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Excitation energies and radiative transition rates of isoelectronic sequences of Li-like ions with Z = 6–51

ZHAO Jiaxun ,  WU Chensheng ,  SONG Qinghe

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Excitation energies and radiative transition rates of isoelectronic sequences of Li-like ions with Z = 6–51

ZHAO Jiaxun, WU Chensheng, SONG Qinghe
Acta Phys. Sin., 2025, 74(15): 153102.
doi: 10.7498/aps.74.20250611
cstr: 32037.14.aps.74.20250611
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  • Abstract

    Li-like ions widely exist in astrophysical and laboratory plasmas, and their precise atomic parameters (e.g. excitation energies and transition rates) are very important for plasma diagnostics and spectral analysis. In this work, we employ the GRASP2018 software package, which is widely used in atomic structure calculations, to systematically compute the lowest 15 energy levels and the electric dipole (E1), magnetic dipole (M1), and electric quadrupole (E2) transition rates between them of 17 Li-like ions across the isoelectronic sequence (Z = 6–51: C3+, F6+, Mg9+, P12+, Ar15+, Sc18+, Cr21+, Co24+, Zn27+, As30+, Kr33+, Y36+, Mo39+, Rh42+, Cd45+, Sn37+, Sb38+). The calculations are based on the multi-configuration Dirac-Fock (MCDF) and configuration interaction (CI) method combined with high-order relativistic corrections and quantum electrodynamics effects such as Breit interaction, self-energy correction and vacuum polarization. The computational convergence is achieved. The calculated excitation energies and transition rates are compared with the NIST database and previous theoretical results. Due to the reasonable construction and larger scale of baseset, the current computational results show evident improvement compared with the results obtained using the same MCDF+CI method previously. Particularly for the two lowest excited states, [1s22p]1/2 and [1s22p]3/2, which exhibit slower convergence, the relative difference between current results and the NIST data is reduced by one to two orders of magnitude compared with previous MCDF+CI calculations. This accuracy even approaches that achieved by S-matrix methods specifically optimized for the ground state and these two lowest excited states. For transition rates, except for certain weak transitions with rates below $ {10}^{3}\;{{{\mathrm{s}}}}^{{-1}} $, the difference between our calculations and previous theoretical results obtained using the MCDF+CI method is still within 1%. Furthermore, our calculations accord with the NIST data within 5% for the majority of transitions. A comparison of NIST data with other previous theoretical results shows evident discrepancies between our calculations and the NIST data for some excitation energies and transition rates. Our results are consistent with other theoretical results for these specific values, indicating that these particular energy levels and transitions need more detailed theoretical and experimental investigation. This work provides highly accurate data for supporting experimental diagnostics and theoretical modeling of astrophysical and laboratory plasmas in future research. The datasets presented in this paper are openly available at https://www.doi.org/10.57760/sciencedb.j00213.00154.

    Authors and contacts

    • Department of Physics, Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China

      • Corresponding author: WU Chensheng, 20220209@kust.edu.cn ; SONG Qinghe, songqinghe@kust.edu.cn
    • Funds: Project supported by the the National Natural Science Foundation of China (Grant No. 12204057), the Applied Basic Research Program of Yunnan Province, China (Grant No. 202401CF070090), and the National Key Laboratory of Computational Physics.

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  • 图 1  Mg9+, Cr21+, Mo39+三种离子两个激发态[1s22p]1/2和[1s24f]5/2的激发能随着基组扩大的收敛情况

    Figure 1.  Convergence of the excitation energy for two excited states [1s22p]1/2 and [1s24f]5/2 of Mg9+, Cr21+ and Mo39+ ions with basis set expansion.

    DownLoad: Full-Size Img PowerPoint

    图 2  Mg9+, Cr21+, Mo39+三种离子能级间E1, M1, E2跃迁的跃迁速率与相对不确定度之间的关系

    Figure 2.  Relationship between the calculated transition rates (E1, M1, E2) and the relative uncertainties of the results for level transitions in the Mg9+, Cr21+ and Mo39+ ions.

    DownLoad: Full-Size Img PowerPoint

    表 1  准完备基组的构建

    Table 1.  Construction of the quasi-complete basis.

