American Journal of Optics and Photonics
Volume 4, Issue 1, February 2016, Pages: 1-13

Configuration Interaction Calculations of Energy Levels and Radiative Parameters of Calcium-Like Ions, 22 ≤ Z ≤ 30

Zaher Samak1,*, Ahmed Abou El-Maaref2, Sami Allam3, Tharwat El-Sherbini3

1Department of Physics, Cairo University, Giza, Egypt

2Department of Physics, Al-Azhar University Assiut, Assiut, Egypt

3Laboratory of Lasers and New Materials, Physics Department, Cairo University, Giza, Egypt

Email address:

(Z. Samak)

*Corresponding author

To cite this article:

Zaher Samak, Ahmed Abou El-Maaref, Sami Allam, Tharwat El-Sherbini. Configuration Interaction Calculations of Energy Levels and Radiative Parameters of Calcium-Like Ions, 22 ≤ Z ≤ 30. American Journal of Optics and Photonics. Vol. 4, No. 1, 2016, pp. 1-13. doi: 10.11648/j.ajop.20160401.11

Received: March 29, 2016; Accepted: April 15, 2016; Published: May 4, 2016


Abstract: The energy levels, oscillator strengths, and E1 transition probabilities have been calculated for calcium-like ions with Z = 2230 (excluding iron). The calculations have been executed using the CIV3 and LANL codes for a set of configuration arrays including 63 fine structure levels (in this paper we mentioned for examples about 40 energy levels) belonging to 3p63d2 and 3p63d4l configurations, where l = s, p, d, f. The correlations up to 6l orbitals are included to optimize the wave functions generated by the CIV3 code. In spite of the complexity of the Ca sequence, the present results are in fairly good agreement with the experimental and theoretical data available in the literature. The present study provides calculations of various atomic structure data which are necessary for many fields of researches and applications, especially in the astrophysics and plasma diagnostics.

Keywords: Energy Level, Oscillator Strength, Radiative Rates, Configuration Interaction


1. Introduction

Members of the calcium isoelectronic sequence such as vanadium, iron, cobalt, and nickel are of importance for astrophysics as well as for plasma modeling. The importance of calcium-like ions (vanadium through zinc) for astrophysics lies within its abundance in the solar system, so, transitions arise from these atomic systems possible to appear in the solar spectra and in stellar corona. The spectra of calcium isoelectronic sequence had been studied early by many authors [14], these works had provided results of observed transition parameters and energies of Ca-like manganese, scandium, cobalt, iron, nickel, copper, and zinc. Fawcett and Cowan [5] have studied the spectral lines arise from Ca-like iron (Fe VII), the atomic self-consistent field calculations have been applied to identify the spectra belonging to the 3d2 - 3p53d3 transition arrays. The spectrum of Fe VII has been observed by Ekberg [6] using low- and high-voltage sliding spark, as well as the Fe VII spectra has been studied in many other dierent works such as [720]. A measured values of lifetimes for some transitions of the 3d2 → 3d4p arrays in Ti III have been reported [21,22] using the beam-foil technique. Abbott [23] has used the non-relativistic SUPERSTRUCTURE program to calculate the transition probabilities of calcium-like ionized Cr, Mn, Fe, and Ni, the calculations have been carried out for transitions belonging to 3d2, 3d4s, 3d4p, 4s4p, 3d4d, and 3d4f. Many lines in Ca I, Ti III, Cr V, Mn VI, Fe VII, and Ni IX observed in the solar spectra have been identified in works such as [24,25]. Resonance transitions in Co VIII, Ni IX and Cu X have been analyzed as well as the energies and weighted oscillator strengths have been calculated for Co VIII by Fawcett et al. [26]. The E1, M1, and M2 transition probabilities of some transitions in Ti III and V IV have been calculated using the orthogonal operator method by Raassen and Uylings [27]. Safronova et al. [28,29] have used the relativistic many-body perturbation theory (RMBPT) to calculate the excitation energies and radiative rates of Ca-like ions. the calculated spectra are arising from E2 and M1 transitions. Observed wavelengths of the 3d4p → 3d4d and 3d4d → 3d4f transitions in the vacuum ultraviolet spectra of calcium-like Mn VI, Fe VII and Co VIII have been identified [30], the MCHF method and isoelectronic comparison have been used for the classification.

The forbidden transitions E2, M1 have been studied using three dierent methods (MCDF, HFR, and SST), transition probabilities and oscillator strengths in Ca-like Ti III have been computed [31]. Oscillator strengths have been calculated for transitions between the 3d2, 3p53d3, 3d4p, 3d4f levels in Ca-like iron, cobalt and nickel using the pseudo-relativistic Hartree-Fock (HFR), the calculated results are reported in Ref. [20]. Recently, observed values of oscillator strengths of Ca I have been reported by Haq et al. [32] using the thermionic diode ion detector in conjunction with a Nd:YAG pumped dye laser system. The spectrum of Cu X has been studied using high-resolution vacuum spectrographs, and the excited energies of the 3d2, 3p53d3, 3d4p, 3d4f levels have been determined using the HF method [33]. Zhang et al. [34] calculated oscillator strengths and transition probabilities of Ti III using the weakest bound electron potential model (WBEPM). The calcium like titanium has been studied again [35] where, the oscillator strengths and radiative rates have been computed using the CIV3 program. The energy levels and collision strengths of Sc II have been computed using R-matrix package, transitions arising from the 3d4s, 3d2, 4s2, 3d4p, 4s4p, 3d5s, 3d4d, 3d5p, 4p2, and 3d4f configurations are included [36].

