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Theoretical study of state-selective charge exchange processes in collisions between highly charged N6+ ions and H atoms

NIU Jiajie ,  ZHANG Weiwei ,  QI Yueying ,  GAO Junwen

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Theoretical study of state-selective charge exchange processes in collisions between highly charged N6+ ions and H atoms

NIU Jiajie, ZHANG Weiwei, QI Yueying, GAO Junwen
Acta Phys. Sin., 2025, 74(15): 153402.
doi: 10.7498/aps.74.20250541
cstr: 32037.14.aps.74.20250541
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  • Abstract

    In this work, we systematically investigate single-electron capture process in the collision between N6+(1s) ions and H(1s) atoms in a wide energy range from 0.25 to 225 keV/u by using a two-electron semiclassical asymptotic-state close-coupling method. Spin-averaged and spin-resolved total cross sections, as well as n-resolved and $n\ell $-resolved partial cross sections, are calculated and comprehensively compared with existing experimental measurements and theoretical predictions. The results show at low energies (<10 keV/u), energy dependence of the total cross section is weak, and it follows a monotonically decreasing trend at higher energies. The analysis of $n\ell $-resolved cross sections reveals the strong coupling effects between various channels at low energies, while at high energies the relative $\ell $ distributions in each $n\ell $-resolved cross section approximately follow the statistical $\ell $ distribution, for which the electrons are therefore mainly captured into subshells of the maximum $\ell $. The present study demonstrates the importance of a two-electron treatment taking into account electronic correlation and the use of extended basis sets in the close-coupling scheme. However, substantial discrepancies exist among theoretical approaches at low energies. It is clear that further experimental and theoretical efforts are required to draw definite conclusions. Our work provides a complete and consistent set of cross sections in a broad range of collision energies, which can be used for various plasma diagnosis and modeling. The datasets presented in this paper are openly available at https://doi.org/10.57760/sciencedb.j00213.00143.

    Authors and contacts

    • 1.

      School of Physics, Hangzhou Normal University, Hangzhou 311121, China

    • 2.

      College of Mechanical Engineering, Jiaxing University, Jiaxing 314001, China

      • Corresponding author: QI Yueying, yying_qi@zjxu.edu.cn ; GAO Junwen, gaojunwen@hznu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12374229).

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  • 图 1  N6+(1s)与H(1s)碰撞自旋态平均单电子俘获总截面随碰撞能量的变化, 以及当前结果同已有的实验数据[31,32,43]和理论计算[35–38]的对比

    Figure 1.  Spin-averaged total single-electron capture cross sections as a function of collision energy for N6+(1s) + H(1s) collisions. Present results are compared with experimental data[31,32,43] and theoretical calculations[35–38].

    DownLoad: Full-Size Img PowerPoint

    图 2  N6+(1s)与H (1s)碰撞自旋平均的主量子数n分辨单电子俘获截面随碰撞能量的变化, 以及当前结果同已有理论计算[36,37]对比　(a) n = 3; (b) n = 4; (c) n = 5

    Figure 2.  Spin-averaged n-resolved single-electron capture cross sections as a function of collision energy for N6+(1s) + H(1s) collisions: (a) n = 3, (b) n = 4, (c) n = 5. Present results are compared with theoretical calculations[36,37].

    DownLoad: Full-Size Img PowerPoint

    图 3  N6+(1s)与H(1s)碰撞中自旋平均的轨道量子数$n\ell $分辨单电子俘获截面随碰撞能量的变化, 以及本工作计算结果同已有的理论计算[36,37]对比　(a) $3\ell $态; (b) $4\ell $态; (c) $5\ell $态

    Figure 3.  Spin-averaged $n\ell $-resolved single-electron capture cross sections as a function of collision energy for N6+(1s) + H(1s) collisions: (a) $3\ell $; (b) $4\ell $; (c) $5\ell $. Present results are compared with theoretical calculations[36,37].

    DownLoad: Full-Size Img PowerPoint

    表 1  不同碰撞能量E (单位: keV/u)下, N6+(1s)离子与H(1s)原子碰撞自旋平均的单电子俘获总截面和俘获至N5+(1s$n\ell $)态分辨截面(单位: 10–16 cm2)

    Table 1.  Spin-averaged total single-electron capture cross sections and state-resolved cross sections for capture into N5+ (1s$n\ell $) states in N6+(1s) + H(1s) collisions at various collision energies E (unit: keV/u). All cross sections are given in units of 10–16 cm2.