    要优化的轨道a) 参考组态选取b) 优化的能级c)
    基组(n ≤ 2) 1s2s2p [1s22s, 1s22p] [1s22s]1/2, [1s22p]1/2, 3/2
    基组(n ≤ 3) 3s3p3d [1s22s, 1s22p, 1s23s, 1s23p, 1s23d] [1s22s]1/2, [1s22p]1/2, 3/2,
    [1s23s]1/2, [1s23p]1/2, 3/2,
    [1s23d]3/2, 5/2
    基组(n ≤ 4) 4s4p4d4f [1s22s, 1s22p, 1s23s, 1s23p, 1s23d,
    1s24s, 1s24p, 1s24d, 1s24f]    		 [1s22s]1/2, [1s22p]1/2, 3/2,
    [1s23s]1/2, [1s23p]1/2, 3/2,
    [1s23d]3/2, 5/2, [1s24s]1/2,
    [1s24p]1/2, 3/2, [1s24d]3/2, 5/2,
    [1s24f]5/2, 7/2
    基组(n ≤ 5) 5s5p5d5f5g [1s22s, 1s22p, 1s23s, 1s23p, 1s23d, 1s24s,
    1s24p, 1s24d, 1s24f→5s5p5d5f5g]S, D    		 同上
    基组(n ≤ 6) 6s6p6d6f6g6h [1s22s, 1s22p, 1s23s, 1s23p, 1s23d, 1s24s, 1s24p,
    1s24d, 1s24f→6s6p6d6f6g6 h]S, D    		 同上
    基组(n ≤ 7) 7s7p7d7f7g7h7i [1s22s, 1s22p, 1s23s, 1s23p, 1s23d, 1s24s, 1s24p,
    1s24d, 1s24f→7s7p7d7f7g7h7i]S, D    		 同上
    基组(n ≤ 8) 8s8p8d8f8g8h8i8k [1s22s, 1s22p, 1s23s, 1s23p, 1s23d, 1s24s, 1s24p,
    1s24d, 1s24f→8s8p8d8f8g8 h8i8k]S, D    		 同上
    基组(n ≤ 9) 9s9p9d9f9g9h9i9k [1s22s, 1s22p, 1s23s, 1s23p, 1s23d, 1s24s, 1s24p,
    1s24d, 1s24f→9s9p9d9f9g9 h9i9k]S, D    		 同上
    注: a)n = 1, 2, 3, 4的轨道为光谱轨道, $ n\geqslant 5 $的轨道为赝轨道; b)1s22s, 1s22p等为非相对论参考组态, “S”, “D”分别表示单、双重激发产生组态; c)MCSCF计算时优化的能级.
    DownLoad: CSV

    表 2  Mg9+激发能(单位: eV)计算结果及其与NIST[26]和其他理论计算结果[11, 15, 16]的比较

    Table 2.  Excitation energy (in eV) data for Mg9+ and its comparison with NIST[26] and other theoretical computational results[11,15,16].

    编号 能级 当前计算 NIST a) 其他理论结果 与NIST的相对差异/%
    MCDF b) MBPT c) S-Matrix d) 当前计算 MCDF MBPT S-Matrix
    1 [1s22s]1/2 0 0 0 — — — — — —
    2 [1s22p]1/2 19.8405 19.83922 19.9758 19.8297 19.8382 0.007 0.688 –0.048 –0.005
    3 [1s22p]3/2 20.3343 20.33202 20.4655 20.3242 20.3315 0.011 0.656 –0.038 –0.003
    4 [1s23s]1/2 208.6336 208.628 208.5291 — — 0.003 –0.047 — —
    5 [1s23p]1/2 214.0728 214.061 214.0012 — — 0.006 –0.028 — —
    6 [1s23p]3/2 214.2184 214.224 214.1457 — — –0.003 –0.037 — —
    7 [1s23d]3/2 216.1664 216.17 216.0475 — — –0.002 –0.057 — —
    8 [1s23d]5/2 216.2115 216.215 216.0921 — — –0.002 –0.057 — —
    9 [1s24s]1/2 279.2771 279.29 279.1520 — — –0.005 –0.049 — —
    10 [1s24p]1/2 281.5067 281.463 281.3948 — — 0.016 –0.024 — —
    11 [1s24p]3/2 281.5680 281.463 281.4556 — — 0.037 –0.003 — —
    12 [1s24d]3/2 282.3775 282.359 282.2479 — — 0.007 –0.039 — —
    13 [1s24d]5/2 282.3965 282.40 282.2667 — — –0.001 –0.047 — —
    14 [1s24f]5/2 282.4407 282.443 282.3021 — — –0.001 –0.050 — —
    15 [1s24f]7/2 282.4510 282.453 282.3114 — — –0.001 –0.050 — —
    注: a) NIST[26]数据库收录数据; b)文献[11]使用MCDF+CI方法的计算结果; c)文献[15]使用MBPT方法的计算结果; d)文献[16]使用S矩阵方法的计算结果.
    DownLoad: CSV

    表 4  Mo39+激发能(单位eV)计算结果及其与NIST[26]和其他理论计算结果[12,15,16]的比较

    Table 4.  Excitation energy (in eV) data for Mo39+ and its comparison with NIST[26] and other theoretical computational results[12,15,16].