The early compilation of atomic data of Ca-like ions performed by Wiese et al. [37], and Smith and Wise [38]. Compiled results including ions belonging to calcium isoelectronic sequence have been presented by Morton [39], the transition probabilities and oscillator strengths of several lines in Ca I, Sc II, and Ti III are reported. Another compilations performed by Corlis and Sugar [40], and Sugar et al. [4143] have reported energy levels of calcium through zinc. Fuhr et al. [44,45] have compiled experimental and theoretical data for transition probabilities for iron through nickel. Another compilations of transition probabilities for scandium through manganese ions have been performed by Martin et al. [46], and for energy levels of all ionization stages of scandium by Kaufman and Sugar [47]. The compilation processes still go on where, Shirai et al. [48,49] have collected experimental and theoretical results of energy levels, oscillator strengths, and transition probabilities of Cr V and Co VIII, and for Ca-like Ti through Cu in the published monograph [50]. Wavelengths, energy levels, level classifications, oscillator strengths, and radiative transition probabilities for the nickel ions Ni IX to Ni XXVIII have been collected by Shirai et al. [51].

From the previous review we can figure out that the calcium isoelectronic sequence has been widely studied, despite this a limited works have provided an extensive calculations of energies and radiative parameters of many ionic species in this sequence, but for most of ions we still lack abundance of atomic data, especially for nickel and zinc. In the present study, the configuration interaction calculations for calcium isoelectronic sequence with atomic charge Z=22 to 30 have been performed using the non-relativistic CIV3 code [52,53], and Los Alamos atomic physics code (LANL) based on Cowan’s method which publicly available via website (http://aphysics2.lanl.gov/cgi-bin/ION/runlanl08d.pl). The iron ion was excluded from the study. The configuration groups 3d2, 3d4s, 3d4p, 3d4d, and 3d4f with different angular momenta (J) and parities are included in the configuration state list.

2. The Choice of Wave Functions

The present calculations have been performed using the configuration interaction method (CIV3 code) including relativistic effects of Hibbert [52,53]. The LS states belonging to configurations of Ca-like Ti III to

Zn XI give 63 fine structure level, and about 150 or more up to 227 transitions between levels corresponding to various J values (in this paper we mentioned for examples about 40 transitions). All intermediate coupling (LS-coupling) atomic states under consideration are expressed as linear combinations of configuration wave functions in the form:

(1)

The single configuration wave functions ϕi are consist of one electron functions. αi,LS defines the coupling of angular momenta to form a total L and S common to all configurations in Eq 1. The CIV3 method theory has been described in details in many previous works, for example Refs. [5262]. In the present calculations the 1s, 2s, 2p, 3s, 3p and 3d radial functions are taken as the Hartree-Fock orbitals of the ground state 3p63d2 of Ca-like ions as given by Clementi and Roetti [63]. The other radial functions for 4l are chosen as a spectroscopic type and are optimized using the CIV3 program [52]. The 5s, 5p, 5d, and 5f, 6s-6f orbitals are chosen as a correlation orbitals (contributions from higher order levels with n + 2 to improve the wave functions of the spectroscopic orbitals). The oscillator strengths in length and velocity gauge forms are given by:

(2)

(3)

The LANL atomic code based on Cowan method is described in details in Ref. [64]. Extensive configuration-interaction (CI) wave functions in intermediate coupling scheme have been generated. Despite that, the produced results are in LSJ-coupling, the intermediate LS coupling configuration state list is successfully effective in the evaluation of the Hamiltonian matrix elements [65,66]. These wave functions are used to calculate the excitation energies, oscillator strengths and transition probabilities for allowed electric-dipole and intercombination transitions among the states of Ca-like ions with 22 ≤ Z ≤ 30.

Table 1. Energy levels of Ca-like Ti III and V IV.

