Extended calculations of energy levels, radiative properties, and lifetimes for nitrogen-like Zr XXXIV

Journal of Quantitative Spectroscopy & Radiative Transfer 237 (2019) 106640

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Extended calculations of energy levels, radiative properties, and lifetimes for nitrogen-like Zr XXXIV Kai Wang a,b, Zhan Bin Chen c,∗, Xiao Hui Zhao a,∗, Chong Yang Chen b, Jun Yan d a

Hebei Key Lab of Optic-electronic Information and Materials, The College of Physics Science and Technology, Hebei University, Baoding 071002, China Shanghai EBIT Lab, Key Laboratory of Nuclear Physics and Ion-beam Application, Institute of Modern Physics, Department of Nuclear Science and Technology, Fudan University, Shanghai 200433, China c School of Science, Hunan University of Technology, Zhuzhou 412007, China d Institute of Applied Physics and Computational Mathematics, Beijing 100088, China b

a r t i c l e

i n f o

Article history: Received 22 August 2019 Revised 3 September 2019 Accepted 4 September 2019 Available online 5 September 2019 Keywords: Atomic data N-like Zr XXXIV Many-body perturbation theory Multiconfiguration Dirac–Fock method

a b s t r a c t Highly accurate calculations are performed for the lowest 272 fine-structure levels arising from the 2s2 2p3 , 2s2p4 , 2p5 , 2s2 2p2 3l, 2s2p3 3l, and 2p4 3l configurations in N-like Zr XXXIV using two state-of-theart methods, second-order many-body perturbation theory and multiconfiguration Dirac–Fock. Complete and consistent atomic data, including excitation energies, wavelengths, E1, E2, M1, M2 line strengths, oscillator strengths, transition rates, and lifetimes for these 272 levels, are provided. Comparisons are made between the present two data sets, as well as with other available results. The present data are accurate enough for identification and deblending of emission lines involving the n = 3 levels and are also useful for modeling and diagnosing fusion plasmas. These data can be considered as a benchmark for other calculations. © 2019 Elsevier Ltd. All rights reserved.

1. Introduction Structural materials of fusion reactors often contain alloys of zirconium (Zr), and ions of Zr are present in the plasmas due to sputtering from structural materials [1,2]. Therefore, in order to simulate and diagnose plasmas that contain Zr as a constituent, accurate atomic data for different Zr ions are required. In view of this, X-ray spectra of the 2l - 3l transitions from Alcator C and Alcator C-Mod plasmas were measured for different Zr ions [3]. On the theoretical side, excitation energies and radiative transition rates for the low-lying levels of the (1s2 )2s2 2p3 , 2s2p4 , and 2p5 configurations in N-like Zr XXXIV were provided [4–7]. Atomic parameters of the n > 2 levels are also needed for applications in plasma physics [3,8]. The present work will provide a complete accurate data set of energy levels, lifetimes, and radiative transition parameters involving levels with principal quantum numbers n = 3 in N-like Zr XXXIV. This work is an extension of our previous study on N-like ions [9]. Excitation energies, wavelengths, line strengths, oscillator strengths, transition rates, and lifetimes are provided here for the lowest 272 levels of the 2s2 2p3 , 2s2p4 , 2p5 , 2s2 2p2 3l (l = s, p, d),

∗

Corresponding authors. E-mail addresses: [email protected] (Z.B. Chen), [email protected] (X.H. Zhao). https://doi.org/10.1016/j.jqsrt.2019.106640 0022-4073/© 2019 Elsevier Ltd. All rights reserved.

2s2p3 3l (l = s, p, d), and 2p4 3l (l = s, p, d) configurations using the many-body perturbation theory (MBPT) method [10–14]. In order to assess the accuracy of our MBPT calculations, the multiconfiguration Dirac–Fock (MCDF) and relativistic configuration interaction (RCI) method [15,16] is used to calculate the corresponding data. The present study significantly increases the amount of accurate data for the n = 3 levels of N-like Zr. The accuracy of our results is sufficient to directly aid and confirm experimental identifications. 2. Calculations The MBPT method integrated in the FAC code [17] and the MCDF method implemented in the GRASP2K code [18,19] are used to perform the calculations. Both of the methods have been successfully used to calculate atomic parameters for L- and M-shells systems with high accuracy [9,20–44]. Since these two methods are described in our earlier work in detail, we only give an outline of the MBPT and MCDF calculations. 2.1. MBPT In the MBPT method, the Hilbert space of the system is divided into two subspaces, including a model space M and an orthogonal space N. By means of solving the eigenvalue problem of a non–Hermitian effective Hamiltonian in the space M, we can

2

K. Wang, Z.B. Chen and X.H. Zhao et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 237 (2019) 106640

Table 1 Excitation energies (E in cm−1 ) and lifetimes (τ in s−1 ) for the lowest 272 levels arising from the 2s2 2p3 , 2s2p4 , 2p5 , 2s2 2p2 3l, 2s2p3 3l, and 2p4 3l configurations of N-like Zr XXXIV from the present MBPT and MCDF calculations. Jπ : the total quantum number J and parity π ; E – the differences (in cm−1 ) between the MBPT and MCDF calculated excitation energies. Key

LSJ-coupled CSF

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68

2s 2 p3 43 S 4 S3◦ /2 2s2 2 p3 23 D 2 D◦3/2 2s2 2 p3 23 D 2 D◦5/2 2s2 2 p3 21 P 2 P1◦/2 2s2 2 p3 21 P 2 P3◦/2 2s 2 S 2 p4 32 P 4 P5/2 2s 2 S 2 p4 32 P 4 P1/2 2s 2 S 2 p4 32 P 4 P3/2 2s 2 S 2 p4 12 D 2 D3/2 2s 2 S 2 p4 12 D 2 D5/2 2s 2 S 2 p4 32 P 2 P1/2 2s 2 S 2 p4 32 P 2 P3/2 2s 2 S 2 p4 10 S 2 S1/2 2 p5 2 P3◦/2 2 p5 2 P1◦/2 2s2 2 p2 32 P 3 P 3s 4 P1/2 2s2 2 p2 32 P 3 P 3 p 4 D◦1/2 2s2 2 p2 32 P 3 P 3 p 4 P3◦/2 2s2 2 p2 32 P 3 P 3s 4 P3/2 2s2 2 p2 32 P 3 P 3s 2 P1/2 2s2 2 p2 12 D 1 D 3s 2 D5/2 2s2 2 p2 12 D 1 D 3s 2 D3/2 2s2 2 p2 32 P 3 P 3d 2 P3/2 2s2 2 p2 32 P 3 P 3 p 2 S1◦ /2 2s2 2 p2 32 P 3 P 3 p 4 D◦3/2 2s2 2 p2 32 P 3 P 3d 2 F5/2 2s2 2 p2 12 D 1 D 3 p 2 F5◦/2 2s2 2 p2 32 P 3 P 3 p 4 D◦5/2 2s2 2 p2 32 P 3 P 3 p 4 S3◦ /2 2s2 2 p2 32 P 3 P 3 p 4 P1◦/2 2s2 2 p2 32 P 3 P 3 p 2 D◦3/2 2s2 2 p2 12 D 1 D 3 p 2 F7◦/2 2s2 2 p2 12 D 1 D 3 p 2 P3◦/2 2s2 2 p2 12 D 1 D 3 p 2 D◦5/2 2s2 2 p2 32 P 3 P 3s 4 P5/2 2s2 2 p2 32 P 3 P 3 p 2 P1◦/2 2s2 2 p2 32 P 3 P 3s 2 P3/2 2s 2 S 2 p3 43 S 5 S 3s 6 S5◦ /2 2s2 2 p2 32 P 3 P 3d 4 F3/2 2s2 2 p2 32 P 3 P 3d 4 F5/2 2s2 2 p2 32 P 3 P 3d 4 D1/2 2s2 2 p2 32 P 3 P 3d 4 F7/2 2s2 2 p2 10 S 1 S 3s 2 S1/2 2s2 2 p2 32 P 3 P 3d 4 D7/2 2s2 2 p2 32 P 3 P 3d 4 P5/2 2s 2 S 2 p3 43 S 5 S 3s 4 S3◦ /2 2s2 2 p2 32 P 3 P 3d 4 D3/2 2s2 2 p2 12 D 1 D 3d 2 G9/2 2s2 2 p2 32 P 3 P 3d 4 D5/2 2s2 2 p2 32 P 3 P 3d 4 P3/2 2s2 2 p2 32 P 3 P 3d 4 P1/2 2s2 2 p2 12 D 1 D 3d 2 F5/2 2s2 2 p2 12 D 1 D 3 p 2 D◦3/2 2s2 2 p2 12 D 1 D 3d 2 G7/2 2s2 2 p2 32 P 3 P 3d 2 D3/2 2s2 2 p2 32 P 3 P 3 p 2 D◦5/2 2s2 2 p2 32 P 3 P 3d 2 P1/2 2s 2 S 2 p3 43 S 5 S 3 p 6 P3/2 2s 2 S 2 p3 23 D 3 D 3s 4 D◦1/2 2s 2 S 2 p3 43 S 5 S 3 p 6 P5/2 2s2 2 p2 32 P 3 P 3 p 4 P5◦/2 2s 2 S 2 p3 23 D 3 D 3s 4 D◦3/2 2s2 2 p2 32 P 3 P 3 p 4 D◦7/2 2s2 2 p2 12 D 1 D 3 p 2 P1◦/2 2s2 2 p2 10 S 1 S 3 p 2 P1◦/2 2s 2 S 2 p3 43 S 5 S 3 p 6 P7/2 2s2 2 p2 32 P 3 P 3 p 2 P3◦/2 2s 2 S 2 p3 43 S 5 S 3 p 4 P3/2 2

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (

( ( ( ( (

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( ) ) ) ) ) ) ) ) ( ) ) ) ) ) ) ) ) ) ) ) ) ( ) ( ) ( ) ) ( ) ) ) ) ( ) ) ( )

Jπ

EMBPT

EMCDF

E

τ MBPT

τ MCDF

jj-coupled CSFa ,b ,c

3/2− 3/2− 5/2− 1/2− 3/2− 5/2+ 1/2+ 3/2+ 3/2+ 5/2+ 1/2+ 3/2+ 1/2+ 3/2− 1/2− 1/2+ 1/2− 3/2− 3/2+ 1/2+ 5/2+ 3/2+ 3/2+ 1/2− 3/2− 5/2+ 5/2− 5/2− 3/2− 1/2− 3/2− 7/2− 3/2− 5/2− 5/2+ 1/2− 3/2+ 5/2− 3/2+ 5/2+ 1/2+ 7/2+ 1/2+ 7/2+ 5/2+ 3/2− 3/2+ 9/2+ 5/2+ 3/2+ 1/2+ 5/2+ 3/2− 7/2+ 3/2+ 5/2− 1/2+ 3/2+ 1/2− 5/2+ 5/2− 3/2− 7/2− 1/2− 1/2− 7/2+ 3/2− 3/2+

0 631775 751658 908912 1540501 1797810 2136812 2138805 2594621 2760087 2936855 3031008 3710257 4328290 5064079 19208348 19563496 19819200 19851258 19893181 19948037 19979749 20192538 20204111 20240497 20298114 20310886 20423896 20432506 20448627 20486673 20524483 20563737 20618853 20668799 20692862 20706462 20811098 20841909 20854559 20859902 20888282 20903529 20930120 20946165 20947118 20954084 20987553 21014772 21026423 21046006 21082398 21095522 21101039 21109186 21122898 21126336 21192809 21200226 21207788 21233803 21237057 21241227 21251496 21345303 21388926 21433285 21442900

0 631609 751623 908903 1540307 1797057 2136266 2138224 2593895 2759459 2936260 3030476 3709575 4327414 5063010 19208622 19563595 19819345 19851508 19893643 19948387 19980255 20192959 20204216 20240654 20298595 20311084 20423942 20432940 20448775 20486931 20524630 20564093 20619253 20669156 20693432 20706989 20810573 20842417 20855127 20860366 20888766 20903751 20930748 20946758 20947181 20954629 20988188 21015405 21026965 21046592 21083166 21095882 21101879 21109972 21123396 21126939 21191670 21200267 21206748 21233979 21237082 21241370 21251698 21345544 21387737 21433827 21442014

0 −166 −35 −9 −194 −752 −546 −581 −726 −628 −595 −532 −682 −876 −1069 274 99 145 250 462 350 505 421 105 157 481 197 46 435 147 258 146 357 400 358 570 527 −525 508 568 465 484 221 628 593 63 545 635 634 542 586 767 360 840 785 498 602 −1138 41 −1040 176 25 142 202 241 −1189 542 −886