    编号 能级 当前计算 NIST a) 其他理论结果 与NIST的相对差异/%
    MCDF b) MBPT c) S-Matrix d) 当前计算 MCDF MBPT S-Matrix
    1 [1s22s]1/2 0 0 — — — — — — —
    2 [1s22p]1/2 86.1124 86.108 86.2085 86.1764 86.1041 0.005 0.117 0.079 –0.005
    3 [1s22p]3/2 212.0023 211.9956 212.1476 212.1689 211.982 0.003 0.072 0.082 –0.006
    4 [1s23s]1/2 3206.9762 3207.1 3206.7966 — — –0.004 –0.009 — —
    5 [1s23p]1/2 3230.8215 3230.8 3230.8328 — — 0.001 0.001 — —
    6 [1s23p]3/2 3268.1729 3268.1 3268.1355 — — 0.002 0.001 — —
    7 [1s23d]3/2 3276.6290 3276.5 3276.5429 — — 0.004 0.001 — —
    8 [1s23d]5/2 3288.2659 3288.1 3288.1599 — — 0.005 0.002 — —
    9 [1s24s]1/2 4314.1977 4313.9 — — — 0.007 — — —
    10 [1s24p]1/2 4323.9937 4323.8 — — — 0.004 — — —
    11 [1s24p]3/2 4339.7142 4339.5 — — — 0.005 — — —
    12 [1s24d]3/2 4343.2364 4343.1 — — — 0.003 — — —
    13 [1s24d]5/2 4348.1528 4348.0 — — — 0.004 — — —
    14 [1s24f]5/2 4348.3516 — — — — — — — —
    15 [1s24f]7/2 4350.7885 — — — — — — — —
    注: a) NIST[26]数据库收录数据; b)文献[12]使用MCDF+CI方法的计算结果; c)文献[15]使用MBPT方法的计算结果; d)文献[16]使用S矩阵方法的计算结果.
    DownLoad: CSV

    表 3  Cr21+激发能(单位: eV)计算结果及其与NIST[26]和其他理论计算结果[10,15,16]的比较

    Table 3.  Excitation energy (in eV) data for Cr21+ and its comparison with NIST[26] and other theoretical computational results[10,15,16].

    编号 能级 当前计算 NIST a) 其他理论结果 与NIST的相对差异/%
    MCDF b) MBPT c) S-Matrix d) 当前计算 MCDF MBPT S-Matrix
    1 [1s22s]1/2 0 0 0 — — — — — —
    2 [1s22p]1/2 44.3259 44.3322 44.4933 44.3417 44.3209 –0.014 0.363 0.021 –0.025
    3 [1s22p]3/2 55.6001 55.5958 55.7466 55.6222 55.5918 0.008 0.271 0.047 –0.007
    4 [1s23s]1/2 967.4110 967.40 967.2840 — — 0.001 –0.012 — —
    5 [1s23p]1/2 979.7019 979.68 979.6261 — — 0.002 –0.005 — —
    6 [1s23p]3/2 983.0371 983.02 982.9546 — — 0.002 –0.007 — —
    7 [1s23d]3/2 987.7139 987.70 987.5784 — — 0.001 –0.012 — —
    8 [1s23d]5/2 988.7666 988.75 988.6288 — — 0.002 –0.012 — —
    9 [1s24s]1/2 1300.2631 1300.12 1300.1223 — — 0.011 0.000 — —
    10 [1s24p]1/2 1305.3243 1305.28 1305.2034 — — 0.003 –0.006 — —
    11 [1s24p]3/2 1306.7288 1306.69 1306.6053 — — 0.003 –0.006 — —
    12 [1s24d]3/2 1308.6689 1308.66 1308.5255 — — 0.001 –0.010 — —
    13 [1s24d]5/2 1309.1131 1309.10 1308.9686 — — 0.001 –0.010 — —
    14 [1s24f]5/2 1309.2268 — 1309.0709 — — — — — —
    15 [1s24f]7/2 1309.4480 — 1309.2923 — — — — — —
    注: a) NIST[26]数据库收录数据; b)文献[10]使用MCDF+CI方法的计算结果; c)文献[15]使用MBPT方法的计算结果; d)文献[16]使用S矩阵方法的计算结果.
    DownLoad: CSV

    表 5  Mg9+跃迁速率(单位: s–1)计算结果及其与NIST[26]数据及其他理论计算结果[11]的比较

    Table 5.  Comparison of transition rates (in s–1) calculations for Mg9+ with NIST[26] data and other Ref. [11].