      Ti III V IV
Index Level Term LANL CIV3 NIST LANL CIV3 NIST
1 3d2 3F2 0 0 0 0 0 0
2 3F3 194.59 182.9 184.9 331.75 316.73 325.4
3 3F4 447.19 423.03 420.4 758.71 732.87 734.7
4 1D2 9049.5 8781.64 8473.5 11625 11069.39 10959.3
5 3P0 10923 10519.8 10538 13687 12994.95 13122.8
6 3P1 10991 10581.46 10604 13804 13101.02 13239.2
7 3P2 11134 10706.07 10721 14059 13287.89 13458.3
8 1G4 14170 14050.72 14398 17897 17534.39 18391.2
9 1S0 33786 32973.27 32476 42920 41754.26 42462.1
10 3d4p 1D2 73975 75255.85 75198 144130 144103.62 144273.1
11 3D1 75174 77289.25 77000 145340 146211.58 146117.7
12 3D2 75362 77330.2 77167 145660 146373.9 146429.3
13 3D3 75608 77444.78 77424 146060 146614.52 146855.1
14 3F2 75840 77466.03 77422 146490 147094.32 147135.2
15 3F3 76116 77607.81 77746 146940 147272.85 147656.5
16 3F4 76503 77658.11 78159 147590 147512.76 148369.2
17 3P0 78937 80967.72 80945 150350 151321.82 151449.1
18 3P1 78959 81069.84 80939 150360 151485.42 151427
19 3P2 79072 81287.24 81024 150540 151818.24 151567.3
20 1F3 80824 84265.47 83117 152370 155088.17 153918.7
21 1P1 82241 81069.84 83797 154310 157289.38 155565.5
22 3d4d 1F3 124300 129425.9 127791 213540 216896.02 215957.7
23 3D1 124790 129757 128433 214280 217816.48 216905
24 3D2 124910 129823 128546 214470 217924.32 217108
25 3D3 125050 129922 128690 214710 218086.29 217350
26 3G3 125320 130127.9 129093 215060 218684.65 217836.3
27 3G4 125480 130259.9 129253 215320 218900.37 218100
28 3G5 125700 130425.1 129469 215670 219170.61 218463.6
29 1P1 125620 129823 129253 215520 219011.68 217990.7
30 3S1 126820 131202.7 130740 217380 221169.09 220343.5
31 1D2 136100 134413.7 135405 227320 226146.02 225804.1
32 3P0 136620 134863.2 135541 228110 226763.72 226521.6
33 3P1 136670 134896 135601 228210 226816.35 226617.1
34 3P2 136780 134977.5 135722 228380 226918.72 226796.3
35 1G4 137220 134275.7 136340 228970 227461.36 227712.5
36 1S0 141430 136611.8 140019 234710 238887.5 234121.8
37 3d4f 1G4 155950 159671.5 158285 261320 259873.08 263111.4
38 3F2 156180 159684.3 158537 261760 261448.24 263593
39 3F3 156190 159732.5 158558 261830 261514.7 263608.3
40 3F4 156320 159796.9 158691 262010 261603.98 264113.1

3. Results and Discussions

3.1. Energy Levels

The calculated values of energies of 40 fine structure levels of Ca-like ions (Z = 22 − 30) are listed in Tables 1-3 the data of iron ion have been excluded because we believe that we will not provide any significant results more than hitherto published. The present energies from CIV3 and LANL codes have been arranged in ascending order and compared with the energy values taken from NIST atomic database [67]. The comparisons show good agreement with those in the literature, where the deviations from the values of NIST are better than 1.0% for most calculated levels. The cited values by NIST [67] are primarily taken from the compiled experimental and theoretical results by Sugar and Corliss [41] for Ca-like Ti III− Ni IX ions, from [42] for Cu X, and from [43] for Zn XI.

Table 2. Energy levels of Ca-like Cr V, Mn VI and Co VIII.

      Cr V Mn VI Co VII
Index Level Term LANL CIV3 NIST LANL CIV3 NIST LANL CIV3 NIST
1 3d2 3F2 0 0 0 0 0 0 0 0 0
2 3F3 513.4 484.17 508.2 749.24 711.28 746 1426.3 1420.64 1430
3 3F4 1167.6 1120.47 1141.7 1693.4 1647.03 1669 3177.8 3291.94 3144
4 1D2 13924 12946.3 13188 16134 14905.23 15336 20537 20181.34 19624
5 3P0 16236 15042.46 15491.8 18665 17113.28 17782 23406 22683.42 22304
6 3P1 16419 15204.17 15676.6 18937 17351.22 18057 23944 23160.62 22839
7 3P2 16830 15490.82 16041 19559 17776.67 18628 25219 24022.64 24055
8 1G4 21379 21160.7 22019.2 24720 24988.51 25511 31367 30257.95 32360
9 1S0 51460 49304.46 51146.4 59361 56819.76 59265 74667 71654.49 74247
10 3d4p 1D2 227050 225814.5 226119.8 321800 319083.1 319821 545380 538332 542430
11 3D1 228290 228148.1 228001.8 323090 321519.1 321694 546830 541105.5 542701
12 3D2 228790 228397.1 228489.1 323820 321891.7 322410 548270 541825.6 544314
13 3D3 229380 228765.9 229120.8 324640 322443.9 323283 549590 542893 545834
14 3F2 229830 229804.9 229551.7 325010 323950.7 323796 549660 544317.6 547400
15 3F3 230510 230081.8 230316.3 325960 324369.7 324849 551280 545113.9 548799
16 3F4 231500 230453.9 231392.9 327380 324932.4 326373 553780 546184.4 551524
17 3P0 234520 235043.9 234668.5 330590 330093.1 329729 557070 552120.1 549153.1
18 3P1 234510 235291 234618.4 330540 330457.7 329635 556860 552840.3 549634.9
19 3P2 234790 235794.1 234846.4 330960 331199.4 329992 557780 554307.5 551248.9
20 1F3 236890 239661.2 237529.5 333290 335394.1 333055 560570 559452.3 557736
21 1P1 239410 242835.7 239917.5 336340 339462.2 336131 564760 564772.7 563271
22 3d4d 1F3 315590 317266 316674.9 428990 428995 429105 689550 693978.6 _
23 3D1 316480 318315.5 317893.8 430070 431447.9 429105 690890 696773.5 _
24 3D2 316790 318490.8 318227.6 430520 431739.6 431059 691800 697350.9 _
25 3D3 317160 318754.1 318601.7 431060 432177.8 431607 692990 698219.2 _
26 3G3 317480 319313.9 319119.1 431340 433026.2 432091 692600 699375.3 _
27 3G4 317860 319663.9 319516.8 431870 433608.1 432653 693700 700534 _
28 3G5 318410 320102.3 320074.4 432660 434337.4 433464 695190 701987.4 _
29 1P1 318140 319808.7 319284 432250 433780.1 436451 694360 700807.7 _
30 3S1 320570 322443.9 322528.1 435350 438207.8 436451 698830 708820 _
31 1D2 332210 329232.1 329350.3 448430 451241.7 444637 714820 732765.1 _
32 3P0 333110 329906.6 330084.8 449450 452170.7 452173.7 716020 734726.6 _
33 3P1 333250 329990.2 330245.1 449670 452307 445591 716470 735014.4 _
34 3P2 333530 330150.7 330536.8 450090 452562.8 446044 717330 735539.2 _
35 1G4 334440 333215.1 331811.2 451180 443481.3 447702 718720 739418.4 _
36 1S0 343460 336956.7 _ 462230 449183.5 _ 733990 765972.9 _
37 3d4f 1G4 380420 381453.4 _ 511690 509423.6 518905 808340 808844.6 811205
38 3F2 381120 382358.2 _ 512730 510090.7 501976 810200 809975.1 812862
39 3F3 381250 382463.7 _ 512950 510251.1 502639 810640 810285.2 813298
40 3F4 381670 382605.1 _ 513460 510465.6 503432 811530 810700.4 814130

