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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 .
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Keywords:
- photoionization /
- relativistic effect /
- shape resonance /
- Cooper minima
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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图 1 (a) C5+, (b) Al12+ 和 (c) W73+ 离子初态为1s1/2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 1s1/2 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.
图 2 W73+ 离子初态为1s1/2的跃迁 (a) 1s1/2→εp1/2, (b) 1s1/2→εp3/2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) 1s1/2→εp1/2, (b) 1s1/2→εp3/2 and (c) total 1s1/2 photoionization cross sections of W73+ ion as a function of scaled photoelectron energy. The colors of the lines are for different scaled screening lengths.
图 3 (a) C5+, (b) Al12+ 和 (c) W73+ 离子初态为2s1/2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 2s1/2 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.
图 4 (a) C5+, (b) Al12+ 和 (c) W73+ 离子初态为2s1/2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 2s1/2 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
图 5 W73+ 离子跃迁 (a) 2s1/2→εp1/2和 (b) 2s1/2→εp3/2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) 2s1/2→εp1/2 and (b) 2s1/2→εp3/2 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.
图 6 (a) C5+, (b) Al12+ 和 (c) W73+ 离子初态为2p1/2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 2p1/2 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.
图 7 (a) C5+, (b) Al12+ 和 (c) W73+ 离子初态为2p3/2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 2p3/2 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.
图 8 Al12+ 离子跃迁 (a) 2p3/2→εs1/2, (b) 2p3/2→εd3/2和(c) 2p3/2→εd5/2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) 2p3/2→εs1/2, (b) 2p3/2→εd3/2, and (c) 2p3/2→εd5/2 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.
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 s1/2 p1/2 p3/2 d3/2 d5/2 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 -
[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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