. Commun. 177 597 Google Scholar
[42]	Tews M G, Perger W F 2001 Comput. Phys. Commun. 141 205 Google Scholar
[43]	Perger W F, Halabuka Z, Trautmann D 1993 Comput. Phys. Commun. 76 250 Google Scholar
[44]	Landau L D, Lifshitz E M 1958 Quantum Mechanics: Non-Relativistic Theory (London: Pergamon
[45]	Bilycki M, Stachov A, Karwowski J, Mukherjee P K 2007 Chem. Phys. 331 346 Google Scholar

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