1.869E-07 1.020E-06 1.872E-07 7.123E-08 2.312E-11 7.295E-12 5.308E-12 6.193E-12 7.628E-12 2.953E-12 2.554E-12 2.789E-12 2.650E-12 2.108E-12 7.953E-14 7.655E-12 5.443E-12 1.029E-13 4.977E-14 7.468E-14 5.239E-14 5.630E-14 8.564E-12 1.000E-11 1.351E-14 8.171E-12 5.115E-12 1.224E-12 6.087E-12 4.997E-12 1.013E-11 1.044E-12 2.204E-12 6.278E-14 1.270E-12 4.825E-14 3.041E-13 3.203E-14 6.784E-14 6.129E-14 2.828E-13 5.292E-14 9.375E-12 1.074E-14 5.957E-14 1.727E-14 1.454E-10 8.650E-15 6.699E-15 6.856E-15 6.042E-15 1.545E-12 7.241E-15 9.880E-15 4.431E-12 9.009E-15 3.991E-13 9.998E-14 1.270E-13 5.115E-12 1.155E-13 6.493E-12 2.168E-13 3.437E-12 2.163E-12 7.939E-13 3.718E-14

1.869E-07 1.020E-06 1.871E-07 7.120E-08 2.310E-11 7.286E-12 5.306E-12 6.183E-12 7.620E-12 2.949E-12 2.551E-12 2.785E-12 2.647E-12 2.106E-12 7.938E-14 7.589E-12 5.392E-12 1.028E-13 4.964E-14 7.455E-14 5.226E-14 5.622E-14 8.489E-12 9.948E-12 1.349E-14 8.119E-12 5.071E-12 1.207E-12 6.036E-12 4.955E-12 1.009E-11 1.036E-12 2.186E-12 6.267E-14 1.258E-12 4.813E-14 3.038E-13 3.198E-14 6.755E-14 6.120E-14 2.827E-13 5.286E-14 8.982E-12 1.072E-14 5.946E-14 1.724E-14 1.445E-10 8.639E-15 6.690E-15 6.843E-15 6.025E-15 1.531E-12 7.228E-15 9.854E-15 4.389E-12 8.985E-15 4.016E-13 9.934E-14 1.270E-13 5.079E-12 1.152E-13 6.464E-12 2.173E-13 3.399E-12 2.150E-12 7.884E-13 3.704E-14

2p+1(3)3 2p-1(1)1.2p+2(4)3 2p-1(1)1.2p+2(4)5 2p-1(1)1.2p+2(0)1 2p+3(3)3 2s+1(1)1.2p+2(4)5 2s+1(1)1.2p+2(0)1 2s+1(1)1.2p+2(4)3 2s+1(1)1.2p-1(1)0.2p+3(3)3 2s+1(1)1.2p-1(1)2.2p+3(3)5 2s+1(1)1.2p-1(1)2.2p+3(3)1 2s+1(1)1.2p-1(1)2.2p+3(3)3 2s+1(1)1 2p+3(3)3 2p-1(1)1 3s+1(1)1 3p-1(1)1 3p+1(3)3 2p-1(1)1.2p+1(3)2.3s+1(1)3 2p-1(1)1.2p+1(3)2.3s+1(1)1 2p-1(1)1.2p+1(3)4.3s+1(1)5 2p-1(1)1.2p+1(3)4.3s+1(1)3 3d-1(3)3 2p-1(1)1.2p+1(3)2.3p-1(1)1 2p-1(1)1.2p+1(3)2.3p-1(1)3 3d+1(5)5 2p-1(1)1.2p+1(3)4.3p-1(1)5 2p-1(1)1.2p+1(3)2.3p+1(3)5 2p-1(1)1.2p+1(3)4.3p-1(1)3 2p-1(1)1.2p+1(3)2.3p+1(3)1 2p-1(1)1.2p+1(3)2.3p+1(3)3 2p-1(1)1.2p+1(3)4.3p+1(3)7 2p-1(1)1.2p+1(3)4.3p+1(3)3 2p-1(1)1.2p+1(3)4.3p+1(3)5 2p+2(4)4.3s+1(1)5 2p-1(1)1.2p+1(3)4.3p+1(3)1 2p+2(4)4.3s+1(1)3 2s+1(1)1.2p+1(3)4.3s+1(1)5 2p-1(1)1.2p+1(3)2.3d-1(3)3 2p-1(1)1.2p+1(3)2.3d-1(3)5 2p-1(1)1.2p+1(3)2.3d-1(3)1 2p-1(1)1.2p+1(3)2.3d+1(5)7 2p+2(0)0.3s+1(1)1 2p-1(1)1.2p+1(3)4.3d-1(3)7 2p-1(1)1.2p+1(3)2.3d+1(5)5 2s+1(1)1.2p+1(3)4.3s+1(1)3 2p-1(1)1.2p+1(3)2.3d+1(5)3 2p-1(1)1.2p+1(3)4.3d+1(5)9 2p-1(1)1.2p+1(3)4.3d-1(3)5 2p-1(1)1.2p+1(3)4.3d-1(3)3 2p-1(1)1.2p+1(3)4.3d-1(3)1 2p-1(1)1.2p+1(3)4.3d+1(5)5 2p+2(4)4.3p-1(1)3 2p-1(1)1.2p+1(3)4.3d+1(5)7 2p-1(1)1.2p+1(3)4.3d+1(5)3 2p+2(4)4.3p-1(1)5 2p-1(1)1.2p+1(3)4.3d+1(5)1 2s+1(1)1.2p+1(3)4.3p-1(1)3 2s+1(1)1.2p+1(3)2.3s+1(1)1 2s+1(1)1.2p+1(3)4.3p-1(1)5 2p+2(4)4.3p+1(3)5 2s+1(1)1.2p+1(3)2.3s+1(1)3 2p+2(4)4.3p+1(3)7 2p+2(4)4.3p+1(3)1 2p+2(0)0.3p-1(1)1 2s+1(1)1.2p+1(3)4.3p+1(3)7 2p+2(4)4.3p+1(3)3 2s+1(1)1.2p+1(3)4.3p+1(3)3 (continued on next page)

K. Wang, Z.B. Chen and X.H. Zhao et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 237 (2019) 106640

Table 1 (continued) Key

LSJ-coupled CSF

Jπ

EMBPT

EMCDF

E

τ MBPT

τ MCDF

jj-coupled CSFa ,b ,c

69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138

2s 2 S 2 p3 (23 D ) 3 D 3s 4 D◦5/2 2s 2 S 2 p3 (43 S ) 5 S 3 p 4 P5/2 2s 2 S 2 p3 (43 S ) 5 S 3 p 4 P1/2 2s2 2 p2 (10 S ) 1 S 3 p 2 P3◦/2 2s 2 S 2 p3 (23 D ) 3 D 3 p 4 F3/2 2s 2 S 2 p3 (23 D ) 3 D 3 p 4 D1/2 2s 2 S 2 p3 (23 D ) 3 D 3s 2 D◦3/2 2s 2 S 2 p3 (23 D ) 3 D 3s 4 D◦7/2 2s2 2 p2 (12 D ) 1 D 3d 2 F7/2 2s2 2 p2 (12 D ) 1 D 3d 2 D3/2 2s2 2 p2 (32 P ) 3 P 3d 4 F9/2 2s2 2 p2 (12 D ) 1 D 3d 2 D5/2 2s2 2 p2 (12 D ) 1 D 3d 2 P1/2 2s2 2 p2 (32 P ) 3 P 3d 2 F7/2 2s 2 S 2 p3 (23 D ) 3 D 3s 2 D◦5/2 2s 2 S 2 p3 (43 S ) 5 S 3d 6 D◦5/2 2s 2 S 2 p3 (43 S ) 5 S 3d 6 D◦7/2 2s 2 S 2 p3 (43 S ) 5 S 3d 6 D◦3/2 2s 2 S 2 p3 (43 S ) 5 S 3d 6 D◦1/2 2s 2 S 2 p3 (23 D ) 3 D 3 p 4 F5/2 2s2 2 p2 (12 D ) 1 D 3d 2 S1/2 2s 2 S 2 p3 (43 S ) 5 S 3d 6 D◦9/2 2s 2 S 2 p3 (23 D ) 3 D 3 p 4 D3/2 2s2 2 p2 (12 D ) 1 D 3d 2 P3/2 2s2 2 p2 (32 P ) 3 P 3d 2 D5/2 2s 2 S 2 p3 (23 D ) 3 D 3 p 4 P3/2 2s 2 S 2 p3 (23 D ) 3 D 3 p 4 P1/2 2s 2 S 2 p3 (21 P ) 3 P 3s 4 P1◦/2 2s 2 S 2 p3 (23 D ) 3 D 3 p 2 F5/2 2s 2 S 2 p3 (43 S ) 5 S 3d 4 D◦5/2 2s 2 S 2 p3 (21 P ) 3 P 3s 4 P3◦/2 2s 2 S 2 p3 (43 S ) 5 S 3d 4 D◦3/2 2s2 2 p2 (10 S ) 1 S 3d 2 D3/2 2s 2 S 2 p3 (43 S ) 3 S 3s 2 S1◦ /2 2s2 2 p2 (10 S ) 1 S 3d 2 D5/2 2s 2 S 2 p3 (43 S ) 5 S 3d 4 D◦7/2 2s 2 S 2 p3 (23 D ) 1 D 3s 2 D◦5/2 2s 2 S 2 p3 (43 S ) 5 S 3d 4 D◦1/2 2s 2 S 2 p3 (23 D ) 1 D 3s 2 D◦3/2 2s 2 S 2 p3 (23 D ) 3 D 3 p 4 F7/2 2s 2 S 2 p3 (23 D ) 3 D 3 p 4 D5/2 2s 2 S 2 p3 (23 D ) 3 D 3 p 2 F7/2 2s 2 S 2 p3 (43 S ) 3 S 3s 4 S3◦ /2 2s 2 S 2 p3 (23 D ) 3 D 3 p 2 P1/2 2s 2 S 2 p3 (21 P ) 3 P 3s 2 P1◦/2 2s 2 S 2 p3 (23 D ) 3 D 3 p 4 P5/2 2s 2 S 2 p3 (23 D ) 3 D 3d 4 G◦5/2 2s 2 S 2 p3 (23 D ) 3 D 3d 4 F3◦/2 2s 2 S 2 p3 (23 D ) 3 D 3 p 2 D3/2 2s 2 S 2 p3 (23 D ) 3 D 3d 4 P1◦/2 2s 2 S 2 p3 (23 D ) 3 D 3 p 4 F9/2 2s 2 S 2 p3 (23 D ) 3 D 3 p 4 D7/2 2s 2 S 2 p3 (21 P ) 3 P 3 p 4 D1/2 2s 2 S 2 p3 (23 D ) 3 D 3d 4 G◦7/2 2s 2 S 2 p3 (23 D ) 3 D 3 p 2 P3/2 2s 2 S 2 p3 (23 D ) 3 D 3d 2 F5◦/2 2s 2 S 2 p3 (21 P ) 3 P 3 p 4 D3/2 2s 2 S 2 p3 (43 S ) 3 S 3 p 4 P1/2 2s 2 S 2 p3 (23 D ) 3 D 3d 4 S3◦ /2 2s 2 S 2 p3 (23 D ) 1 D 3 p 2 F5/2 2s 2 S 2 p3 (23 D ) 3 D 3 p 2 D5/2 2s 2 S 2 p3 (21 P ) 3 P 3 p 4 S3/2 2s 2 S 2 p3 (23 D ) 3 D 3d 4 D◦3/2 2s 2 S 2 p3 (21 P ) 3 P 3 p 4 P3/2 2s 2 S 2 p3 (23 D ) 3 D 3d 4 F5◦/2 2s 2 S 2 p3 (23 D ) 3 D 3d 4 D◦1/2 2s 2 S 2 p3 (23 D ) 3 D 3d 4 F7◦/2 2s 2 S 2 p3 (23 D ) 3 D 3d 4 G◦9/2 2s 2 S 2 p3 (43 S ) 3 S 3 p 4 P5/2 2s 2 S 2 p3 (21 P ) 3 P 3 p 4 P1/2

5/2− 5/2+ 1/2+ 3/2− 3/2+ 1/2+ 3/2− 7/2− 7/2+ 3/2+ 9/2+ 5/2+ 1/2+ 7/2+ 5/2− 5/2− 7/2− 3/2− 1/2− 5/2+ 1/2+ 9/2− 3/2+ 3/2+ 5/2+ 3/2+ 1/2+ 1/2− 5/2+ 5/2− 3/2− 3/2− 3/2+ 1/2− 5/2+ 7/2− 5/2− 1/2− 3/2− 7/2+ 5/2+ 7/2+ 3/2− 1/2+ 1/2− 5/2+ 5/2− 3/2− 3/2+ 1/2− 9/2+ 7/2+ 1/2+ 7/2− 3/2+ 5/2− 3/2+ 1/2+ 3/2− 5/2+ 5/2+ 3/2+ 3/2− 3/2+ 5/2− 1/2− 7/2− 9/2− 5/2+ 1/2+