    跃迁编号 上能级编号 下能级编号 跃迁类型 当前计算 NIST a) 其他理论结果b) 与NIST的相对差异/%
    当前计算 其他理论结果
    1 2 1 E1 6.982×108 6.95×108 7.176×108 0.45 3.25
    2 5 1 E1 2.149×1011 2.17×1011 2.136×1011 –0.96 –1.55
    3 10 1 E1 9.744×1010 9.93×1010 9.700×1010 –1.88 –2.31
    4 5 4 E1 8.870×107 8.85×107 9.023×107 0.23 1.95
    5 10 4 E1 2.678×1010 2.69×1010 2.672×1010 –0.44 –0.67
    6 10 9 E1 2.060×107 1.91×107 2.090×107 7.84 9.40
    7 3 1 E1 7.530×108 7.51×108 7.736×108 0.27 3.01
    8 6 1 E1 2.135×1011 2.16×1011 2.122×1011 –1.18 –1.76
    9 11 1 E1 9.693×1010 9.88×1010 9.651×1010 –1.89 –2.31
    10 6 4 E1 9.616×107 9.67×107 9.771×107 –0.56 1.04
    11 11 4 E1 2.656×1010 2.68×1010 2.651×1010 –0.89 –1.10
    12 11 9 E1 2.238×107 1.91×107 2.267×107 17.17 18.66
    13 4 2 E1 3.456×1010 3.39×1010 3.428×1010 1.96 1.12
    14 9 2 E1 1.353×1010 1.34×1010 1.340×1010 0.95 0.00
    15 9 5 E1 9.319×109 9.47×109 9.324×109 –1.60 –1.54
    16 7 2 E1 5.569×1011 5.48×1011 5.580×1011 1.62 1.83
    17 12 2 E1 1.826×1011 1.85×1011 1.835×1011 –1.28 –0.79
    18 7 5 E1 3.315×106 3.38×106 3.096×106 –1.92 –8.42
    19 12 5 E1 5.791×1010 5.83×1010 5.795×1010 –0.66 –0.60
    20 12 10 E1 1.018×106 1.11×106 9.542×105 –8.28 –14.04
    21 10 7 E1 4.340×109 4.26×109 4.323×109 1.88 1.48
    22 11 7 E1 4.278×108 4.26×108 4.262×108 0.41 0.04
    23 14 7 E1 1.289×1011 — 1.290×1011 — —
    24 14 12 E1 2.635×102 — 1.704×102 — —
    25 4 3 E1 6.967×1010 6.81×1010 6.909×1010 2.31 1.45
    26 9 3 E1 2.724×1010 2.67×1010 2.694×1010 2.02 0.90
    27 9 6 E1 1.878×1010 1.88×1010 1.878×1010 –0.12 –0.11
    28 7 3 E1 1.111×1011 1.09×1011 1.113×1011 1.94 2.11
    29 12 3 E1 3.637×1010 3.66×1010 3.654×1010 –0.64 –0.16
    30 7 6 E1 5.339×105 5.31×105 4.968×105 0.54 –6.44
    31 12 6 E1 1.160×1010 1.16×1010 1.160×1010 –0.04 0.00
    32 12 11 E1 1.634×105 2.21×105 1.528×105 –26.04 –30.86
    33 8 3 E1 6.666×1011 6.55×1011 6.680×1011 1.77 1.98
    34 13 3 E1 2.183×1011 2.21×1011 2.194×1011 –1.20 –0.71
    35 8 6 E1 3.432×106 3.43×106 3.198×106 0.05 –6.77
    36 13 6 E1 6.950×1010 6.96×1010 6.955×1010 –0.14 –0.08
    37 13 11 E1 1.052×106 1.51×106 9.843×105 –30.36 –34.81
    38 11 8 E1 3.865×109 3.82×109 3.851×109 1.18 0.81
    39 14 8 E1 9.201×109 — 9.202×109 — —
    40 14 13 E1 6.379 — 3.394 — —
    41 15 8 E1 1.380×1011 — 1.381×1011 — —
    42 15 13 E1 1.786×102 — 1.035×102 — —
    43 7 1 E2 7.367×107 — 7.356×107 — —
    44 12 1 E2 1.208×107 — 1.208×107 — —
    45 7 4 E2 36.65 — 36.27 — —
    46 12 4 E2 4.721×106 — 4.718×106 — —
    47 12 9 E2 6.189 — 6.128 — —
    48 8 1 E2 7.372×107 — 7.361×107 — —
    49 13 1 E2 1.212×107 — 1.212×107 — —
    50 8 4 E2 37.81 — 37.40 — —
    51 13 4 E2 4.722×106 — 4.720×106 — —