    E 1s3s 1s3p 1s3d 1s4s 1s4p 1s4d 1s4f 1s5s 1s5p 1s5d 1s5f 1s5g 总截面
    0.25 0.0002 0.0002 0.0002 3.7648 12.7027 8.5685 13.3494 0.1747 0.6930 0.9648 0.4290 2.0774 42.7323
    0.56 0.0002 0.0007 0.0013 6.4063 10.4408 5.2656 13.6226 0.2466 1.9896 0.9673 1.0273 1.4035 41.4063
    1.00
    		 0.0023 0.0054 0.0108 9.2673 9.5404 5.9963 11.9886 0.8304 0.9395 1.0427 1.9539 0.9143 42.5571
    2.25 0.0273 0.0799 0.1115 7.5560 8.9939 7.4811 12.8323 0.6563 0.4619 0.4968 2.3590 2.3944 43.5764
    4.00 0.0927 0.4714 0.2950 5.7645 8.3648 9.1302 12.2192 0.3532 0.4350 0.7830 2.5118 3.1321 43.8349
    6.25 0.2357 0.6419 0.4629 3.3885 6.5808 10.4578 13.2696 0.4157 0.8553 0.9404 2.9255 4.2443 44.7038
    9.00 0.3394 0.6624 0.5941 1.8598 4.7615 9.9354 14.5785 0.2967 0.7135 1.1683 2.7464 5.8699 43.8333
    16.00 0.3529 0.9129 1.1518 0.6615 2.6646 7.6238 14.9072 0.1737 0.5804 1.4345 2.9620 5.9363 39.9444
    25.00 0.3508 1.0430 1.6138 0.3115 1.5698 4.7657 12.1202 0.1464 0.5298 1.3658 3.1366 5.4187 33.7083
    36.00 0.2659 0.9920 1.7688 0.1915 0.9180 2.7773 8.3503 0.1050 0.4919 1.1551 2.9266 4.6950 27.5872
    56.25 0.1245 0.5889 1.5077 0.0920 0.4132 1.1599 4.1918 0.0741 0.4061 0.7697 2.0000 2.7565 19.0517
    100.00 0.0250 0.1622 0.6719 0.0243 0.1261 0.4415 0.9926 0.0292 0.1383 0.3505 0.7732 0.6489 6.8768
    156.25 0.0103 0.0393 0.2537 0.0096 0.0326 0.1687 0.1934 0.0105 0.0340 0.1390 0.2303 0.1001 1.8768
    225.00 0.0035 0.0209 0.0742 0.0026 0.0170 0.0480 0.0392 0.0022 0.0130 0.0392 0.0594 0.0148 0.5114
    DownLoad: CSV

    表 2  不同碰撞能量E (单位: keV/u)下, N6+(1s)离子与H(1s)原子碰撞自旋单重态下的单电子俘获总截面和俘获至N5+(1s$n\ell $ 1L)态分辨截面(单位: 10–16 cm2)

    Table 2.  Spin-singlet total single-electron capture cross sections and state-resolved cross sections for capture into N5+(1s$n\ell $ 1L) states in N6+(1s) + H(1s) collisions at various collision energies E (unit: keV/u). All cross sections are given in units of 10–16 cm2.