21494270 21495891 21502136 21512359 21580248 21583556 21593380 21667956 21691711 21706719 21708246 21709313 21710806 21740734 21761569 21786039 21792265 21792303 21794249 21794855 21796049 21824366 21828872 21846367 21865517 21866240 21873224 21883110 21918220 21941831 21949343 21970430 21978165 21989063 21990488 22006100 22037020 22040051 22045413 22046798 22073573 22080123 22081260 22120749 22141805 22167683 22192961 22202371 22210801 22239657 22245806 22252109 22252326 22262880 22279725 22306720 22325350 22333589 22333659 22374217 22389807 22423160 22478940 22482334 22483079 22492259 22498587 22516547 22516850 22521271

21493978 21495133 21501403 21512584 21579604 21582966 21593527 21667819 21692300 21707336 21708912 21709943 21711389 21741615 21761771 21784822 21791053 21791034 21792958 21794201 21796697 21823099 21828644 21846304 21866338 21865646 21872881 21882859 21917466 21940924 21949010 21969831 21978663 21989125 21990914 22005371 22037080 22039326 22045536 22046029 22072683 22079258 22081240 22120054 22141987 22167430 22192317 22201679 22210293 22239009 22245077 22251363 22251456 22262231 22279141 22306076 22324639 22332973 22333095 22373664 22389389 22422518 22477966 22481552 22482084 22491264 22497601 22515601 22516114 22520727

−292 −758 −733 225 −644 −590 147 −137 589 617 666 630 583 881 202 −1217 −1212 −1269 −1292 −654 648 −1266 −228 −63 821 −594 −343 −251 −754 −907 −332 −598 498 62 427 −729 60 −726 124 −769 −890 −865 −19 −695 182 −253 −644 −691 −508 −647 −729 −745 −870 −649 −584 −644 −711 −616 −564 −553 −417 −642 −974 −782 −995 −995 −986 −946 −736 −543

1.086E-13 3.754E-14 4.619E-14 1.002E-12 7.002E-14 2.779E-14 6.912E-14 6.854E-14 2.545E-13 9.661E-15 1.434E-10 9.288E-15 1.816E-14 8.006E-15 6.312E-14 1.205E-13 6.209E-13 8.723E-14 2.867E-13 8.304E-14 8.448E-15 1.188E-10 1.894E-14 1.357E-14 8.357E-15 4.003E-14 2.194E-13 7.816E-14 6.439E-14 1.923E-14 3.367E-14 4.605E-14 7.271E-15 4.420E-14 9.022E-15 9.693E-15 8.987E-14 1.281E-14 4.863E-14 1.959E-13 5.601E-14 1.143E-13 7.762E-14 3.443E-14 7.419E-14 8.473E-14 2.744E-13 1.905E-14 3.597E-14 6.233E-14 1.358E-11 6.745E-14 9.783E-14 6.405E-14 3.110E-14 9.495E-15 6.865E-14 3.976E-14 1.446E-14 1.660E-13 2.341E-14 4.652E-14 4.236E-14 7.667E-14 2.748E-14 9.469E-14 2.871E-14 2.832E-11 6.464E-14 4.213E-13

1.082E-13 3.740E-14 4.608E-14 9.847E-13 6.991E-14 2.772E-14 6.901E-14 6.819E-14 2.509E-13 9.646E-15 1.426E-10 9.271E-15 1.812E-14 7.979E-15 6.305E-14 1.195E-13 6.237E-13 8.713E-14 2.866E-13 8.298E-14 8.442E-15 1.184E-10 2.016E-14 1.326E-14 8.365E-15 3.753E-14 2.157E-13 7.786E-14 6.441E-14 1.918E-14 3.281E-14 4.736E-14 7.249E-15 4.385E-14 8.976E-15 9.659E-15 8.945E-14 1.277E-14 4.842E-14 1.986E-13 5.578E-14 1.139E-13 7.723E-14 3.434E-14 7.386E-14 8.438E-14 2.747E-13 1.898E-14 3.584E-14 6.215E-14 1.355E-11 6.729E-14 9.761E-14 6.411E-14 3.099E-14 9.466E-15 6.843E-14 3.965E-14 1.443E-14 1.696E-13 2.322E-14 4.643E-14 4.225E-14 7.647E-14 2.737E-14 9.448E-14 2.865E-14 2.813E-11 6.447E-14 4.180E-13

2s+1(1)1.2p-1(1)0.2p+2(4)4.3s+1(1)5 2s+1(1)1.2p+1(3)4.3p+1(3)5 2s+1(1)1.2p+1(3)4.3p+1(3)1 2p+2(0)0.3p+1(3)3 2s+1(1)1.2p+1(3)2.3p-1(1)3 2s+1(1)1.2p+1(3)2.3p-1(1)1 2s+1(1)1.2p-1(1)0.2p+2(4)4.3s+1(1)3 2s+1(1)1.2p-1(1)2.2p+2(4)6.3s+1(1)7 2p+2(4)4.3d+1(5)7 2p+2(4)4.3d-1(3)3 2p+2(4)4.3d+1(5)9 2p+2(4)4.3d-1(3)5 2p+2(4)4.3d-1(3)1 2p+2(4)4.3d-1(3)7 2s+1(1)1.2p-1(1)2.2p+2(4)6.3s+1(1)5 2s+1(1)1.2p+1(3)4.3d-1(3)5 2s+1(1)1.2p+1(3)4.3d-1(3)7 2s+1(1)1.2p+1(3)4.3d-1(3)3 2s+1(1)1.2p+1(3)4.3d-1(3)1 2s+1(1)1.2p+1(3)2.3p+1(3)5 2p+2(4)4.3d+1(5)1 2s+1(1)1.2p+1(3)4.3d+1(5)9 2s+1(1)1.2p+1(3)2.3p+1(3)3 2p+2(4)4.3d+1(5)3 2p+2(4)4.3d+1(5)5 2s+1(1)1.2p-1(1)0.2p+2(4)4.3p-1(1)3 2s+1(1)1.2p+1(3)2.3p+1(3)1 2s+1(1)1.2p-1(1)0.2p+2(0)0.3s+1(1)1 2s+1(1)1.2p-1(1)0.2p+2(4)4.3p-1(1)5 2s+1(1)1.2p+1(3)4.3d+1(5)5 2s+1(1)1.2p-1(1)2.2p+2(4)2.3s+1(1)3 2s+1(1)1.2p+1(3)4.3d+1(5)3 2p+2(0)0.3d-1(3)3 2s+1(1)1.2p-1(1)2.2p+2(4)2.3s+1(1)1 2p+2(0)0.3d+1(5)5 2s+1(1)1.2p+1(3)4.3d+1(5)7 2s+1(1)1.2p-1(1)2.2p+2(4)4.3s+1(1)5 2s+1(1)1.2p+1(3)4.3d+1(5)1 2s+1(1)1.2p-1(1)2.2p+2(4)4.3s+1(1)3 2s+1(1)1.2p-1(1)2.2p+2(4)6.3p-1(1)7 2s+1(1)1.2p-1(1)0.2p+2(4)4.3p+1(3)5 2s+1(1)1.2p-1(1)0.2p+2(4)4.3p+1(3)7 2s+1(1)1.2p-1(1)2.2p+2(0)2.3s+1(1)3 2s+1(1)1.2p-1(1)0.2p+2(4)4.3p+1(3)1 2s+1(1)1.2p-1(1)2.2p+2(0)2.3s+1(1)1 2s+1(1)1.2p-1(1)2.2p+2(4)6.3p-1(1)5 2s+1(1)1.2p+1(3)2.3d-1(3)5 2s+1(1)1.2p+1(3)2.3d-1(3)3 2s+1(1)1.2p-1(1)0.2p+2(4)4.3p+1(3)3 2s+1(1)1.2p+1(3)2.3d-1(3)1 2s+1(1)1.2p-1(1)2.2p+2(4)6.3p+1(3)9 2s+1(1)1.2p-1(1)2.2p+2(4)6.3p+1(3)7 2s+1(1)1.2p-1(1)0.2p+2(0)0.3p-1(1)1 2s+1(1)1.2p+1(3)2.3d+1(5)7 2s+1(1)1.2p-1(1)2.2p+2(4)6.3p+1(3)3 2s+1(1)1.2p+1(3)2.3d+1(5)5 2s+1(1)1.2p-1(1)2.2p+2(4)2.3p-1(1)3 2s+1(1)1.2p-1(1)2.2p+2(4)2.3p-1(1)1 2s+1(1)1.2p+1(3)2.3d+1(5)3 2s+1(1)1.2p-1(1)2.2p+2(4)6.3p+1(3)5 2s+1(1)1.2p-1(1)2.2p+2(4)6.3p+1(3)5 2s+1(1)1.2p-1(1)2.2p+2(0)2.3p-1(1)3 2s+1(1)1.2p-1(1)0.2p+2(4)4.3d-1(3)3 2s+1(1)1.2p-1(1)0.2p+2(0)0.3p+1(3)3 2s+1(1)1.2p-1(1)0.2p+2(4)4.3d-1(3)5 2s+1(1)1.2p-1(1)0.2p+2(4)4.3d-1(3)1 2s+1(1)1.2p-1(1)0.2p+2(4)4.3d+1(5)7 2s+1(1)1.2p-1(1)0.2p+2(4)4.3d+1(5)9 2s+1(1)1.2p-1(1)2.2p+2(4)2.3p+1(3)5 2s+1(1)1.2p-1(1)2.2p+2(4)2.3p+1(3)1 (continued on next page)

3

4

K. Wang, Z.B. Chen and X.H. Zhao et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 237 (2019) 106640

Table 1 (continued) Key

LSJ-coupled CSF

Jπ

EMBPT

EMCDF

E

τ MBPT

τ MCDF

jj-coupled CSFa ,b ,c

139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208

2s 2 S 2 p3 (43 S ) 3 S 3 p 4 P3/2 2s 2 S 2 p3 (21 P ) 3 P 3 p 2 P1/2 2s 2 S 2 p3 (21 P ) 3 P 3 p 2 D3/2 2s 2 S 2 p3 (23 D ) 3 D 3d 2 G◦7/2 2s 2 S 2 p3 (21 P ) 3 P 3s 4 P5◦/2 2s 2 S 2 p3 (23 D ) 1 D 3 p 2 F7/2 2s 2 S 2 p3 (23 D ) 1 D 3 p 2 D5/2 2s 2 S 2 p3 (21 P ) 3 P 3 p 2 S1/2 2s 2 S 2 p3 (23 D ) 3 D 3d 2 P1◦/2 2s 2 S 2 p3 (21 P ) 3 P 3s 2 P3◦/2 2s 2 S 2 p3 (23 D ) 3 D 3d 4 F9◦/2 2s 2 S 2 p3 (23 D ) 3 D 3d 4 P5◦/2 2s 2 S 2 p3 (21 P ) 3 P 3 p 4 D5/2 2s 2 S 2 p3 (23 D ) 1 D 3 p 2 D3/2 2s 2 S 2 p3 (23 D ) 3 D 3d 2 D◦3/2 2s 2 S 2 p3 (23 D ) 3 D 3d 4 G◦11/2 2s 2 S 2 p3 (23 D ) 3 D 3d 4 D◦7/2 2s 2 S 2 p3 (23 D ) 3 D 3d 2 G◦9/2 2s 2 S 2 p3 (23 D ) 3 D 3d 4 D◦5/2 2s 2 S 2 p3 (23 D ) 3 D 3d 4 P3◦/2 2s 2 S 2 p3 (43 S ) 3 S 3 p 2 P1/2 2s 2 S 2 p3 (43 S ) 3 S 3 p 2 P3/2 2s 2 S 2 p3 (23 D ) 3 D 3d 2 S1◦ /2 2s 2 S 2 p3 (23 D ) 3 D 3d 2 P3◦/2 2s 2 S 2 p3 (23 D ) 3 D 3d 2 F7◦/2 2s 2 S 2 p3 (23 D ) 3 D 3d 2 D◦5/2 2s 2 S 2 p3 (21 P ) 3 P 3d 4 F3◦/2 2s 2 S 2 p3 (21 P ) 1 P 3s 2 P3◦/2 2s 2 S 2 p3 (21 P ) 1 P 3s 2 P1◦/2 2s 2 S 2 p3 (21 P ) 3 P 3d 4 F5◦/2 2s 2 S 2 p3 (43 S ) 3 S 3d 4 D◦1/2 2s 2 S 2 p3 (21 P ) 3 P 3d 4 P5◦/2 2s 2 S 2 p3 (43 S ) 3 S 3d 4 D◦3/2 2s 2 S 2 p3 (21 P ) 3 P 3d 4 F7◦/2 2s 2 S 2 p3 (23 D ) 1 D 3d 2 G◦7/2 2s 2 S 2 p3 (21 P ) 3 P 3d 4 D◦3/2 2s 2 S 2 p3 (21 P ) 3 P 3d 4 D◦5/2 2s 2 S 2 p3 (23 D ) 1 D 3 p 2 P3/2 2s 2 S 2 p3 (21 P ) 3 P 3 p 2 D5/2 2s 2 S 2 p3 (23 D ) 1 D 3d 2 G◦9/2 2s 2 S 2 p3 (21 P ) 3 P 3d 2 F5◦/2 2s 2 S 2 p3 (23 D ) 1 D 3d 2 F7◦/2 2s 2 S 2 p3 (43 S ) 3 S 3d 4 D◦5/2 2s 2 S 2 p3 (23 D ) 1 D 3d 2 P1◦/2 2s 2 S 2 p3 (23 D ) 1 D 3d 2 P3◦/2 2s 2 S 2 p3 (21 P ) 1 P 3d 2 D◦3/2 2s 2 S 2 p3 (43 S ) 3 S 3d 4 D◦7/2 2s 2 S 2 p3 (21 P ) 3 P 3d 4 D◦1/2 2s 2 S 2 p3 (23 D ) 1 D 3d 2 S1◦ /2 2s 2 S 2 p3 (21 P ) 3 P 3d 2 D◦5/2 2s 2 S 2 p3 (21 P ) 3 P 3 p 4 D7/2 2 p4 (32 P ) 3 P 3s 4 P5/2 2s 2 S 2 p3 (21 P ) 3 P 3d 2 D◦3/2 2s 2 S 2 p3 (21 P ) 3 P 3 p 2 P3/2 2s 2 S 2 p3 (21 P ) 3 P 3d 2 P3◦/2 2s 2 S 2 p3 (21 P ) 3 P 3 p 4 P5/2 2s 2 S 2 p3 (43 S ) 3 S 3d 2 D◦5/2 2 p4 (32 P ) 3 P 3s 2 P3/2 2s 2 S 2 p3 (23 D ) 1 D 3 p 2 P1/2 2s 2 S 2 p3 (21 P ) 1 P 3 p 2 P1/2 2s 2 S 2 p3 (21 P ) 1 P 3 p 2 D3/2 2 p4 (10 S ) 1 S 3s 2 S1/2 2s 2 S 2 p3 (21 P ) 1 P 3 p 2 D5/2 2s 2 S 2 p3 (21 P ) 1 P 3 p 2 P3/2 2 p4 (32 P ) 3 P 3 p 4 P3◦/2 2 p4 (32 P ) 3 P 3 p 2 D◦5/2 2s 2 S 2 p3 (21 P ) 3 P 3d 4 F9◦/2 2s 2 S 2 p3 (21 P ) 3 P 3d 4 P1◦/2 2s 2 S 2 p3 (21 P ) 3 P 3d 4 P3◦/2 2s 2 S 2 p3 (21 P ) 1 P 3 p 2 S1/2