    52 13 9 E2 6.386 — 6.321 — —
    53 3 2 E2 1.824×10–6 — 1.755×10–6 — —
    54 6 2 E2 1.263×107 — 1.261×107 — —
    55 11 2 E2 5.390×106 — 5.420×106 — —
    56 6 5 E2 1.544×10–7 — 1.468×10–7 — —
    57 11 5 E2 1.329×106 — 1.328×106 — —
    58 11 10 E2 2.373×10–8 — 2.187×10–8 — —
    59 14 2 E2 4.816×107 — 4.180×107 — —
    60 14 5 E2 5.013×106 — 4.997×106 — —
    61 14 10 E2 7.343×10–3 — 6.368×10–3 — —
    62 9 7 E2 4.852×105 — 4.852×105 — —
    63 12 7 E2 8.342×105 — 8.342×105 — —
    64 8 7 E2 6.385×10–11 — 6.073×10–11 — —
    65 13 7 E2 2.383×105 — 2.383×105 — —
    66 13 12 E2 1.368×10–11 — 1.291×10–11 — —
    67 5 3 E2 2.521×107 — 2.517×107 — —
    68 10 3 E2 1.071×107 — 1.076×107 — —
    69 10 6 E2 2.655×106 — 2.654×106 — —
    70 6 3 E2 1.259×107 — 1.257×107 — —
    71 11 3 E2 5.359×106 — 5.384×106 — —
    72 11 6 E2 1.326×106 — 1.326×106 — —
    73 14 3 E2 1.376×107 — 1.374×107 — —
    74 14 6 E2 1.422×106 — 1.418×106 — —
    75 14 11 E2 1.491×10–3 — 1.286×10–3 — —
    76 15 3 E2 6.186×107 — 6.180×107 — —
    77 15 6 E2 6.405×106 — 6.384×106 — —
    78 15 11 E2 7.114×10–3 — 6.118×10–3 — —
    79 9 8 E2 7.277×105 — 7.278×105 — —
    80 12 8 E2 3.572×105 — 3.572×105 — —
    81 13 8 E2 9.526×105 — 9.526×105 — —
    82 15 14 E2 1.519×10–13 — 1.057×10–13 — —
    83 4 1 M1 31.71 — 29.21 — —
    84 9 1 M1 26.58 — 24.18 — —
    85 9 4 M1 2.899×10–1 — 2.728×10–1 — —
    86 7 1 M1 1.639 — 1.625 — —
    87 12 1 M1 9.801×10–1 — 9.693×10–1 — —
    88 7 4 M1 6.509×10–6 — 6.565×10–6 — —
    89 12 4 M1 5.915×10–3 — 5.842×10–3 — —
    90 12 9 M1 2.665×10–7 — 2.683×10–7 — —
    91 5 2 M1 6.256 — 5.847 — —
    92 10 2 M1 4.903 — 4.585 — —
    93 10 5 M1 7.465×10–2 — 7.429×10–2 — —
    94 3 2 M1 5.674×10–1 — 5.534×10–1 — —
    95 6 2 M1 41.41 — 39.89 — —
    96 11 2 M1 21.22 — 20.35 — —
    97 6 5 M1 1.456×10–2 — 1.421×10–2 — —
    98 11 5 M1 2.307 — 2.258 — —
    99 11 10 M1 1.084×10–3 — 1.060×10–3 — —
    100 9 7 M1 7.338×10–5 — 8.191×10–5 — —
    101 12 7 M1 1.849×10–1 — 1.841×10–1 — —
    102 8 7 M1 5.203×10–4 — 5.012×10–4 — —
    103 13 7 M1 1.458×10–1 — 1.410×10–1 — —
    104 13 12 M1 3.887×10–5 — 3.748×10–5 — —
    105 5 3 M1 1.550×102 — 1.543×102 — —
    106 10 3 M1 90.07 — 89.89 — —
    107 10 6 M1 6.361 — 6.287 — —
    108 6 3 M1 42.40 — 43.34 — —
    109 11 3 M1 33.34 — 34.06 — —
    110 11 6 M1 5.226×10–1 — 5.291×10–1 — —
    111 14 3 M1 4.582×10–1 — 4.541×10–1 — —
    112 14 6 M1 1.620×10–2 — 1.619×10–2 — —
    113 14 11 M1 1.431×10–9 — 1.290×10–9 — —
    114 12 8 M1 5.510×10–1 — 5.408×10–1 — —
    115 13 8 M1 6.109×10–1 — 6.116×10–1 — —
    116 15 14 M1 6.636×10–6 — 5.095×10–6 — —
    注: a) NIST[26]数据库收录数据; b)文献[11]使用MCDF+CI方法的计算结果.
    DownLoad: CSV