Ti III: The calculated values of energy levels of Ti III have been listed in Table 1 and agree well with the corresponding values of NIST [67], and the maximum deviation was found for the 3d2 1D2 level by value of 3.64% from the corresponding value by NIST (for the calculations using CIV3). For the calculations using the LANL code the maximum deviations from NIST values are recorded for the 3d2 3F3,4 and 1D2 levels with deviations of 5.24, 6.37, 6.8%, respectively. For this ion, it is clear that the calculations using CIV3 are better than those using LANL code.

V IV: When we compared the energies of the calcium-like vanadium (Z = 24) with the compiled results by NIST, we found that most of calculated results show good agreement with those from NIST. The maximum deviation was found for the 3d2 1G4 level by a value of 4.66% for the CIV3 calculations and for the 3d2 1D2 level by a value of 6.1% using the LANL calculations, This data has been listed in Table 1.

Table 3. Energy levels of Ca-like Ni IX, Cu X and Zn XI.

        Ni IX     Cu X     Zn XI  
Index Level Term LANL CIV3 NIST LANL CIV3 NIST LANL CIV3 NIST
1 3d2 3F2 0 0 0 0 0 0 0 0 0
2 3F3 1891.6 1821.22 1880 2459.9 2493.04 2486 3146.3 1802.02 1890
3 3F4 4180.7 4221.67 4070 5389.9 5782.31 5487 6830.8 4164.41 4120
4 1D2 22783 22397.88 21900 25084 24934.14 23900 27459 25581.16 26070
5 3P0 25770 24885.52 _ 28154 27284.57 _ 30567 28643.85 _
6 3P1 26499 25497.8 _ 29122 28122.37 _ 31836 29255.31 _
7 3P2 28248 26608.75 27160 31468 29656.87 30600 34919 30309.36 31330
8 1G4 34761 36858.31 35898 38248 36824.33 _ 41858 38470.6 _
9 1S0 82256 82796.39 _ 89881 85995.92 _ 97592 103377.4 _
10 3d4p 1D2 673780 680134.9 _ 812950 817112.7 _ 962920 876844 _
11 3D1 675370 681778.2 _ 814750 819251.9 _ 964980 879297.6 _
12 3D2 677310 682776.9 _ 817310 820567.8 _ 968310 880165.2 _
13 3D3 678870 684262.3 _ 819080 822522.9 _ 970260 881448.1 _
14 3F2 678820 685948.3 _ 818970 823452.7 _ 970190 882384.1 _
15 3F3 680850 687104.3 _ 821490 824944.5 _ 973240 883149.2 _
16 3F4 684000 688653.6 _ 825340 826946.1 _ 977890 884186.1 _
17 3P0 687140 693169.9 _ 828200 832064.7 _ 980290 888968.4 _
18 3P1 686820 694111.4 _ 827710 833340.4 _ 979610 890080.7 _
19 3P2 688120 696015.4 _ 829520 835928.9 _ 982060 892358.5 _
20 1F3 691130 699267.3 _ 832730 840677.6 _ 985440 896638.7 _
21 1P1 695940 704670.5 _ 838230 846928.1 _ 991680 901391.8 _
22 3d4d 1F3 836440 841290.5 _ 994170 992064.6 _ 1162800 1079148 _
23 3D1 837850 843968.1 _ 995600 994627 _ 1164200 1081443 _
24 3D2 839090 844714.8 _ 997240 995612.4 _ 1166400 1082142 _
25 3D3 840650 845837.5 _ 999280 997093.7 _ 1169000 1083191 _
26 3G3 839890 846521.4 _ 997990 997163.4 _ 1167000 1083737 _
27 3G4 841260 848019.5 _ 999700 999140.2 _ 1169100 1085138 _
28 3G5 843230 849898.2 _ 1002200 1001618 _ 1172300 1086896 _
29 1P1 842110 848383.2 _ 1000800 999631.9 _ 1170400 1085579 _
30 3S1 847270 856674.7 _ 1006600 1008474 _ 1177000 1092758 _
31 1D2 864590 877850.7 _ 1025300 1029314 _ 1196900 1106593 _
32 3P0 865840 879761.5 _ 1026500 1031236 _ 1198200 1108634 _
33 3P1 866460 880139.1 _ 1027400 1031737 _ 1199300 1108995 _
34 3P2 867630 880839 _ 1028900 1032674 _ 1201300 1109663 _
35 1G4 869110 862780 _ 1030500 1036387 _ 1202800 1138016 _
36 1S0 886500 871851.1 _ 1050000 1063559 _ 1224600 1131073 _
37 3d4f 1G4 973200 974774.3 _ 1148800 1132341 _ 1335100 1242394 _
38 3F2 975520 976313.7 977130 1151600 1136300 _ 1338400 1249097 _
39 3F3 976120 976724.5 977680 1152400 1136798 _ 1339400 1249372 _
40 3F4 977290 977274.8 978740 1153900 1137469 _ 1341400 1249751 _