3/2+ 1/2+ 3/2+ 7/2− 5/2− 7/2+ 5/2+ 1/2+ 1/2− 3/2− 9/2− 5/2− 5/2+ 3/2+ 3/2− 11/2− 7/2− 9/2− 5/2− 3/2− 1/2+ 3/2+ 1/2− 3/2− 7/2− 5/2− 3/2− 3/2− 1/2− 5/2− 1/2− 5/2− 3/2− 7/2− 7/2− 3/2− 5/2− 3/2+ 5/2+ 9/2− 5/2− 7/2− 5/2− 1/2− 3/2− 3/2− 7/2− 1/2− 1/2− 5/2− 7/2+ 5/2+ 3/2− 3/2+ 3/2− 5/2+ 5/2− 3/2+ 1/2+ 1/2+ 3/2+ 1/2+ 5/2+ 3/2+ 3/2− 5/2− 9/2− 1/2− 3/2− 1/2+

22530755 22551924 22557171 22559293 22577848 22585838 22636672 22641904 22644696 22650970 22650978 22659405 22662540 22668917 22684076 22685073 22688087 22715086 22717360 22740306 22744571 22752315 22775256 22831941 22840872 22854520 22872796 22915221 22916126 22919219 22938743 22961560 22963182 22965287 23004992 23008593 23009715 23022090 23043151 23047498 23056992 23084392 23088218 23094298 23098135 23112393 23121668 23127843 23131776 23134647 23151852 23164392 23165806 23169533 23193723 23208986 23233755 23243356 23255911 23335032 23343678 23431942 23469957 23491260 23519226 23536104 23589572 23595404 23614380 23620106

22530513 22551498 22556637 22558602 22577655 22585190 22636204 22641303 22643969 22650992 22650174 22658692 22661941 22668452 22683486 22684321 22687302 22714494 22716550 22739518 22744410 22752062 22774533 22831409 22840465 22854002 22871934 22915303 22916120 22918382 22938154 22960856 22962533 22964542 23004443 23007909 23009028 23021561 23042822 23046908 23056415 23083876 23087712 23093675 23097561 23111799 23121055 23127216 23131008 23134190 23151074 23163163 23165240 23168733 23193556 23208195 23233506 23242474 23255473 23334676 23343453 23430763 23469416 23490699 23517658 23534601 23588820 23594478 23613607 23620130

−242 −425 −533 −690 −194 −648 −468 −601 −727 22 −804 −713 −599 −465 −590 −752 −785 −592 −810 −787 −161 −253 −724 −532 −407 −518 −862 81 −6 −837 −588 −704 −650 −746 −550 −684 −687 −529 −329 −590 −577 −516 −506 −622 −574 −594 −613 −627 −769 −457 −778 −1229 −566 −800 −167 −791 −248 −882 −438 −356 −224 −1180 −540 −560 −1568 −1503 −752 −926 −773 25

6.266E-14 4.383E-14 6.759E-14 9.391E-14 3.072E-14 5.133E-14 1.974E-13 4.008E-14 1.955E-14 3.625E-14 2.016E-11 1.304E-14 1.556E-13 1.117E-13 1.117E-14 4.005E-11 1.014E-14 6.546E-12 7.709E-15 6.839E-15 9.282E-14 6.094E-14 1.592E-14 1.009E-14 1.464E-14 1.189E-14 4.003E-14 4.817E-14 3.707E-14 2.439E-14 1.643E-14 3.378E-14 5.079E-14 1.846E-13 4.934E-14 1.220E-14 4.807E-14 1.234E-13 3.666E-14 3.343E-12 4.293E-14 2.112E-14 8.654E-15 7.901E-15 1.058E-14 8.888E-15 1.991E-14 6.941E-15 7.794E-15 9.772E-15 6.956E-13 2.760E-13 1.955E-14 3.788E-14 5.567E-15 9.158E-14 6.997E-15 5.912E-14 2.026E-14 1.785E-13 6.482E-14 1.316E-13 5.981E-14 1.135E-13 3.914E-14 4.305E-14 7.189E-12 8.668E-15 9.612E-15 2.312E-13

6.229E-14 4.369E-14 6.769E-14 9.338E-14 3.046E-14 5.126E-14 1.971E-13 4.001E-14 1.948E-14 3.558E-14 2.013E-11 1.304E-14 1.557E-13 1.117E-13 1.119E-14 3.972E-11 1.010E-14 6.522E-12 7.689E-15 6.823E-15 9.262E-14 6.077E-14 1.588E-14 1.006E-14 1.458E-14 1.185E-14 3.992E-14 4.775E-14 3.646E-14 2.429E-14 1.646E-14 3.370E-14 5.045E-14 1.837E-13 4.931E-14 1.218E-14 4.782E-14 1.232E-13 3.651E-14 3.332E-12 4.290E-14 2.109E-14 8.625E-15 7.876E-15 1.059E-14 8.839E-15 1.981E-14 6.928E-15 7.761E-15 9.719E-15 6.946E-13 2.795E-13 1.951E-14 3.780E-14 5.547E-15 9.109E-14 6.974E-15 5.881E-14 2.021E-14 1.777E-13 6.462E-14 1.310E-13 5.980E-14 1.140E-13 3.912E-14 4.303E-14 7.142E-12 8.643E-15 9.589E-15 2.297E-13

2s+1(1)1.2p-1(1)2.2p+2(4)2.3p-1(1)3 2s+1(1)1.2p-1(1)2.2p+2(0)2.3p-1(1)1 2s+1(1)1.2p-1(1)2.2p+2(4)2.3p+1(3)3 2s+1(1)1.2p-1(1)0.2p+2(4)4.3d-1(3)7 2s+1(1)1.2p+3(3)4.3s+1(1)5 2s+1(1)1.2p-1(1)2.2p+2(4)4.3p+1(3)7 2s+1(1)1.2p-1(1)2.2p+2(4)4.3p+1(3)5 2s+1(1)1.2p-1(1)2.2p+2(0)2.3p+1(3)1 2s+1(1)1.2p-1(1)0.2p+2(4)4.3d+1(5)1 2s+1(1)1.2p+3(3)4.3s+1(1)3 2s+1(1)1.2p-1(1)2.2p+2(4)6.3d-1(3)9 2s+1(1)1.2p-1(1)0.2p+2(4)4.3d+1(5)5 2s+1(1)1.2p-1(1)2.2p+2(0)2.3p+1(3)5 2s+1(1)1.2p-1(1)0.2p+2(4)4.3p+1(3)3 2s+1(1)1.2p-1(1)0.2p+2(4)4.3d+1(5)3 2s+1(1)1.2p-1(1)2.2p+2(4)6.3d+1(5)11 2s+1(1)1.2p-1(1)2.2p+2(4)6.3d-1(3)7 2s+1(1)1.2p-1(1)2.2p+2(4)6.3d+1(5)9 2s+1(1)1.2p-1(1)2.2p+2(4)6.3d-1(3)5 2s+1(1)1.2p-1(1)2.2p+2(4)6.3d-1(3)3 2s+1(1)1.2p-1(1)2.2p+2(4)2.3p+1(3)1 2s+1(1)1.2p-1(1)2.2p+2(4)2.3p+1(3)3 2s+1(1)1.2p-1(1)2.2p+2(4)6.3d+1(5)1 2s+1(1)1.2p-1(1)2.2p+2(4)6.3d+1(5)3 2s+1(1)1.2p-1(1)2.2p+2(4)6.3d+1(5)7 2s+1(1)1.2p-1(1)2.2p+2(4)6.3d+1(5)5 2s+1(1)1.2p-1(1)0.2p+2(0)0.3d-1(3)3 2s+1(1)1.2p+3(3)2.3s+1(1)3 2s+1(1)1.2p+3(3)2.3s+1(1)1 2s+1(1)1.2p-1(1)0.2p+2(0)0.3d+1(5)5 2s+1(1)1.2p-1(1)2.2p+2(4)2.3d-1(3)1 2s+1(1)1.2p-1(1)0.2p+2(0)0.3d+1(5)5 2s+1(1)1.2p-1(1)2.2p+2(4)2.3d-1(3)3 2s+1(1)1.2p-1(1)2.2p+2(4)2.3d+1(5)7 2s+1(1)1.2p-1(1)2.2p+2(4)4.3d-1(3)7 2s+1(1)1.2p-1(1)2.2p+2(4)2.3d+1(5)3 2s+1(1)1.2p-1(1)2.2p+2(4)2.3d+1(5)5 2s+1(1)1.2p+3(3)4.3p-1(1)3 2s+1(1)1.2p+3(3)4.3p-1(1)5 2s+1(1)1.2p-1(1)2.2p+2(4)4.3d+1(5)9 2s+1(1)1.2p-1(1)2.2p+2(0)2.3d-1(3)5 2s+1(1)1.2p-1(1)2.2p+2(4)4.3d+1(5)7 2s+1(1)1.2p-1(1)2.2p+2(4)2.3d-1(3)5 2s+1(1)1.2p-1(1)2.2p+2(4)4.3d-1(3)1 2s+1(1)1.2p-1(1)2.2p+2(4)4.3d-1(3)3 2s+1(1)1.2p-1(1)2.2p+2(0)2.3d-1(3)3 2s+1(1)1.2p-1(1)2.2p+2(0)2.3d+1(5)7 2s+1(1)1.2p-1(1)2.2p+2(0)2.3d-1(3)1 2s+1(1)1.2p-1(1)2.2p+2(4)4.3d+1(5)1 2s+1(1)1.2p-1(1)2.2p+2(4)4.3d+1(5)5 2s+1(1)1.2p+3(3)4.3p+1(3)7 2p+2(4)4.3s+1(1)5 2s+1(1)1.2p-1(1)2.2p+2(0)2.3d+1(5)3 2s+1(1)1.2p+3(3)4.3p+1(3)3 2s+1(1)1.2p-1(1)2.2p+2(4)4.3d+1(5)3 2s+1(1)1.2p+3(3)4.3p+1(3)5 2s+1(1)1.2p-1(1)2.2p+2(0)2.3d+1(5)5 2p+2(4)4.3s+1(1)3 2s+1(1)1.2p+3(3)4.3p+1(3)1 2s+1(1)1.2p+3(3)2.3p-1(1)1 2s+1(1)1.2p+3(3)2.3p-1(1)3 2p+2(0)0.3s+1(1)1 2s+1(1)1.2p+3(3)2.3p+1(3)5 2s+1(1)1.2p+3(3)2.3p+1(3)3 2p+2(4)4.3p-1(1)3 2p+2(4)4.3p-1(1)5 2s+1(1)1.2p+3(3)4.3d+1(5)9 2s+1(1)1.2p+3(3)4.3d-1(3)1 2s+1(1)1.2p+3(3)4.3d-1(3)3 2s+1(1)1.2p+3(3)2.3p+1(3)1 (continued on next page)