    表 6  Cr21+跃迁速率(单位: s–1)计算结果及其与NIST[26]数据及其他理论计算结果[10]的比较

    Table 6.  Comparison of transition rates (in s–1) calculations for Cr21+ with NIST[26] data and other Ref. [10].

    跃迁编号 上能级编号 下能级编号 跃迁类型 当前计算 NIST a) 其他理论结果b) 与NIST的相对差异/%
    当前计算 其他理论结果
    1 2 1 E1 1.642×109 1.65×109 1.660×109 –0.51 0.61
    2 5 1 E1 5.277×1012 5.28×1012 5.260×1012 –0.06 –0.38
    3 10 1 E1 2.325×1012 2.5×1012 2.319×1012 –7.00 –7.24
    4 5 4 E1 2.142×108 — 2.160×108 — —
    5 10 4 E1 6.891×1011 7.100×1011 6.880×1011 –2.95 –3.10
    6 10 9 E1 5.015×107 — 5.060×107 — —
    7 3 1 E1 3.270×109 3.29×109 3.300×109 –0.62 0.30
    8 6 1 E1 5.129×1012 5.13×1012 5.110×1012 –0.02 –0.39
    9 11 1 E1 2.279×1012 2.5×1012 2.270×1012 –8.83 –9.20
    10 6 4 E1 4.428×108 — 4.450×108 — —
    11 11 4 E1 6.661×1011 7.100×1011 6.650×1011 –6.18 –6.34
    12 11 9 E1 1.054×108 — 1.060×108 — —
    13 4 2 E1 6.456×1011 6. ×1011 6.427×1011 7.60 7.12
    14 9 2 E1 2.585×1011 — 2.576×1011 — —
    15 9 5 E1 1.800×1011 — 1.801×1011 — —
    16 7 2 E1 1.296×1013 1.29×1013 1.300×1013 0.50 0.78
    17 12 2 E1 4.220×1012 4.1×1012 4.230×1012 2.93 3.17
    18 7 5 E1 3.793×107 — 3.730×107 — —
    19 12 5 E1 1.366×1012 1.4×1012 1.370×1012 –2.43 –2.14
    20 12 10 E1 1.183×107 — 1.160×107 — —
    21 10 7 E1 9.770×1010 — 9.759×1010 — —
    22 11 7 E1 9.101×109 — 9.090×109 — —
    23 14 7 E1 3.027×1012 — 3.030×1012 — —
    24 14 12 E1 3.741×104 — 3.590×104 — —
    25 4 3 E1 1.350×1012 1.3×1012 1.344×1012 3.88 3.38
    26 9 3 E1 5.386×1011 — 5.353×1011 — —
    27 9 6 E1 3.754×1011 — 3.754×1011 — —
    28 7 3 E1 2.562×1012 2.6×1012 2.320×1012 –1.48 –10.77
    29 12 3 E1 8.256×1011 7.9×1011 8.030×1011 4.51 1.65
    30 7 6 E1 1.502×106 — 1.461×106 — —
    31 12 6 E1 2.745×1011 2.7×1011 2.745×1011 1.65 1.67
    32 12 11 E1 4.591×105 — 4.466×105 — —
    33 8 3 E1 1.537×1013 1.54×1013 1.540×1013 –0.19 0.00
    34 13 3 E1 4.974×1012 4.9×1012 4.990×1012 1.52 1.84
    35 8 6 E1 1.662×107 — 1.630×107 — —
    36 13 6 E1 1.639×1012 1.7×1012 1.640×1012 –3.58 –3.53
    37 13 11 E1 5.139×106 — 5.010×106 — —
    38 11 8 E1 8.356×1010 — 8.349×1010 — —
    39 14 8 E1 2.152×1011 — 2.152×1011 — —
    40 14 13 E1 19.64 — 16.90 — —
    41 15 8 E1 3.231×1012 — 3.230×1012 — —
    42 15 13 E1 8.590×103 — 8.040×103 — —
    43 7 1 E2 7.117×109 — 7.113×109 — —
    44 12 1 E2 9.610×108 — 9.618×108 — —
    45 7 4 E2 2.242×102 — 2.224×102 — —
    46 12 4 E2 4.891×108 — 4.890×108 — —
    47 12 9 E2 39.00 — 38.65 — —
    48 8 1 E2 7.144×109 — 7.140×109 — —
    49 13 1 E2 9.797×108 — 9.806×108 — —
    50 8 4 E2 2.902×102 — 2.879×102 — —
    51 13 4 E2 4.900×108 — 4.899×108 — —
    52 13 9 E2 50.64 — 50.17 — —
    53 3 2 E2 4.938×10–1 — 4.917×10–1 — —