Cr V: In the Cr IV ion the 3d2 3F3 level deviates from the corresponding NIST value by 4.73% for the CIV3 and the value of 5.6% is recorded as a deviation of the 3d2 1D2 level from NIST value for the LANL calculations, the value of energy levels have been listed in Table 2.

Mn VI: The same as Cr IV was figured out for the Mn ion where, the 3d2 3F3 level deviates from the corresponding NIST value by 4.65% for the CIV3 and the value of 5.2% is recorded as a deviation of the 3d2 1D2 level from NIST value for the LANL calculations, as shown in Table 2.

Co VIII: For most of levels calculated using CIV3 the energies agree well with those from NIST and the percent differences are less than 1.0%, except the 3d2 1G4 where the deviation rises to 6.0%. The maximum deviations for the results produced by LANL are 4.9, 4.8, 4.8% for 3d2 3P0,1,2, respectively, as shown in Table 2.

Ni IX: The ground state and excitation energies of Ca-like Ni IX are shown in Table 3, the data have been compared with the minor ones available by NIST atomic spectra database [67], and it is in a reasonable agreement with the literature [67]. But in some cases this agreement disappears for example, the levels 3d2 1D2 and 3d2 3F3,4 which showing differences from NIST by 4.0, 3.1, 3.7%, respectively.

Table 4. Oscillator strengths, wavelengths, and transition probabilities for Ca-like Co VIII.