K. Wang, Z.B. Chen and X.H. Zhao et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 237 (2019) 106640

Table 1 (continued) Key

LSJ-coupled CSF

Jπ

EMBPT

EMCDF

E

τ MBPT

τ MCDF

jj-coupled CSFa ,b ,c

209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272

2s 2 S 2 p3 (23 D ) 1 D 3d 2 D◦5/2 2s 2 S 2 p3 (21 P ) 3 P 3d 4 D◦7/2 2s 2 S 2 p3 (21 P ) 3 P 3d 2 F7◦/2 2s 2 S 2 p3 (23 D ) 1 D 3d 2 F5◦/2 2 p4 (32 P ) 3 P 3 p 2 P1◦/2 2 p4 (32 P ) 3 P 3 p 4 P5◦/2 2s 2 S 2 p3 (23 D ) 1 D 3d 2 D◦3/2 2 p4 (32 P ) 3 P 3 p 4 D◦7/2 2 p4 (32 P ) 3 P 3 p 4 D◦1/2 2s 2 S 2 p3 (21 P ) 3 P 3d 2 P1◦/2 2 p4 (32 P ) 3 P 3s 4 P3/2 2 p4 (32 P ) 3 P 3 p 4 S3◦ /2 2s 2 S 2 p3 (21 P ) 1 P 3d 2 P1◦/2 2s 2 S 2 p3 (21 P ) 1 P 3d 2 F7◦/2 2 p4 (32 P ) 3 P 3s 2 P1/2 2s 2 S 2 p3 (21 P ) 1 P 3d 2 F5◦/2 2s 2 S 2 p3 (21 P ) 1 P 3d 2 P3◦/2 2s 2 S 2 p3 (21 P ) 1 P 3d 2 D◦5/2 2 p4 (32 P ) 3 P 3 p 2 P3◦/2 2 p4 (12 D ) 1 D 3s 2 D5/2 2 p4 (12 D ) 1 D 3s 2 D3/2 2s 2 S 2 p3 (43 S ) 3 S 3d 2 D◦3/2 2 p4 (32 P ) 3 P 3d 4 D5/2 2 p4 (32 P ) 3 P 3d 4 D3/2 2 p4 (32 P ) 3 P 3d 4 D7/2 2 p4 (32 P ) 3 P 3d 2 P1/2 2 p4 (32 P ) 3 P 3d 2 F7/2 2 p4 (32 P ) 3 P 3d 4 F9/2 2 p4 (32 P ) 3 P 3 p 4 P1◦/2 2 p4 (32 P ) 3 P 3d 4 P1/2 2 p4 (32 P ) 3 P 3 p 4 D◦3/2 2 p4 (32 P ) 3 P 3d 4 P3/2 2 p4 (32 P ) 3 P 3d 2 D5/2 2 p4 (12 D ) 1 D 3 p 2 F5◦/2 2 p4 (32 P ) 3 P 3d 4 F3/2 2 p4 (32 P ) 3 P 3 p 4 D◦5/2 2 p4 (32 P ) 3 P 3d 4 P5/2 2 p4 (32 P ) 3 P 3 p 2 S1◦ /2 2 p4 (32 P ) 3 P 3 p 2 D◦3/2 2 p4 (12 D ) 1 D 3 p 2 P3◦/2 2 p4 (12 D ) 1 D 3 p 2 F7◦/2 2 p4 (12 D ) 1 D 3 p 2 D◦3/2 2 p4 (12 D ) 1 D 3 p 2 D◦5/2 2 p4 (12 D ) 1 D 3 p 2 P1◦/2 2 p4 (32 P ) 3 P 3d 4 D1/2 2 p4 (32 P ) 3 P 3d 2 D3/2 2 p4 (32 P ) 3 P 3s 4 P1/2 2 p4 (32 P ) 3 P 3d 4 F7/2 2 p4 (32 P ) 3 P 3d 4 F5/2 2 p4 (32 P ) 3 P 3d 2 F5/2 2 p4 (12 D ) 1 D 3d 2 G7/2 2 p4 (32 P ) 3 P 3d 2 P3/2 2 p4 (12 D ) 1 D 3d 2 G9/2 2 p4 (12 D ) 1 D 3d 2 S1/2 2 p4 (12 D ) 1 D 3d 2 D5/2 2 p4 (12 D ) 1 D 3d 2 P3/2 2 p4 (12 D ) 1 D 3d 2 F5/2 2 p4 (12 D ) 1 D 3d 2 F7/2 2 p4 (12 D ) 1 D 3d 2 D3/2 2 p4 (12 D ) 1 D 3d 2 P1/2 2 p4 (10 S ) 1 S 3 p 2 P1◦/2 2 p4 (10 S ) 1 S 3 p 2 P3◦/2 2 p4 (10 S ) 1 S 3d 2 D5/2 2 p4 (10 S ) 1 S 3d 2 D3/2

5/2− 7/2− 7/2− 5/2− 1/2− 5/2− 3/2− 7/2− 1/2− 1/2− 3/2+ 3/2− 1/2− 7/2− 1/2+ 5/2− 3/2− 5/2− 3/2− 5/2+ 3/2+ 3/2− 5/2+ 3/2+ 7/2+ 1/2+ 7/2+ 9/2+ 1/2− 1/2+ 3/2− 3/2+ 5/2+ 5/2− 3/2+ 5/2− 5/2+ 1/2− 3/2− 3/2− 7/2− 3/2− 5/2− 1/2− 1/2+ 3/2+ 1/2+ 7/2+ 5/2+ 5/2+ 7/2+ 3/2+ 9/2+ 1/2+ 5/2+ 3/2+ 5/2+ 7/2+ 3/2+ 1/2+ 1/2− 3/2− 5/2+ 3/2+

23635510 23638944 23659426 23664133 23705491 23725195 23725837 23727218 23791993 23815508 23889524 23891854 23934230 23934777 23939444 23942123 23945027 23958200 23996461 24004925 24023797 24056689 24111992 24113084 24128809 24131459 24163998 24167066 24217864 24235093 24258330 24285988 24317400 24342587 24396191 24427332 24453842 24457176 24459364 24495088 24537173 24550385 24584557 24747869 24793290 24836527 24847549 24866365 24880475 24917961 24928295 24930939 24972282 25003393 25011416 25031235 25032844 25038241 25140661 25179794 25266585 25398447 25849219 25863162

23634830 23638340 23658857 23663511 23703900 23723644 23725281 23725651 23790727 23814986 23888032 23890955 23933814 23934282 23938343 23941857 23944487 23957685 23995100 24003761 24022763 24056478 24110623 24111679 24127586 24130033 24162862 24165900 24216082 24233759 24256745 24284872 24316513 24341221 24395177 24425516 24452733 24455534 24457899 24494589 24535723 24549039 24583303 24747446 24791674 24835079 24846239 24864964 24879302 24916674 24927432 24929614 24971370 25002078 25010371 25030390 25032136 25037380 25140029 25179202 25265579 25396896 25848013 25862208

−680 −603 −569 −622 −1591 −1551 −556 −1567 −1266 −522 −1492 −899 −416 −494 −1101 −266 −540 −515 −1361 −1164 −1034 −210 −1369 −1405 −1223 −1426 −1136 −1166 −1782 −1334 −1585 −1116 −886 −1365 −1014 −1816 −1109 −1642 −1465 −498 −1449 −1346 −1254 −423 −1617 −1448 −1310 −1401 −1173 −1288 −863 −1325 −912 −1315 −1045 −845 −708 −861 −631 −591 −1006 −1551 −1206 −954

1.604E-14 9.630E-15 5.288E-14 1.371E-14 3.582E-14 3.751E-14 1.396E-14 4.511E-14 2.690E-14 6.284E-15 1.821E-13 3.527E-14 8.333E-15 3.298E-13 5.753E-14 1.248E-14 1.302E-14 2.507E-14 3.559E-14 8.111E-14 7.177E-14 4.843E-15 9.271E-13 6.337E-13 1.213E-12 2.159E-13 1.705E-12 2.927E-12 4.026E-14 1.842E-14 4.201E-14 1.632E-14 1.158E-14 4.864E-14 2.349E-14 4.054E-14 1.854E-14 3.340E-14 3.759E-14 2.937E-14 4.376E-14 3.824E-14 4.336E-14 3.304E-14 7.686E-13 3.286E-13 4.594E-14 2.085E-12 2.736E-14 3.195E-13 2.450E-12 9.024E-14 2.568E-12 8.405E-15 2.413E-13 7.112E-15 8.150E-15 1.049E-12 5.563E-15 4.551E-15 2.893E-14 3.999E-14 5.916E-13 8.623E-15

1.606E-14 9.638E-15 5.122E-14 1.361E-14 3.571E-14 3.740E-14 1.391E-14 4.502E-14 2.738E-14 6.231E-15 1.810E-13 3.513E-14 8.310E-15 3.298E-13 5.722E-14 1.254E-14 1.299E-14 2.441E-14 3.568E-14 8.068E-14 7.138E-14 4.822E-15 9.314E-13 6.311E-13 1.223E-12 2.150E-13 1.694E-12 2.910E-12 4.021E-14 1.837E-14 4.191E-14 1.629E-14 1.155E-14 4.861E-14 2.334E-14 4.046E-14 1.846E-14 3.331E-14 3.759E-14 2.910E-14 4.365E-14 3.814E-14 4.328E-14 3.279E-14 7.670E-13 3.263E-13 4.567E-14 2.076E-12 2.723E-14 3.151E-13 2.436E-12 9.014E-14 2.551E-12 8.383E-15 2.374E-13 7.071E-15 8.098E-15 1.062E-12 5.540E-15 4.528E-15 2.874E-14 3.988E-14 5.961E-13 8.571E-15

2s+1(1)1.2p+3(3)4.3d+1(5)5 2s+1(1)1.2p+3(3)4.3d-1(3)7 2s+1(1)1.2p+3(3)4.3d+1(5)7 2s+1(1)1.2p+3(3)4.3d-1(3)5 2p+2(4)4.3p+1(3)1 2p+2(4)4.3p+1(3)5 2s+1(1)1.2p+3(3)4.3d+1(5)3 2p+2(4)4.3p+1(3)7 2p+2(0)0.3p-1(1)1 2s+1(1)1.2p+3(3)4.3d+1(5)1 2p-1(1)1.2p+3(3)2.3s+1(1)3 2p+2(4)4.3p+1(3)3 2s+1(1)1.2p+3(3)2.3d-1(3)1 2s+1(1)1.2p+3(3)2.3d+1(5)7 2p-1(1)1.2p+3(3)2.3s+1(1)1 2s+1(1)1.2p+3(3)2.3d-1(3)5 2s+1(1)1.2p+3(3)2.3d-1(3)3 2s+1(1)1.2p+3(3)2.3d+1(5)5 2p+2(0)0.3p+1(3)3 2p-1(1)1.2p+3(3)4.3s+1(1)5 2p-1(1)1.2p+3(3)4.3s+1(1)3 2s+1(1)1.2p+3(3)2.3d+1(5)3 2p+2(4)4.3d-1(3)5 2p+2(4)4.3d-1(3)3 2p+2(4)4.3d-1(3)7 2p+2(4)4.3d-1(3)1 2p+2(4)4.3d+1(5)7 2p+2(4)4.3d+1(5)9 2p-1(1)1.2p+3(3)2.3p-1(1)1 2p+2(4)4.3d+1(5)1 2p-1(1)1.2p+3(3)2.3p-1(1)3 2p+2(4)4.3d+1(5)3 2p+2(4)4.3d+1(5)5 2p-1(1)1.2p+3(3)4.3p-1(1)5 2p+2(0)0.3d-1(3)3 2p-1(1)1.2p+3(3)2.3p+1(3)5 2p+2(0)0.3d+1(5)5 2p-1(1)1.2p+3(3)2.3p+1(3)1 2p-1(1)1.2p+3(3)2.3p+1(3)3 2p-1(1)1.2p+3(3)4.3p-1(1)3 2p-1(1)1.2p+3(3)4.3p+1(3)7 2p-1(1)1.2p+3(3)4.3p+1(3)3 2p-1(1)1.2p+3(3)4.3p+1(3)5 2p-1(1)1.2p+3(3)4.3p+1(3)1 2p-1(1)1.2p+3(3)2.3d-1(3)1 2p-1(1)1.2p+3(3)2.3d-1(3)3 3s+1(1)1 2p-1(1)1.2p+3(3)2.3d+1(5)7 2p-1(1)1.2p+3(3)2.3d-1(3)5 2p-1(1)1.2p+3(3)2.3d+1(5)5 2p-1(1)1.2p+3(3)4.3d-1(3)7 2p-1(1)1.2p+3(3)2.3d+1(5)3 2p-1(1)1.2p+3(3)4.3d+1(5)9 2p-1(1)1.2p+3(3)4.3d-1(3)1 2p-1(1)1.2p+3(3)4.3d+1(5)5 2p-1(1)1.2p+3(3)4.3d-1(3)3 2p-1(1)1.2p+3(3)4.3d-1(3)5 2p-1(1)1.2p+3(3)4.3d+1(5)7 2p-1(1)1.2p+3(3)4.3d+1(5)3 2p-1(1)1.2p+3(3)4.3d+1(5)1 3p-1(1)1 3p+1(3)3 3d+1(5)5 3d-1(3)3

a

The number at the end or in parentheses is 2J. s+ = s1/2 , p− = p1/2 , p+ = p3/2 , d− = d3/2 , d+ = d5/2 , f − = f 5/2 , and f + = f 7/2 . c The number after ± is the occupation number of the corresponding sub-shell. For example, the jj-coupled CSF of level 9 is 2s1/2 2 p1/2 2 p33/2 . The full sub-shell 1s1/2 is omitted. b

5

6

K. Wang, Z.B. Chen and X.H. Zhao et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 237 (2019) 106640

Table 2 ˚ transition rates (A, in s−1 ), oscillator strengths (gf, dimensionless), line strengths (S, in a.u.), and branching fractions (BF) for the transitions Wavelengths (λ, in vacuum A), among the 272 levels listed in Table 1 from the present MBPT and MCDF calculations. The two first columns (i and j) refer to the keys of Table 1. The last column represents the estimated accuracies of the S values using the terminology of the NIST ASD [46]. Only transitions with BF ≥ 10−5 are presented. i

j

Type

λMBPT

AMBPT

gfMBPT

SMBPT

BFMBPT

λMCDF

AMCDF

gfMCDF

SMCDF

BFMCDF

Acc.