    54 6 2 E2 1.408×109 — 1.408×109 — —
    55 11 2 E2 6.093×108 — 6.122×108 — —
    56 6 5 E2 4.167×10–2 — 4.114×10–2 — —
    57 11 5 E2 1.493×108 — 1.493×108 — —
    58 11 10 E2 6.296×10–3 — 6.130×10–3 — —
    59 14 2 E2 5.450×109 — 5.446×109 — —
    60 14 5 E2 5.589×108 — 5.585×108 — —
    61 14 10 E2 3.995×10–1 — 3.805×10–1 — —
    62 9 7 E2 5.199×107 — 5.199×107 — —
    63 12 7 E2 9.476×107 — 9.476×107 — —
    64 8 7 E2 1.884×10–5 — 1.872×10–5 — —
    65 13 7 E2 2.707×107 — 2.707×107 — —
    66 13 12 E2 4.064×10–6 — 4.010×10–6 — —
    67 5 3 E2 2.795×109 — 2.794×109 — —
    68 10 3 E2 1.183×109 — 1.186×109 — —
    69 10 6 E2 2.974×108 — 2.973×108 — —
    70 6 3 E2 1.390×109 — 1.390×109 — —
    71 11 3 E2 5.952×108 — 5.965×108 — —
    72 11 6 E2 1.480×108 — 1.480×108 — —
    73 14 3 E2 1.555×109 — 1.554×109 — —
    74 14 6 E2 1.545×108 — 1.544×108 — —
    75 14 11 E2 1.221×10–2 — 1.142×10–2 — —
    76 15 3 E2 6.974×109 — 6.972×109 — —
    77 15 6 E2 6.973×108 — 6.968×108 — —
    78 15 11 E2 8.422×10–2 — 7.921×10–2 — —
    79 9 8 E2 7.807×107 — 7.806×107 — —
    80 12 8 E2 4.045×107 — 4.045×107 — —
    81 13 8 E2 1.079×108 — 1.078×108 — —
    82 15 14 E2 3.185×10–8 — 3.199×10–8 — —
    83 4 1 M1 6.556×104 — 6.418×104 — —
    84 9 1 M1 5.548×104 — 5.416×104 — —
    85 9 4 M1 6.576×102 — 6.488×102 — —
    86 7 1 M1 3.608×103 — 3.594×103 — —
    87 12 1 M1 2.117×103 — 2.106×103 — —
    88 7 4 M1 2.540×10–3 — 2.558×10–3 — —
    89 12 4 M1 15.42 — 15.34 — —
    90 12 9 M1 1.094×10–4 — 1.099×10–4 — —
    91 5 2 M1 1.541×104 — 1.484×104 — —
    92 10 2 M1 1.210×104 — 1.164×104 — —
    93 10 5 M1 1.910×102 — 1.877×102 — —
    94 3 2 M1 6.737×103 6.76×103 6.699×103 –0.33 –0.90
    95 6 2 M1 1.044×105 — 1.029×105 — —
    96 11 2 M1 5.354×104 — 5.263×104 — —
    97 6 5 M1 1.747×102 — 1.737×102 — —
    98 11 5 M1 5.859×103 — 5.820×103 — —
    99 11 10 M1 13.06 — 12.98 — —
    100 9 7 M1 1.938×10–1 — 2.052×10–1 — —
    101 12 7 M1 4.925×102 — 4.915×102 — —
    102 8 7 M1 6.596 — 6.552 — —
    103 13 7 M1 3.830×102 — 3.821×102 — —
    104 13 12 M1 4.957×10–1 — 4.921×10–1 — —
    105 5 3 M1 3.847×105 — 3.855×105 — —
    106 10 3 M1 2.239×105 — 2.248×105 — —
    107 10 6 M1 1.598×104 — 1.595×104 — —
    108 6 3 M1 1.033×105 — 1.045×105 — —
    109 11 3 M1 8.104×104 — 8.197×104 — —
    110 11 6 M1 1.318×103 — 1.325×103 — —
    111 14 3 M1 1.198×103 — 1.193×103 — —
    112 14 6 M1 41.17 — 41.19 — —
    113 14 11 M1 7.411×10–7 — 7.092×10–7 — —
    114 12 8 M1 1.449×103 — 1.449×103 — —
    115 13 8 M1 1.620×103 — 1.622×103 — —
    116 15 14 M1 6.561×10–2 — 6.579×10–2 — —
    注: a) NIST[26]数据库收录数据; b)文献[10]使用MCDF+CI方法的计算结果.
    DownLoad: CSV