Index UL. LL. λ fL fV fLANL AL L/V
1 3d2(3F2) 3d4p(3D1) 184.81 6.91E-02 7.50E-02 7.90E-02 2.25E+10 0.92
2   3d4p(3D2) 184.56 1.28E-02 1.39E-02 1.90E-02 2.51E+09 0.92
3   3d4p(3D3) 184.2 3.67E-04 3.95E-04 2.43E-03 5.15E+07 0.93
4   3d4p(3F2) 183.72 3.68E-02 3.94E-02 2.29E-02 7.27E+09 0.93
5   3d4p(3F3) 183.45 4.61E-03 4.92E-03 3.46E-03 6.52E+08 0.94
6   3d4f(3F2) 123.46 8.21E-02 8.70E-02 1.46E-01 3.59E+10 0.94
7   3d4f(3F3) 123.41 1.03E-02 1.09E-02 6.35E-02 3.21E+09 0.94
8   3d4f(3G3) 122.97 2.81E-01 2.76E-01 5.39E-01 8.85E+10 1.02
9   3d4f(3D1) 122.7 6.30E-03 6.16E-03 1.34E-02 4.65E+09 1.02
10   3d4f(3D2) 122.7 1.17E-03 1.14E-03 1.12E-03 5.17E+08 1.02
11   3d4f(3D3) 122.71 3.34E-05 3.27E-05 1.54E-02 1.06E+07 1.02
12 3d2(3F3) 3d4p(3D2) 185.05 7.34E-02 7.94E-02 7.10E-02 2.00E+10 0.92
13   3d4p(3D3) 184.68 9.19E-03 9.90E-03 3.27E-02 1.80E+09 0.93
14   3d4p(3F2) 184.2 3.29E-03 3.53E-03 1.60E-02 9.06E+08 0.93
15   3d4p(3F3) 183.93 3.49E-02 3.73E-02 1.97E-02 6.88E+09 0.94
16   3d4p(3F4) 183.57 3.34E-03 3.56E-03 4.05E-03 5.15E+08 0.94
17   3d4f(3D2) 122.91 6.66E-03 6.54E-03 1.59E-02 4.12E+09 1.02
18   3d4f(3D3) 122.92 8.34E-04 8.19E-04 5.19E-03 3.68E+08 1.02
19   3d4f(3G3) 123.19 1.75E-02 1.73E-02 5.56E-02 7.71E+09 1.01
20   3d4f(3G4) 123.1 2.63E-01 2.59E-01 5.14E-01 9.02E+10 1.02
21   3d4f(3F2) 123.68 7.32E-03 7.79E-03 9.71E-03 4.47E+09 0.94
22   3d4f(3F3) 123.63 7.76E-02 8.25E-02 1.16E-01 3.39E+10 0.94
23   3d4f(3F4) 123.57 7.44E-03 7.90E-03 3.61E-02 2.53E+09 0.94
24 3d2(3F4) 3d4p(3D3) 185.32 8.29E-02 8.93E-02 6.38E-02 2.07E+10 0.93
25   3d4p(3F3) 184.56 2.60E-03 2.78E-03 3.39E-02 6.55E+08 0.94
26   3d4p(3F4) 184.2 3.91E-02 4.16E-02 4.70E-02 7.69E+09 0.94
27   3d4f(3F4) 123.85 8.67E-02 9.25E-02 1.19E-01 3.77E+10 0.94
28   3d4f(3F3) 123.92 5.77E-03 6.16E-03 6.19E-03 3.22E+09 0.94
29   3d4f(3G3) 123.47 2.16E-04 2.14E-04 3.54E-04 1.22E+08 1.01
30   3d4f(3G4) 123.38 1.36E-02 1.35E-02 5.43E-02 5.98E+09 1.01
31   3d4f(3G5) 123.27 2.67E-01 2.64E-01 5.67E-01 9.60E+10 1.01
32   3d4f(3D3) 123.2 7.49E-03 7.39E-03 1.59E-02 4.23E+09 1.01
33 3d2(3P0) 3d4p(3D1) 192.89 3.19E-02 3.41E-02 4.52E-02 1.90E+09 0.93
34   3d4p(3P1) 188.62 9.77E-02 1.00E-01 9.78E-02 6.10E+09 0.98
35   3d4f(3D1) 126.21 2.47E-01 2.48E-01 7.02E-01 3.45E+10 0.99
36   3d4f(3P1) 125.99 1.25E-01 1.26E-01 9.44E-02 1.76E+10 0.99
37 3d2(3P1) 3d4p(3D1) 193.07 7.97E-03 8.53E-03 6.30E-03 1.43E+09 0.93
38   3d4p(3D2) 192.8 2.39E-02 2.56E-02 3.25E-02 2.58E+09 0.94
39   3d4p(3P1) 188.79 2.44E-02 2.50E-02 3.02E-02 4.57E+09 0.98
40   3d4p(3P0) 189.05 3.25E-02 3.34E-02 3.82E-02 1.82E+10 0.97

Table 5. Oscillator strengths, wavelengths, and transition probabilities for Ca-like Ni IX.