1 1 1 1 2 1 1 2 1 2 2 3 3 4 4 1 2 3 5 1 2 4 5 1 2 3 4 5 1 2 3 4 5 6 1 2 3 5 6 1 2 4 5 8 1 2 3 4 5 1 2 4 5 9 11 6 7 8 9 10 11 12 13 7 8 9 11 12 13 14

2 2 3 3 3 4 4 4 5 5 5 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 8 9 9 9 9 9 9 10 10 10 10 10 11 11 11 11 11 12 12 12 12 12 13 13 13 13 13 13 14 14 14 14 14 14 14 14 15 15 15 15 15 15 15

M1 E2 M1 E2 M1 M1 E2 M1 M1 M1 E2 M1 E2 M1 E2 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 M1 E1 E1 E1 E1 M1 E1 E1 E1 E1 M1 E1 E1 E1 E1 E1 E1 E1 E1 E1 M1 M1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 M1

1.58284E+02 1.58284E+02 1.33039E+02 1.33039E+02 8.34148E+02 1.10022E+02 1.10022E+02 3.60833E+02 6.49140E+01 1.10044E+02 1.10044E+02 1.26768E+02 1.26768E+02 1.58331E+02 1.58331E+02 5.56232E+01 8.57607E+01 9.55884E+01 3.88638E+02 4.67987E+01 6.64436E+01 8.14398E+01 1.67698E+02 4.67551E+01 6.63557E+01 7.20904E+01 8.13079E+01 1.67139E+02 3.85413E+01 5.09464E+01 5.42604E+01 5.93222E+01 9.48659E+01 1.25500E+02 3.62307E+01 4.69856E+01 4.97901E+01 8.19950E+01 1.03920E+02 3.40500E+01 4.33824E+01 4.93111E+01 7.16151E+01 1.25305E+02 3.29923E+01 4.16800E+01 4.38721E+01 4.71232E+01 6.70912E+01 2.69523E+01 3.24835E+01 3.56971E+01 4.60881E+01 8.96349E+01 1.29299E+02 3.95182E+01 4.56313E+01 4.56728E+01 5.76811E+01 6.37672E+01 7.18682E+01 7.70842E+01 1.61804E+02 3.41615E+01 3.41848E+01 4.04947E+01 4.70096E+01 4.91867E+01 7.38650E+01 1.35909E+02

5.349E+06 5.009E+02 9.681E+05 2.704E+03 9.188E+03 5.325E+06 4.893E+03 1.068E+04 1.067E+05 1.033E+07 2.109E+03 2.311E+06 7.334E+03 1.281E+06 5.198E+02 3.162E+10 8.712E+09 2.923E+09 1.748E+06 1.243E+11 1.936E+09 1.079E+10 5.272E+07 1.782E+11 1.783E+09 7.986E+09 1.920E+08 2.197E+08 1.978E+10 1.326E+11 6.753E+09 2.119E+09 2.284E+08 2.446E+06 6.560E+07 3.261E+09 1.172E+11 1.057E+10 4.383E+06 1.837E+10 2.137E+11 1.036E+11 2.973E+09 8.030E+06 1.750E+10 5.584E+07 3.022E+11 5.562E+10 1.613E+10 4.530E+07 3.106E+10 1.842E+09 3.256E+11 1.162E+07 5.827E+06 5.225E+10 2.664E+10 1.322E+11 4.749E+10 6.803E+10 1.860E+10 3.200E+10 1.536E+08 3.331E+09 1.608E+10 3.958E+10 8.315E+10 2.799E+11 5.238E+10 7.068E+06

8.036E-05 7.528E-09 1.541E-05 4.304E-08 5.752E-06 1.932E-05 1.776E-08 4.168E-07 2.696E-07 7.500E-05 1.532E-08 2.227E-05 7.068E-08 1.926E-05 7.814E-09 8.800E-02 5.764E-02 2.402E-02 2.375E-04 8.164E-02 2.563E-03 2.146E-02 4.444E-04 2.336E-01 4.708E-03 2.489E-02 7.612E-04 3.680E-03 1.762E-02 2.064E-01 1.192E-02 4.472E-03 1.232E-03 2.311E-05 7.744E-05 6.476E-03 2.613E-01 6.392E-02 4.258E-05 6.388E-03 1.206E-01 7.554E-02 4.572E-03 3.781E-05 1.142E-02 5.816E-05 3.488E-01 7.406E-02 4.356E-02 9.868E-06 9.828E-03 7.038E-04 2.074E-01 2.800E-05 2.920E-05 4.893E-02 3.326E-02 1.654E-01 9.476E-02 1.659E-01 5.760E-02 1.140E-01 2.412E-03 1.165E-03 5.636E-03 1.946E-02 5.510E-02 2.030E-01 8.568E-02 3.915E-05

3.146E+00 1.778E-04 5.071E-01 6.037E-04 1.186E+00 5.258E-01 1.409E-04 3.720E-02 4.327E-03 2.041E+00 1.216E-04 6.981E-01 8.575E-04 7.541E-01 1.847E-04 1.611E-02 1.627E-02 7.560E-03 3.038E-04 1.258E-02 5.606E-04 5.751E-03 2.454E-04 3.595E-02 1.028E-03 5.907E-03 2.038E-04 2.025E-03 2.235E-03 3.461E-02 2.130E-03 8.732E-04 3.849E-04 7.171E-01 9.239E-06 1.002E-03 4.283E-02 1.725E-02 1.094E+00 7.160E-04 1.722E-02 1.226E-02 1.078E-03 1.172E+00 1.241E-03 7.982E-06 5.038E-02 1.149E-02 9.619E-03 8.755E-07 1.051E-03 8.270E-05 3.147E-02 6.205E-01 9.339E-01 6.366E-03 4.997E-03 2.487E-02 1.799E-02 3.482E-02 1.363E-02 2.894E-02 1.285E-03 1.311E-04 6.341E-04 2.594E-03 8.526E-03 3.287E-02 2.084E-02 1.316E+00

9.999E-01 9.363E-05 9.879E-01 2.759E-03 9.376E-03 9.971E-01 9.162E-04 2.000E-03 7.600E-03 7.358E-01 1.502E-04 1.646E-01 5.224E-04 9.125E-02 3.703E-05 7.310E-01 2.014E-01 6.757E-02 4.041E-05 9.068E-01 1.412E-02 7.871E-02 3.846E-04 9.460E-01 9.465E-03 4.239E-02 1.019E-03 1.166E-03 1.225E-01 8.211E-01 4.182E-02 1.312E-02 1.414E-03 1.515E-05 5.004E-04 2.487E-02 8.940E-01 8.062E-02 3.343E-05 5.424E-02 6.310E-01 3.059E-01 8.779E-03 2.371E-05 4.470E-02 1.426E-04 7.719E-01 1.421E-01 4.120E-02 1.263E-04 8.662E-02 5.137E-03 9.081E-01 3.241E-05 1.625E-05 1.385E-01 7.059E-02 3.503E-01 1.258E-01 1.803E-01 4.929E-02 8.480E-02 4.070E-04 7.021E-03 3.389E-02 8.343E-02 1.753E-01 5.900E-01 1.104E-01 1.490E-05

1.58326E+02 1.58326E+02 1.33046E+02 1.33046E+02 8.33239E+02 1.10023E+02 1.10023E+02 3.60629E+02 6.49221E+01 1.10048E+02 1.10048E+02 1.26793E+02 1.26793E+02 1.58377E+02 1.58377E+02 5.56465E+01 8.58039E+01 9.56540E+01 3.89483E+02 4.68107E+01 6.64603E+01 8.14755E+01 1.67797E+02 4.67678E+01 6.63740E+01 7.21188E+01 8.13457E+01 1.67247E+02 3.85521E+01 5.09610E+01 5.42808E+01 5.93475E+01 9.49138E+01 1.25496E+02 3.62390E+01 4.69958E+01 4.98049E+01 8.20242E+01 1.03907E+02 3.40569E+01 4.33905E+01 4.93253E+01 7.16356E+01 1.25308E+02 3.29981E+01 4.16863E+01 4.38817E+01 4.71348E+01 6.71064E+01 2.69573E+01 3.24890E+01 3.57057E+01 4.60985E+01 8.96314E+01 1.29313E+02 3.95201E+01 4.56382E+01 4.56790E+01 5.76861E+01 6.37773E+01 7.18828E+01 7.71047E+01 1.61854E+02 3.41677E+01 3.41905E+01 4.05003E+01 4.70201E+01 4.91997E+01 7.38861E+01 1.35944E+02

5.351E+06 5.013E+02 9.687E+05 2.706E+03 9.226E+03 5.328E+06 4.898E+03 1.074E+04 1.076E+05 1.033E+07 2.110E+03 2.313E+06 7.339E+03 1.282E+06 5.197E+02 3.166E+10 8.712E+09 2.920E+09 1.743E+06 1.245E+11 1.940E+09 1.078E+10 5.273E+07 1.783E+11 1.776E+09 7.982E+09 1.919E+08 2.200E+08 1.984E+10 1.328E+11 6.775E+09 2.120E+09 2.272E+08 2.445E+06 6.582E+07 3.263E+09 1.173E+11 1.057E+10 4.383E+06 1.842E+10 2.139E+11 1.037E+11 2.970E+09 8.039E+06 1.751E+10 5.587E+07 3.026E+11 5.566E+10 1.614E+10 4.521E+07 3.111E+10 1.835E+09 3.261E+11 1.163E+07 5.830E+06 5.228E+10 2.664E+10 1.323E+11 4.764E+10 6.812E+10 1.863E+10 3.204E+10 1.539E+08 3.335E+09 1.606E+10 3.963E+10 8.325E+10 2.802E+11 5.245E+10 7.077E+06

8.043E-05 7.535E-09 1.542E-05 4.308E-08 5.762E-06 1.934E-05 1.778E-08 4.186E-07 2.720E-07 7.504E-05 1.532E-08 2.230E-05 7.075E-08 1.928E-05 7.818E-09 8.817E-02 5.770E-02 2.403E-02 2.379E-04 8.178E-02 2.570E-03 2.146E-02 4.451E-04 2.338E-01 4.691E-03 2.490E-02 7.615E-04 3.691E-03 1.768E-02 2.068E-01 1.197E-02 4.478E-03 1.227E-03 2.310E-05 7.776E-05 6.483E-03 2.618E-01 6.399E-02 4.256E-05 6.407E-03 1.208E-01 7.568E-02 4.570E-03 3.785E-05 1.143E-02 5.823E-05 3.495E-01 7.415E-02 4.360E-02 9.850E-06 9.846E-03 7.015E-04 2.078E-01 2.801E-05 2.923E-05 4.897E-02 3.328E-02 1.656E-01 9.507E-02 1.662E-01 5.772E-02 1.142E-01 2.418E-03 1.168E-03 5.631E-03 1.949E-02 5.519E-02 2.034E-01 8.585E-02 3.921E-05