    E 1s3s 1S 1s3p 1P 1s3d 1D 1s4s 1S 1s4p 1P 1s4d 1D 1s4f 1F 1s5s 1S 1s5p 1P 1s5d 1D 1s5f 1F 1s5g 1G 总截面1L
    0.25 0.0001 0.0002 0.0002 4.9841 4.1948 6.0168 13.7765 0.1364 1.1173 0.7492 0.4985 3.0177 34.5024
    0.56 0.0003 0.0010 0.0013 6.6345 3.7956 8.0072 13.0620 0.3696 1.9096 1.1744 1.0736 1.6679 37.7347
    1.00 0.0023 0.0073 0.0076 8.8291 4.8926 9.4065 12.8317 0.9635 1.1060 0.8840 1.9907 0.9559 41.9406
    2.25 0.0314 0.0879 0.0599 6.6027 5.3151 11.9836 14.0620 0.6144 0.5642 0.4328 2.4516 2.4166 44.7399
    4.00 0.1416 0.4313 0.2924 5.0184 5.9133 12.5596 13.2306 0.2941 0.4484 0.7915 2.4992 3.1441 45.0342
    6.25 0.3049 0.6447 0.4420 2.8775 5.0788 12.7611 14.0163 0.3535 0.7570 0.9597 2.8547 4.2684 45.5828
    9.00 0.3949 0.7666 0.6046 1.5960 3.9072 11.1796 15.1420 0.2527 0.6901 1.1460 2.6755 5.7122 44.3560
    16.00 0.3889 1.0895 1.2582 0.5916 2.5040 7.9453 14.9587 0.1480 0.6129 1.3966 2.9507 5.7149 40.1231
    25.00 0.3696 1.1997 1.7008 0.2885 1.6088 4.8367 11.9200 0.1366 0.5699 1.3379 3.0703 5.4103 33.7599
    36.00 0.2757 1.1118 1.8295 0.1861 0.9715 2.7831 8.2105 0.0998 0.5225 1.1366 2.8470 4.7282 27.6453
    56.25 0.1240 0.6285 1.5212 0.0906 0.4484 1.1474 4.1679 0.0700 0.4274 0.7624 1.9865 2.7557 19.0999
    100.00 0.0249 0.1684 0.6648 0.0245 0.1309 0.4330 0.9952 0.0297 0.1417 0.3476 0.7773 0.6477 6.8638
    156.25 0.0101 0.0413 0.2503 0.0092 0.0340 0.1657 0.1940 0.0101 0.0347 0.1368 0.2312 0.1003 1.8767
    225.00 0.0033 0.0222 0.0735 0.0024 0.0180 0.0474 0.0392 0.0021 0.0136 0.0387 0.0594 0.0148 0.5149
    DownLoad: CSV

    表 3  不同碰撞能量E (单位: keV/u)下, N6+(1s)离子与H(1s)原子碰撞自旋三重态下的单电子俘获总截面和俘获至N5+(1s$n\ell $ 3L)态分辨截面(单位:10–16 cm2)

    Table 3.  Spin-triplet total single-electron capture cross sections and state-resolved cross sections for capture into N5+(1s$n\ell $ 3L) states in N6+(1s) + H(1s) collisions at various collision energies E (unit: keV/u). All cross sections are given in units of 10–16 cm2.

    E 1s3s 3S 1s3p 3P 1s3d 3D 1s4s 3S 1s4p 3P 1s4d 3D 1s4f 3F 1s5s 3S 1s5p 3P 1s5d 3D 1s5f 3F 1s5g 3G 总截面3L
    0.25 0.0002 0.0002 0.0002 3.3584 15.5386 9.4191 13.2070 0.1875 0.5515 1.0366 0.4058 1.7640 45.4756
    0.56 0.0002 0.0006 0.0013 6.3302 12.6558 4.3517 13.8094 0.2056 2.0162 0.8983 1.0119 1.3154 42.6301
    1.00 0.0022 0.0048 0.0119 9.4133 11.0897 4.8596 11.7075 0.7860 0.8840 1.0955 1.9416 0.9004 42.7626
    2.25 0.0260 0.0772 0.1287 7.8738 10.2202 5.9803 12.4224 0.6703 0.4279 0.5181 2.3282 2.3870 43.1886
    4.00 0.0764 0.4847 0.2958 6.0132 9.1819 7.9870 11.8821 0.3729 0.4305 0.7801 2.5160 3.1281 43.4352
    6.25 0.2126 0.6409 0.4699 3.5588 7.0815 9.6901 13.0207 0.4365 0.8881 0.9340 2.9492 4.2362 44.4108
    9.00 0.3208 0.6277 0.5906 1.9477 5.0463 9.5207 14.3906 0.3114 0.7213 1.1757 2.7700 5.9224 43.6591
    16.00 0.3409 0.8540 1.1163 0.6848 2.7181 7.5166 14.8900 0.1822 0.5696 1.4472 2.9658 6.0101 39.8848
    25.00 0.3445 0.9908 1.5849 0.3192 1.5568 4.7420 12.1870 0.1497 0.5165 1.3750 3.1587 5.4216 33.6911
    36.00 0.2626 0.9520 1.7486 0.1933 0.9002 2.7754 8.3969 0.1067 0.4817 1.1613 2.9532 4.6839 27.5678
    56.25 0.1247 0.5757 1.5031 0.0924 0.4014 1.1641 4.1998 0.0755 0.3991 0.7721 2.0045 2.7568 19.0356
    100.00 0.0250 0.1601 0.6743 0.0243 0.1245 0.4443 0.9917 0.0290 0.1372 0.3515 0.7718 0.6493 6.8811
    156.25 0.0104 0.0387 0.2549 0.0098 0.0321 0.1697 0.1932 0.0106 0.0338 0.1398 0.2300 0.1001 1.8769
    225.00 0.0036 0.0204 0.0745 0.0027 0.0167 0.0482 0.0392 0.0023 0.0127 0.0394 0.0595 0.0148 0.5102
    DownLoad: CSV
  • [1]