Index UL. LL. λ fL fV fLANL AL L/V
1 3d2(3F2) 3d4p(3D1) 146.68 5.87E-02 5.31E-02 7.36E-02 3.03E+10 1.11
2   3d4p(3D2) 146.46 1.09E-02 9.82E-03 1.69E-02 3.39E+09 1.11
3   3d4p(3D3) 146.14 3.12E-04 2.80E-04 2.79E-03 6.95E+07 1.11
4   3d4p(3F2) 145.78 3.12E-02 2.79E-02 1.76E-02 9.81E+09 1.12
5   3d4p(3F3) 145.54 3.91E-03 3.49E-03 2.71E-03 8.80E+08 1.12
6   3d4f(3G3) 101.92 3.16E-01 3.40E-01 6.08E-01 1.45E+11 0.93
7   3d4f(3D1) 101.7 7.08E-03 7.58E-03 1.48E-02 7.61E+09 0.93
8   3d4f(3D3) 101.71 3.75E-05 4.02E-05 1.75E-02 1.73E+07 0.93
9 3d2(3F3) 3d4p(3D2) 146.85 6.24E-02 5.62E-02 6.44E-02 2.70E+10 1.11
10   3d4p(3D3) 146.53 7.81E-03 7.01E-03 3.54E-02 2.43E+09 1.11
11   3d4p(3F2) 146.17 2.80E-03 2.50E-03 1.68E-02 1.22E+09 1.12
12   3d4p(3F3) 145.93 2.97E-02 2.64E-02 1.38E-02 9.29E+09 1.12
13   3d4p(3F4) 145.6 2.84E-03 2.52E-03 3.81E-03 6.96E+08 1.13
14   3d4f(3D2) 101.89 7.49E-03 8.05E-03 1.72E-02 6.74E+09 0.93
15   3d4f(3D3) 101.9 9.38E-04 1.01E-03 6.10E-03 6.03E+08 0.93
16   3d4f(3G3) 102.11 1.97E-02 2.13E-02 6.13E-02 1.26E+10 0.93
17   3d4f(3G4) 102.03 2.96E-01 3.19E-01 5.80E-01 1.48E+11 0.93
18 3d2(3F4) 3d4p(3D3) 147.05 7.05E-02 6.32E-02 5.01E-02 2.80E+10 1.12
19   3d4p(3F3) 146.44 2.21E-03 1.97E-03 4.11E-02 8.85E+08 1.12
20   3d4p(3F4) 146.11 3.33E-02 2.94E-02 4.42E-02 1.04E+10 1.13
21   3d4f(3G3) 102.36 2.43E-04 2.63E-04 3.19E-04 1.99E+08 0.92
22   3d4f(3G4) 102.28 1.54E-02 1.66E-02 6.06E-02 9.79E+09 0.92
23   3d4f(3G5) 102.17 3.01E-01 3.25E-01 6.39E-01 1.57E+11 0.93
24   3d4f(3D3) 102.15 8.44E-03 9.10E-03 1.88E-02 6.93E+09 0.93
25 3d2(3P0) 3d4p(3D1) 152.23 2.72E-02 2.42E-02 4.46E-02 2.61E+09 1.12
26   3d4p(3P1) 149.43 8.30E-02 7.11E-02 8.84E-02 8.27E+09 1.17
27   3d4f(3D1) 104.34 2.74E-01 3.04E-01 8.00E-01 5.61E+10 0.9
28   3d4f(3P1) 104.19 1.40E-01 1.55E-01 9.15E-02 2.86E+10 0.9
29 3d2(3P1) 3d4p(3D1) 152.38 6.80E-03 6.04E-03 5.48E-03 1.95E+09 1.12
30   3d4p(3D2) 152.14 2.04E-02 1.81E-02 3.18E-02 3.53E+09 1.13
31   3d4p(3P1) 149.56 2.08E-02 1.78E-02 2.87E-02 6.19E+09 1.17
32   3d4p(3P0) 149.78 2.77E-02 2.38E-02 3.59E-02 2.47E+10 1.16
33   3d4p(3P2) 149.14 3.47E-02 2.96E-02 3.66E-02 6.25E+09 1.17
34   3d4f(3D1) 104.41 6.86E-02 7.60E-02 8.75E-02 4.20E+10 0.9
35   3d4f(3D2) 104.41 2.06E-01 2.28E-01 5.60E-01 7.56E+10 0.9
36   3d4f(3P1) 104.25 3.49E-02 3.88E-02 1.39E-01 2.14E+10 0.9
37   3d4f(3P0) 104.18 4.65E-02 5.16E-02 9.97E-02 8.58E+10 0.9
38 3d2(3P2) 3d4p(3P1) 149.81 2.08E-02 1.78E-02 1.76E-02 1.03E+10 1.17
39   3d4p(3P2) 149.39 6.26E-02 5.33E-02 8.15E-02 1.87E+10 1.17
40   3d4p(3D2) 152.4 4.09E-03 3.62E-03 2.58E-03 1.17E+09 1.13
41 3d4p(3D1) 3d4d(3F2) 546.64 3.99E-01 3.38E-01 5.52E-01 5.34E+09 1.18
42   3d4d(3P0) 505.1 3.85E-02 2.80E-02 7.20E-02 3.02E+09 1.37
43   3d4d(3P1) 504.14 2.89E-02 2.10E-02 2.35E-02 7.58E+08 1.38
44   3d4d(3D2) 613.74 5.57E-02 5.89E-02 6.44E-02 5.91E+08 0.95
45   3d4d(3D1) 616.57 1.66E-01 1.77E-01 2.60E-01 2.92E+09 0.94
46 3d4p(3D2) 3d4d(3F2) 549.64 4.41E-02 3.78E-02 7.96E-02 9.73E+08 1.17
47   3d4d(3F3) 546.3 3.55E-01 3.00E-01 4.21E-01 5.66E+09 1.18
48   3d4d(3P1) 506.69 5.18E-02 3.79E-02 9.65E-02 2.24E+09 1.36
49   3d4d(3P2) 504.9 1.73E-02 1.26E-02 1.34E-02 4.53E+08 1.37
50   3d4d(3D1) 620.39 3.30E-02 3.57E-02 3.21E-02 9.54E+08 0.93

Table 6. Oscillator strengths, wavelengths, and transition probabilities for Ca-like Cu X.