3.149E+00 1.781E-04 5.074E-01 6.043E-04 1.187E+00 5.262E-01 1.410E-04 3.733E-02 4.366E-03 2.042E+00 1.216E-04 6.991E-01 8.589E-04 7.550E-01 1.850E-04 1.615E-02 1.630E-02 7.567E-03 3.050E-04 1.260E-02 5.622E-04 5.756E-03 2.459E-04 3.600E-02 1.025E-03 5.911E-03 2.039E-04 2.032E-03 2.245E-03 3.469E-02 2.139E-03 8.749E-04 3.835E-04 7.167E-01 9.277E-06 1.003E-03 4.292E-02 1.728E-02 1.094E+00 7.184E-04 1.725E-02 1.229E-02 1.078E-03 1.173E+00 1.242E-03 7.991E-06 5.048E-02 1.151E-02 9.632E-03 8.742E-07 1.053E-03 8.246E-05 3.153E-02 6.209E-01 9.347E-01 6.371E-03 5.000E-03 2.490E-02 1.805E-02 3.489E-02 1.366E-02 2.900E-02 1.288E-03 1.313E-04 6.338E-04 2.599E-03 8.542E-03 3.294E-02 2.088E-02 1.318E+00

1.000E+00 9.369E-05 9.881E-01 2.760E-03 9.411E-03 9.969E-01 9.164E-04 2.009E-03 7.661E-03 7.355E-01 1.502E-04 1.647E-01 5.225E-04 9.128E-02 3.700E-05 7.313E-01 2.012E-01 6.745E-02 4.026E-05 9.071E-01 1.413E-02 7.854E-02 3.842E-04 9.461E-01 9.423E-03 4.235E-02 1.018E-03 1.167E-03 1.227E-01 8.211E-01 4.189E-02 1.311E-02 1.405E-03 1.512E-05 5.015E-04 2.486E-02 8.938E-01 8.054E-02 3.340E-05 5.432E-02 6.308E-01 3.058E-01 8.759E-03 2.371E-05 4.467E-02 1.425E-04 7.719E-01 1.420E-01 4.117E-02 1.259E-04 8.664E-02 5.110E-03 9.082E-01 3.239E-05 1.624E-05 1.384E-01 7.052E-02 3.502E-01 1.261E-01 1.803E-01 4.931E-02 8.481E-02 4.074E-04 7.024E-03 3.382E-02 8.346E-02 1.753E-01 5.901E-01 1.105E-01 1.490E-05

AA A+ AA A+ AA AA A+ A A AA A+ AA A+ AA A+ AA AA A+ A+ AA A+ A+ A+ AA A+ A+ A+ A+ A+ AA A+ A+ A+ AA C+ A+ AA AA AA A+ AA AA A+ AA A+ C+ AA AA A+ E A+ B+ AA AA AA A+ A+ AA AA AA AA AA A+ A+ A+ A+ A+ AA AA AA

Only transitions among the lowest 15 levels of the n = 2 configurations are shown here. Table 2 is available online in its entirety at the JQSRT website.

K. Wang, Z.B. Chen and X.H. Zhao et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 237 (2019) 106640

find the true eigenvalues of the Dirac–Coulomb–Breit Hamiltonian. The configuration interaction effects in the M space are considered exactly, while the interaction between the spaces M and N is accounted for with the many-body perturbation theory up to the second order. In the calculations, we include all states of the 2s2 2p3 , 2s2p4 , 2p5 , 2s2 2p2 3l (l = s, p, d), 2s2p3 3l (l = s, p, d), 2p4 3l (l = s, p, d), 2s2 2p2 4l (l = s, p, d, f ), and 2s2p3 4l (l = s, p, d, f ) configurations in the model space M. Through single and double (SD) virtual excitations of the states spanning the M space, all interacting virtual states necessary to properly describe inter-electron correlations are contained in the space N. The maximum n values for the single/double excitations are 200/65, respectively, while the maximum l value is 20. The leading quantum electrodynamic (QED) effects are also considered in our work. 2.2. MCDF The MCDF method has been described by Froese Fischer et al. [16]. Based on the active space (AS) approach [45] for the generation of the configuration state function (CSF) expansions, separate MCDF calculations are done for the even and odd parity states. We start the calculation without any excitation from the reference configurations, which is usually referred to as the Dirac–Fock (DF) calculation. The reference configurations are the same as those included in the M space of the MBPT calculations described above. Subsequently, the CSFs expansions are obtained through the SD excitations from the shells of the reference configurations up to a nmax lmax orbital, with nmax ≤ 8 and lmax ≤ 5. To reduce the number of CSFs, the 1s2 core is closed during the relativistic self-consistent field (RSCF) calculations, but is opened during the RCI calculations, where the Breit interaction and QED effects, i.e., vacuum polarization and self- energy, are included in the Hamiltonian. The number of CSFs in the final even and odd state expansions are approximately 5 018 0 0 0 and 4 619 0 0 0, respectively, distributed over the different J symmetries. To provide the LSJ labeling system used in databases such as the Atomic Spectra Database (ASD) of the National Institute of Standards and Technology (NIST) [46], the wave functions in both the MCDF and MBPT calculations are transformed from a jj-coupled CSF basis into a LSJ-coupled CSF basis using the methods developed by Gaigalas et al. [47,48]. 3. Results and discussions The computed excitation energies for the lowest 272 levels of the 2s2 2p3 , 2s2p4 , 2p5 , 2s2 2p2 3l (l = s, p, d), 2s2p3 3l (l = s, p, d), and 2p4 3l (l = s, p, d) configurations from our MBPT and MCDF calculations are listed in Table 1, along with the radiative lifetimes estimated from E1, E2, M1, M2 transition rates, and the LSJ-coupled and jj-coupled labels obtained from our calculations. Table 2 lists wavelengths λij , and E1, E2, M1, M2 line strengths Sji , oscillator strengths gi fji , and radiative rates Aji among the 272 energy levels along with branching fractions (BF ji =

A ji  j−1 k=1

A jk

), ob-

tained from both the MBPT and MCDF methods. All the E1 and E2 values are computed in the Babushkin gauge (equivalent to the non-relativistic length form), which is considered to be more accurate than the Coulomb gauge (equivalent to the non-relativistic velocity form). 3.1. Excitation energies Since excitation energies for N-like Zr are only available for the n = 2 levels in the previous studies [4–7], the MBPT and MCDF excitation energies are compared with the other theoretical results calculated by Gu [7] in Table 3. The average difference with the

7

standard deviation from the MBPT values are −528 ± 316 cm−1 for MCDF, and 155 ± 169 cm−1 for Gu, respectively. For the remaining levels belonging to the n = 3 configurations, the relative difference between our two calculations for each level is shown in Table 1. The average absolute difference with standard deviation of the present MBPT and MCDF energy values are −490 ± 631 cm−1 , corresponding to the average relative difference with the standard deviation of −0.002 % ± 0.003 %, which are satisfactory. 3.2. Wavelengths, transition rates, and lifetimes In the spirit of the uncertainty estimation method suggested by Kramida [49–51], the difference δ S of line strengths S from the MBPT and MCDF calculations for each E1 transition is defined as δ S = |SMCDF − SMBPT |/exp((ln(SMCDF ) + ln(SMCDF ))/2 ). The averaged uncertainties δ Sav for line strengths S from the present MBPT and MCDF calculations for E1 transitions in various ranges of S are assessed to 0.4 % for S ≥ 100 ; 0.9 % for 100 > S ≥ 10−1 ; 1.4 % for 10−1 > S ≥ 10−2 ; 2.0 % for 10−2 > S ≥ 10−3 ; 3.2 % for 10−3 > S ≥ 10−4 , 12 % for 10−4 > S ≥ 10−5 , and 75 % for 10−5 > S ≥ 10−6 . Then, the larger of δ Sij and δ Sav is accepted as the uncertainty of each particular line strength. About 13 % all E1 S-values have uncertainties of ≤ 1 % (the category AA), 51 % have uncertainties of ≤ 2 % (the category A+), 6 % have uncertainties of ≤ 3 % (the category A), 19 % have uncertainties of ≤ 7 % (the category B+), 1.5 % have uncertainties of ≤ 10 % (the category B), 6 % have uncertainties of ≤ 18 % (the category C+), 0.15 % have uncertainties of ≤ 25 % (the category C), and 0.04 % have uncertainties of ≤ 40 % (the category D+), while 2.6 % have uncertainties of > 40 % (categories D and E). Again, using the method suggested in Kramida [49–51], the uncertainties of the S values for E2, M1, and M2 transitions are estimated. The estimated uncertainties for all E1, E2, M1, and M2 transitions with BF ≥ 10−5 are listed in Table 2. Our MBPT and MCDF lifetimes for the lowest 272 levels of the n ≤ 3 configurations in N-like Zr XXXIV, which are calculated by considering all possible E1, E2, M1, and M2 transitions, are listed in Table 1. For the lowest 15 levels of the n = 2 complex, the MCDF lifetimes agree very well with the MBPT results, and the differences are within 1 %. For the remaining 257 levels belonging to the n = 3 configurations, the average difference with the standard deviation is −0.4 % ± 0.8 %. 4. Conclusions Employing two state-of-the-art methods (MBPT and MCDF), excitation energies and lifetimes of the lowest 272 levels for the n ≤ 3 configurations have been calculated for N-like Zr XXXIV. Wavelengths, E1, E2, M1, and M2 transition rates, line strengths, and oscillator strengths for the transitions among these 272 levels are also reported. The accuracy of energy levels and transition probabilities is estimated by comparing the MBPT and MCDF results with available theoretical data. The average difference with the standard deviation between the MBPT and MCDF values for the n = 2 levels are −528 ± 316 cm−1 , For the n = 3 levels, the average absolute difference of the present MBPT and MCDF energy values is −490 ± 631 cm−1 , corresponding to the average relative difference of −0.002 % ± 0.003 %, where the standard deviations are indicated after the values. The above information indicates the high accuracy of the present two calculations. The uncertainty of the line strength is assessed for each transition, and is available in Table 2. The present calculations provide a consistent and accurate data set for line identification and modeling purposes, which can also be considered as a benchmark for other calculations.

8

K. Wang, Z.B. Chen and X.H. Zhao et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 237 (2019) 106640 Table 3 Energy levels (in cm−1 ) relative to the ground state for the n = 2 states. MBPT – the present MBPT results; MCDF – the present MCDF results; Gu – the theoretical values from Gu [7]; E – the differences (in cm−1 ) between calculated energies from different calculations and the MBPT values. Key

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

State

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

2s 2 p3 43 S 4 S3◦ /2 2s2 2 p3 23 D 2 D◦3/2 2s2 2 p3 23 D 2 D◦5/2 2s2 2 p3 21 P 2 P1◦/2 2s2 2 p3 21 P 2 P3◦/2 2s 2 S 2 p4 32 P 4 P5/2 2s 2 S 2 p4 32 P 4 P1/2 2s 2 S 2 p4 32 P 4 P3/2 2s 2 S 2 p4 12 D 2 D3/2 2s 2 S 2 p4 12 D 2 D5/2 2s 2 S 2 p4 32 P 2 P1/2 2s 2 S 2 p4 32 P 2 P3/2 2s 2 S 2 p4 10 S 2 S1/2 2 p5 2 P3◦/2 2 p5 2 P1◦/2 2

MBPT

MCDF

E

E

E

E

E

0 631775 751658 908912 1540501 1797810 2136812 2138805 2594621 2760087 2936855 3031008 3710257 4328290 5064079

0 631609 751623 908903 1540307 1797057 2136266 2138224 2593895 2759459 2936260 3030476 3709575 4327414 5063010

0 −166 −35 −9 −194 −752 −546 −581 −726 −628 −595 −532 −682 −876 −1069

631696 751583 908979 1540414 1798173 2137167 2139248 2594750 2760295 2937108 3031112 3710319 4328511 5064290

−79 −75 67 −87 363 355 443 129 208 253 104 62 221 211

Acknowledgments We acknowledge the support from the National Key Research and Development Program of China under Grant No. 2017YFA0403200, the Science Challenge Project of China Academy of Engineering Physics (CAEP) under Grant No. TZ2016005, the National Natural Science Foundation of China (Grant Nos. 11703004, 11674066, 11504421, and 11474034), the Natural Science Foundation of Hebei Province, China (A2019201300 and A2017201165), and the Natural Science Foundation of Educational Department of Hebei Province, China (BJ2018058). Kai Wang expresses his gratitude to the support from the visiting researcher program of Fudan University.

[10]

[11]

[12]

[13]

[14] [15]

Supplementary materials

[16]

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.jqsrt.2019.106640.