    Fritsch W, Lin C D 1991 Phys. Rep. 202 1Google Scholar

    [2]

    Fogle M, Wulf D, Morgan K, McCammon D, Seely D G, Draganić I N, Havener C C 2014 Phys. Rev. A 89 042705Google Scholar

    [3]

    Gu L, Kaastra J, Raassen A J J 2016 A&A 588 A52Google Scholar

    [4]

    Anderson H, von Hellermann M G, Hoekstra R, Horton L D, Howman A C, Konig R W T, Martin R, Olson R E, Summers H P 2000 Plasma Phys. Control. Fusion 42 781Google Scholar

    [5]

    Delabie E, Brix M, Giroud C, Jaspers R J E, Marchuk O, O'Mullane M G, Ralchenko Y, Surrey E, von Hellermann M G, Zastrow K D, Contributors J E 2010 Plasma Phys. Control. Fusion 52 125008Google Scholar

    [6]

    Isler R C 1977 Phys. Rev. Lett. 38 1359Google Scholar

    [7]

    Isler R C 1994 Plasma Phys. Control. Fusion 36 171Google Scholar

    [8]

    von Hellermann M G, Bertschinger G, Biel W, Giroud C, Jaspers R, Jupen C, Marchuk O, Mullane M O, Summers H P, Whiteford A, Zastrow K D 2005 Phys. Scr. 2005 19Google Scholar

    [9]

    McDermott R M, Dux R, Pütterich T, Geiger B, Kappatou A, Lebschy A, Bruhn C, Cavedon M, Frank A, Harder N D, Viezzer E, the A U T 2018 Plasma Phys. Control. Fusion 60 095007Google Scholar

    [10]

    Lisse C M, Dennerl K, Englhauser J, Harden M, Marshall F E, Mumma M J, Petre R, Pye J P, Ricketts M J, Schmitt J, Trumper J, West R G 1996 Science 274 205Google Scholar

    [11]

    Cravens T E 1997 Geophys. Res. Lett. 24 105Google Scholar

    [12]

    Hoekstra R, Anderson H, Bliek F W, Hellermann M v, Maggi C F, Olson R E, Summers H P 1998 Plasma Phys. Control. Fusion 40 1541Google Scholar

    [13]

    Cravens T E 2000 Astrophys. J. 532 L153Google Scholar

    [14]

    Cravens T E 2002 Science 296 1042Google Scholar

    [15]

    Holmstrom M, Barabash S, Kallio E 2001 Geophys. Res. Lett. 28 1287Google Scholar

    [16]

    Beiersdorfer P, Boyce K R, Brown G V, Chen H, Kahn S M, Kelley R L, May M, Olson R E, Porter F S, Stahle C K, Tillotson W A 2003 Science 300 1558Google Scholar

    [17]

    Lallement R 2004 A&A 418 143Google Scholar

    [18]

    Branduardi-Raymont G, Bhardwaj A, Elsner R F, Gladstone G R, Ramsay G, Rodriguez P, Soria R, Waite Jr J H, Cravens T E 2007 A&A 463 761Google Scholar

    [19]

    Robertson I P, Kuntz K D, Collier M R, Cravens T E, Snowden S L 2009 AIP Conference Proceedings 1156 52Google Scholar

    [20]

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  • Received Date:  24 April 2025
  • Accepted Date:  15 May 2025
  • Available Online:  06 June 2025
  • Published Online:  05 August 2025

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