    表 7  Mo39+跃迁速率(单位: s–1)计算结果及其与其他理论结果[12]的比较

    Table 7.  Comparison of transition rates (in s–1) calculations for Mo39+ with other Ref. [12].

    跃迁编号 上能级编号 下能级编号 跃迁类型 当前计算 NIST a) 其他理论结果b) 与NIST的相对差异
    当前计算 其他理论结果
    1 2 1 E1 3.549×109 — 3.54×109 — —
    2 5 1 E1 6.057×1013 — 6.06×1013 — —
    3 10 1 E1 2.625×1013 — — — —
    4 5 4 E1 4.656×108 — — — —
    5 10 4 E1 8.009×1012 — — — —
    6 10 9 E1 1.085×108 — — — —
    7 3 1 E1 5.448×1010 — 5.48×1010 — —
    8 6 1 E1 5.520×1013 — 5.52×1013 — —
    9 11 1 E1 2.466×1013 — — — —
    10 6 4 E1 7.999×109 — — — —
    11 11 4 E1 7.165×1012 — — — —
    12 11 9 E1 1.949×109 — — — —
    13 4 2 E1 6.644×1012 — 6.64×1012 — —
    14 9 2 E1 2.681×1012 — — — —
    15 9 5 E1 1.867×1012 — — — —
    16 7 2 E1 1.442×1014 — 1.44×1014 — —
    17 12 2 E1 4.742×1013 — — — —
    18 7 5 E1 2.118×109 — — — —
    19 12 5 E1 1.493×1013 — — — —
    20 12 10 E1 6.753×108 — — — —
    21 10 7 E1 1.211×1012 — — — —
    22 11 7 E1 9.602×1010 — — — —
    23 14 7 E1 3.331×1013 — — — —
    24 14 12 E1 8.822×106 — — — —
    25 4 3 E1 1.547×1013 — 1.55×1013 — —
    26 9 3 E1 6.168×1012 — — — —
    27 9 6 E1 4.307×1012 — — — —
    28 7 3 E1 2.770×1013 — — — —
    29 12 3 E1 8.805×1012 — — — —
    30 7 6 E1 2.566×106 — — — —
    31 12 6 E1 3.034×1012 — — — —
    32 12 11 E1 8.156×105 — — — —
    33 8 3 E1 1.663×1014 — 1.66×1014 — —
    34 13 3 E1 5.364×1013 — — — —
    35 8 6 E1 2.143×108 — — — —
    36 13 6 E1 1.794×1013 — — — —
    37 13 11 E1 6.846×107 — — — —
    38 11 8 E1 9.245×1011 — — — —
    39 14 8 E1 2.344×1012 — — — —
    40 14 13 E1 22.52 — — — —
    41 15 8 E1 3.528×1013 — — — —
    42 15 13 E1 1.295×106 — — — —
    43 7 1 E2 2.551×1011 — — — —
    44 12 1 E2 3.348×1010 — — — —
    45 7 4 E2 9.550×103 — — — —
    46 12 4 E2 1.786×1010 — — — —
    47 12 9 E2 1.729×103 — — — —
    48 8 1 E2 2.584×1011 — — — —
    49 13 1 E2 3.573×1010 — — — —
    50 8 4 E2 2.102×104 — — — —
    51 13 4 E2 1.797×1010 — — — —
    52 13 9 E2 3.821×103 — — — —
    53 3 2 E2 7.513×103 — — — —
    54 6 2 E2 5.155×1010 — — — —
    55 11 2 E2 2.269×1010 — — — —
    56 6 5 E2 6.462×102 — — — —
    57 11 5 E2 5.488×109 — — — —
    58 11 10 E2 97.35 — — — —
    59 14 2 E2 1.960×1011 — — — —
    60 14 5 E2 2.172×1010 — — — —
    61 14 10 E2 3.443×102 — — — —
    62 9 7 E2 1.898×109 — — — —
    63 12 7 E2 3.444×109 — — — —
    64 8 7 E2 2.786×10–1 — — — —
    65 13 7 E2 9.830×108 — — — —
    66 13 12 E2 6.059×10–2 — — — —
    67 5 3 E2 1.003×1011 — — — —
    68 10 3 E2 4.105×1010 — — — —
    69 10 6 E2 1.083×1010 — — — —
    70 6 3 E2 4.946×1010 — — — —
    71 11 3 E2 2.108×1010 — — — —
    72 11 6 E2 5.347×109 — — — —
    73 14 3 E2 5.576×1010 — — — —
    74 14 6 E2 5.558×109 — — — —
    75 14 11 E2 5.488×10–1 — — — —
    76 15 3 E2 2.483×1011 — — — —
    77 15 6 E2 2.528×1010 — — — —
    78 15 11 E2 8.617 — — — —
    79 9 8 E2 2.856×109 — — — —
    80 12 8 E2 1.457×109 — — — —
    81 13 8 E2 3.883×109 — — — —
    82 15 14 E2 4.660×10–4 — — — —
    83 4 1 M1 2.594×107 — — — —
    84 9 1 M1 2.189×107 — — — —
    85 9 4 M1 2.650×105 — — — —
    86 7 1 M1 1.438×106 — — — —
    87 12 1 M1 8.373×105 — — — —
    88 7 4 M1 1.138 — — — —
    89 12 4 M1 6.242×103 — — — —
    90 12 9 M1 5.005×10–2 — — — —
    91 5 2 M1 6.440×106 — — — —
    92 10 2 M1 5.038×106 — — — —
    93 10 5 M1 8.012×104 — — — —
    94 3 2 M1 9.297×106 — — — —
    95 6 2 M1 4.442×107 — — — —
    96 11 2 M1 2.269×107 — — — —
    97 6 5 M1 2.443×105 — — — —
    98 11 5 M1 2.493×106 — — — —
    99 11 10 M1 1.825×104 — — — —
    100 9 7 M1 80.40 — — — —
    101 12 7 M1 1.985×105 — — — —
    102 8 7 M1 8.877×103 — — — —
    103 13 7 M1 1.564×105 — — — —
    104 13 12 M1 6.709×102 — — — —
    105 5 3 M1 1.540×108 — — — —
    106 10 3 M1 8.971×107 — — — —
    107 10 6 M1 6.495×106 — — — —
    108 6 3 M1 3.961×107 — — — —
    109 11 3 M1 3.100×107 — — — —
    110 11 6 M1 5.186×105 — — — —
    111 14 3 M1 4.714×105 — — — —
    112 14 6 M1 1.633×104 — — — —
    113 14 11 M1 3.355×10–4 — — — —
    114 12 8 M1 5.801×105 — — — —
    115 13 8 M1 6.412×105 — — — —
    116 15 14 M1 87.54 — — — —
    注: a) NIST[26]数据库当前对该元素跃迁速率数据无收录; b)文献[12]使用MCDF+CI方法的计算结果.
    DownLoad: CSV
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  • supplement 2025年第74卷第15期153102补充材料.zip supplement
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  • Received Date:  08 May 2025
  • Accepted Date:  14 July 2025
  • Available Online:  17 July 2025
  • Published Online:  05 August 2025

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