[17] [18]

References [1] Doidge PS. Improved documentation of spectral lines for inductively coupled plasma emission spectrometry. Spectrochim Acta, Part B 2018;143:78–90. [2] Sahan H, Tel E, Sahan M, Aydin A, Sarpun IH, Kara A, Doner M. A study on nuclear properties of Zr, Nb, and Ta nuclei used as structural material in fusion reactor. In: European Physical Journal Web of Conferences, vol. 100; 2015. p. 01007. [3] Rice JE, Fournier KB, Goetz JA, Marmar ES, Terry JL. X-ray observations of 2l-nl’ transitions and configuration-interaction effects from Kr, Mo, Nb and Zr in near neon-like charge states from tokamak plasmas. J Phys B At Mol Opt Phys 20 0 0;33:5435–62. [4] Fontes CJ, Zhang HL. Relativistic distorted-wave collision strengths for the 49 n = 0 optically allowed transitions with n = 2 in the 67 N-like ions with 26≤Z≤92. At Data Nucl Data Tables 2014;100:1292–321. [5] Han X, Gao X, Zeng D, Jin R, Yan J, Li J. Scaling law for transition probabilities in 2p3 configuration from LS coupling to jj coupling. Phys Rev A 2014;89:042514. [6] Wang XL, Lu WL, Gao X, Li JM. Effect of Electron Correlations and Breit Interactions on Ground-State Fine-Structures along the Nitrogen-Like Isoelectronic Sequence. Chin Phys Lett 2009;26:043101. [7] Gu MF. Energies of 1s22lq (1 ≤ q ≤ 8) states for Z ≤ 60 with a combined configuration interaction and many-body perturbation theory approach. At Data Nucl Data Tables 2005;89:267–93. [8] Kink I, Laming JM, Takács E, Porto JV, Gillaspy JD, Silver E, Schnopper H, Bandler SR, Barbera M, Brickhouse N, Murray S, Madden N, Landis D, Beeman J, Haller EE. Analysis of broadband x-ray spectra of highly charged krypton from a microcalorimeter detector of an electron-beam ion trap. Phys Rev E 2001;63:046409. [9] Wang K, Li S, Jönsson P, Fu N, Dang W, Guo X, Chen C, Yan J, Chen Z, Si R. Calculations with spectroscopic accuracy for energies, transition rates, hyperfine

[19]

[20]

[21]

[22]

[23]

[24]

[25]

[26]

Gu

interaction constants, and Landé gJ-factors in nitrogen-like Kr XXX. J Quant Spectrosc Radiat Transf 2017;187:375–402. Lindgren I. The Rayleigh-Schrodinger perturbation and the linked-diagram theorem for a multi-configurational model space. J Phys B At Mol Opt Phys 1974;7:2441. Safronova MS, Johnson WR, Safronova UI. Relativistic many-body calculations of the energies of n =2 states for the berylliumlike isoelectronic sequence. Phys Rev A 1996;53:4036–53. Vilkas MJ, Ishikawa Y, Koc K. Relativistic multireference many-body perturbation theory for quasidegenerate systems: Energy levels of ions of the oxygen isoelectronic sequence. Phys Rev A 1999;60:2808–21. Gu MF. Wavelengths of 2l-3l’ Transitions in L-Shell Ions of Iron and Nickel: A Combined Configuration Interaction and Many-Body Perturbation Theory Approach. Astrophys J Suppl Ser 2005;156:105. Gu MF. Many-Body Perturbation Theory Wavelengths of High-n X-Ray Transitions of Fe and Ni L-shell Ions. Astrophys J Suppl Ser 2007;169:154. Grant IP. Relativistic quantum theory of atoms and molecules. New York, NY: Springer; 2007. doi:10.1007/978- 0- 387- 35069- 1. Froese Fischer C, Godefroid M, Brage T, Jönsson P, Gaigalas G. Advanced multiconfiguration methods for complex atoms: I. Energies and wave functions. J Phys B At Mol Opt Phys 2016;49:182004. Gu MF. The flexible atomic code. Can J Phys 2008;86:675–89. Jönsson P, He X, Froese Fischer C, Grant I. The grasp2K relativistic atomic structure package. Comput Phys Commun 2007;177:597–622. Jönsson P, Gaigalas G, Bieron´ J, Froese Fischer C, Grant IP. New version: GRASP2K relativistic atomic structure package. Comput Phys Commun 2013;184:2197–203. Wang K, Li DF, Liu HT, Han XY, Duan B, Li CY, Li JG, Guo XL, Chen CY, Yan J. Systematic Calculations of Energy Levels and Transition Rates of C-like Ions with Z = 13-36. Astrophys J Suppl Ser 2014;215:26. Wang K, Guo XL, Liu HT, Li DF, Long FY, Han XY, Duan B, Li JG, Huang M, Wang YS, Hutton R, Zou YM, Zeng JL, Chen CY, Yan J. Systematic Calculations of Energy Levels and Transition Rates of Be-like Ions with Z = 10–30 Using a Combined Configuration Interaction and Many-body Perturbation Theory Approach. Astrophys J Suppl Ser 2015;218:16. Wang K, Si R, Dang W, Jönsson P, Guo XL, Li S, Chen ZB, Zhang H, Long FY, Liu HT, Li DF, Hutton R, Chen CY, Yan J. Calculations with Spectroscopic Accuracy: Energies and Transition Rates in the Nitrogen Isoelectronic Sequence from Ar XII to Zn XXIV. Astrophys J Suppl Ser 2016;223:3. Wang K, Chen ZB, Si R, Jönsson P, Ekman J, Guo XL, Li S, Long FY, Dang W, Zhao XH, Hutton R, Chen CY, Yan J, Yang X. Extended relativistic configuration interaction and many-body perturbation calculations of spectroscopic data for the n≤6 configurations in Ne-like ions between Cr XV and Kr XXVII. Astrophys J Suppl Ser 2016;226:14. Wang K, Jönsson P, Ekman J, Brage T, Chen CY, Froese Fischer C, Gaigalas G, Godefroid M. Comment on “Theoretical Confirmation of the Low Experimental 3C/3D f -Value Ratio in Fe xvii”. Phys Rev Lett 2017;119:189301. Wang K, Jönsson P, Ekman J, Si R, Chen Z, Li Y, Chen C, Yan J. Extended calculations of energy levels, radiative properties, AJ , BJ hyperfine interaction constants, and Landé gJ -factors for oxygen-like Kr XXIX. J Quant Spectrosc Radiat Transf 2017;194:108–12. Wang K, Jönsson P, Ekman J, Gaigalas G, Godefroid MR, Si R, Chen ZB, Li S, Chen CY, Yan J. Extended Calculations of Spectroscopic Data: Energy Levels, Lifetimes, and Transition Rates for O-like Ions from Cr xvii to Zn xxiii. Astrophys J Suppl Ser 2017;229:37.

K. Wang, Z.B. Chen and X.H. Zhao et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 237 (2019) 106640 ¯ e˙ L, Rynkun P, Del Zanna G, Chen CY. [27] Wang K, Jönsson P, Gaigalas G, Radžiut Energy Levels, Lifetimes, and Transition Rates for P-like Ions from Cr x to Zn xvi from Large-scale Relativistic Multiconfiguration Calculations. Astrophys J Suppl Ser 2018;235:27. [28] Wang K, Song CX, Jönsson P, Del Zanna G, Schiffmann S, Godefroid M, Gaigalas G, Zhao XH, Si R, Chen CY, Yan J. Benchmarking Atomic Data from Large-scale Multiconfiguration Dirac-Hartree-Fock Calculations for Astrophysics: S-like Ions from Cr ix to Cu xiv. Astrophys J Suppl Ser 2018;239:30. [29] Wang K, Chen ZB, Zhang CY, Si R, Jönsson P, Hartman H, Gu MF, Chen CY, Yan J. Benchmarking Atomic Data for Astrophysics: Be-like Ions between B ii and Ne vii. Astrophys J Suppl Ser 2018;234:40. [30] Wang K, Zhang C, Jönsson P, Si R, Zhao X, Chen Z, Guo X, Chen C, Yan J. Extended calculations of energy levels, radiative properties, AJ , BJ hyperfine interaction constants, and Landé gJ -factors for nitrogen-like Ge XXVI. J Quant Spectrosc Radiat Transf 2018;208:134–51. [31] Wang K, Song CX, nsson PJA, Ekman J, Godefroid M, Zhang CY, Si R, Zhao XH, Chen CY, Yan J. Large-scale Multiconfiguration Dirac-Hartree-Fock and Relativistic Configuration Interaction Calculations of Transition Data for B-like S xii. Astrophys J 2018;864:127. [32] Wang K, Wang Y, Zhang CY, Zhao XH, Chen ZB, Si R, Chen CY, Yan J. Extended calculations of energy levels, radiative properties, AJ , BJ hyperfine interaction constants, and Landé gJ -factors for Nitrogen-like Se XXVIII. J Quant Spectrosc Radiat Transf 2018;220:5–27. [33] Wang K, Zheng W, Zhao XH, Chen ZB, Chen CY, Yan J. Extended calculations of energy levels, radiative properties, and lifetimes for oxygen-like Mo XXXV. J Quant Spectrosc Radiat Transfer 2019;236:106586. [34] Chen ZB, Ma K, Wang HJ, Wang K, Liu XB, Zeng JL. Energy levels, oscillator strengths, line strengths, and transition probabilities in Si-like ions of La XLIII, Er LIV, Tm LV, and Yb LVI. At Data Nucl Data Tables 2017;113:258–92. [35] Chen ZB, Guo XL, Wang K. Theoretical energies, transition rates, lifetimes, hyperfine interaction constants and Landé gJ -factors for the Se XXVII spectrum of fusion interest. J Quant Spectrosc Radiat Transfer 2018;206:213–32. [36] Chen ZB, Wang K. Study of relativistic excitation energies and transition data for EUV and SXR spectral lines in Ge XXIX and Kr XXXIII of fusion interest. J Quant Spectrosc Radiat Transf 2019;234:90–7. [37] Chen ZB, Sang CC, Wang K. Theoretical determination of energies, wavelengths, and transition probabilities for EUV and SXR spectral lines in Rb XXXIV, Sr XXXV, Zr XXXVII, and Nb XXXVIII. J Quant Spectrosc Radiat Transf 2019;225:76–83. [38] Chen ZB, Wang K, Ma K, Hu F. Study of energies and oscillator strengths of Fe XXI including plasma shielding effects. J Quant Spectrosc Radiat Transf 2019;236:106584.

9

[39] Guo XL, Huang M, Yan J, Li S, Si R, Li CY, Chen CY, Wang YS, Zou YM. Relativistic many-body calculations on wavelengths and transition probabilities for forbidden transitions within the 3dk ground configurations in Co- through K– like ions of hafnium, tantalum, tungsten and gold. J Phys B Atom Mol Phys 2015;48:144020. [40] Guo XL, Si R, Li S, Huang M, Hutton R, Wang YS, Chen CY, Zou YM, Wang K, Yan J, Li CY, Brage T. Multiconfiguration Dirac-Hartree-Fock Calculations of the Electric Dipole Moment of Radium Induced by the Nuclear Schiff Moment. Phys Rev A 2016;93:012513. [41] Si R, Li S, Guo XL, Chen ZB, Brage T, Jönsson P, Wang K, Yan J, Chen CY, Zou YM. Extended calculations with spectroscopic accuracy: energy levels and transition properties for the fluorine-like isoelectronic sequence with Z = 24-30. Astrophys J Suppl Ser 2016;227:16. [42] Si R, Zhang C, Liu Y, Chen Z, Guo X, Li S, Yan J, Chen C, Wang K. Extensive and accurate energy levels and transition rates for Al-like Zn XVIII. J Quant Spectrosc Radiat Transf 2017;189:249–57. [43] Si R, Zhang CY, Cheng ZY, Wang K, Jönsson P, Yao K, Gu MF, Chen CY. Energy Levels, Transition Rates and Electron Impact Excitation Rates for the B-like Isoelectronic Sequence with Z = 24-30. Astrophys J Suppl Ser 2018;239:3. [44] Zhao Z, Wang K, Li S, Si R, Chen CY, Chen ZB, Yan J, Ralchenko Y. Multi-configuration Dirac-Hartree-Fock calculations of forbidden transitions within the 3dk ground configurations of highly charged ions (Z=72-83). At Data Nucl Data Tables 2018;119:314–53. [45] Sturesson L, Jönsson P, Froese Fischer C. JJGEN: A flexible program for generating lists of jj-coupled configuration state functions. Comput Phys Commun 2007;177:539–50. [46] Kramida A, Ralchenko Yu, Reader J, and NIST ASD Team, NIST Atomic Spectra Database (ver.5.6.1), 2018. [Online]. Available: https://physics.nist.gov/asd [2019, May 27]. National Institute of Standards and Technology, Gaithersburg, MD. [47] Gaigalas G, Zalandauskas T, Fritzsche S. Spectroscopic LSJ notation for atomic levels obtained from relativistic calculations. Comput Phys Commun 2004;157:239–53. [48] Gaigalas G, Froese Fischer C, Rynkun P, Jönsson P. JJ2LSJ Transformation and Unique Labeling for Energy Levels. Atoms 2017;5:6. [49] Kramida A. Critical Evaluation of Data on Atomic Energy Levels, Wavelengths, and Transition Probabilities. Fusion Sci Technol 2013;63:313–23. [50] Kramida A. Assessing Uncertainties of Theoretical Atomic Transition Probabilities with Monte Carlo Random Trials. Atoms 2014;2:86–122. [51] Kramida A. Energy Levels and Spectral Lines of Quadruply Ionized Iron (Fe V). Astrophys J Suppl Ser 2014;212:11.