Index UL. LL. λ fL fV fLANL AL L/V
1 3d2(3F2) 3d4p(3D1) 123.84 6.02E-02 6.12E-02 6.88E-02 4.36E+10 0.98
2   3d4p(3D2) 123.63 1.12E-02 1.13E-02 1.47E-02 4.87E+09 0.99
3   3d4p(3D3) 123.34 3.20E-04 3.23E-04 3.06E-03 1.00E+08 0.99
4   3d4p(3F2) 123.19 3.20E-02 3.22E-02 1.33E-02 1.41E+10 0.99
5   3d4p(3F3) 122.97 4.01E-03 4.02E-03 2.09E-03 1.26E+09 1
6   3d4f(3F2) 88.87 2.62E-01 2.37E-01 1.82E-01 2.21E+11 1.11
7   3d4f(3F3) 88.83 3.27E-02 2.96E-02 7.62E-02 1.98E+10 1.11
8 3d2(3F3) 3d4p(3D2) 124.01 6.40E-02 6.48E-02 5.91E-02 3.88E+10 0.99
9   3d4p(3D3) 123.71 8.02E-03 8.08E-03 3.70E-02 3.49E+09 0.99
10   3d4p(3F2) 123.57 2.86E-03 2.88E-03 1.71E-02 1.75E+09 0.99
11   3d4p(3F3) 123.34 3.04E-02 3.05E-02 9.20E-03 1.33E+10 1
12   3d4p(3F4) 123.04 2.91E-03 2.91E-03 3.60E-03 9.98E+08 1
13   3d4f(3F2) 89.06 2.33E-02 2.12E-02 1.18E-02 2.75E+10 1.1
14   3d4f(3F3) 89.02 2.47E-01 2.24E-01 1.44E-01 2.08E+11 1.1
15   3d4f(3F4) 88.97 2.37E-02 2.15E-02 4.46E-02 1.55E+10 1.1
16 3d2(3F4) 3d4p(3D3) 124.21 7.24E-02 7.29E-02 3.85E-02 4.02E+10 0.99
17   3d4p(3F3) 123.84 2.27E-03 2.27E-03 4.70E-02 1.27E+09 1
18   3d4p(3F4) 123.54 3.41E-02 3.40E-02 4.17E-02 1.49E+10 1
19   3d4f(3F4) 89.23 2.76E-01 2.51E-01 1.46E-01 2.31E+11 1.1
20   3d4f(3F3) 89.28 1.84E-02 1.67E-02 7.49E-03 1.98E+10 1.1
21 3d2(3P0) 3d4p(3D1) 128.13 2.78E-02 2.77E-02 4.43E-02 3.76E+09 1
22   3d4p(3P1) 125.86 8.47E-02 8.17E-02 7.99E-02 1.19E+10 1.04
23 3d2(3P1) 3d4p(3D1) 128.27 6.96E-03 6.94E-03 4.74E-03 2.82E+09 1
24   3d4p(3D2) 128.05 2.09E-02 2.08E-02 3.14E-02 5.10E+09 1.01
25   3d4p(3P1) 125.99 2.12E-02 2.04E-02 2.73E-02 8.90E+09 1.04
26   3d4p(3P0) 126.2 2.82E-02 2.73E-02 3.39E-02 3.54E+10 1.03
27   3d4p(3P2) 125.58 3.54E-02 3.39E-02 3.32E-02 8.99E+09 1.04
28 3d2(3P2) 3d4p(3P1) 126.23 2.12E-02 2.05E-02 1.47E-02 1.48E+10 1.04
29   3d4p(3P2) 125.82 6.39E-02 6.12E-02 7.69E-02 2.69E+10 1.04
30   3d4p(3D2) 128.3 4.19E-03 4.16E-03 2.20E-03 1.70E+09 1.01
31   3d4p(3D3) 127.98 2.35E-02 2.32E-02 1.22E-02 6.84E+09 1.01
32 3d2(1D2) 3d4p(1D2) 128.1 6.49E-02 6.47E-02 4.01E-02 2.64E+10 1
33   3d4p(1F3) 124.35 7.61E-03 7.18E-03 6.28E-03 2.34E+09 1.06
34   3d4p(1P1) 123.39 4.02E-02 3.74E-02 3.40E-02 2.94E+10 1.08
35 3d2(1G4) 3d4p(1F3) 126.2 1.16E-01 1.08E-01 1.31E-01 6.24E+10 1.07
36 3d2(1D2) 3d4f(1D2) 90.35 3.82E-01 3.44E-01 2.43E-01 3.12E+11 1.11
37 3d4s(3D1) 3d4p(3P0) 747.94 7.31E-02 6.58E-02 9.24E-02 2.62E+09 1.11
38   3d4p(3P1) 740.87 5.54E-02 4.89E-02 1.03E-01 6.73E+08 1.13
39   3d4p(3D1) 827.29 1.49E-01 1.64E-01 1.68E-01 1.45E+09 0.91
40   3d4p(3D2) 818.38 5.02E-02 5.40E-02 2.30E-02 3.00E+08 0.93

Cu X: The energy levels of Cu X have been listed in Table 3 and have been compared with the corresponding values of NIST. For the few available levels by NIST the comparisons show good agreement and the maximum deviation is found for the 3d2 3F4 where the error value is about 5.38%.

Zn XI: The Zn XI data are tabulated in Table 3, it is clear that the computed energies using the CIV3 code are much more better than those computed using LANL, we can figure out this from the results deviations from NIST values. The deviation of the 3d2 3F3 level is about 4.65% for the CIV3 calculations and about 66% for the LANL calculations. This worse deviation appears in the calculated values by LANL code is a little bit confuse us, because the Z-dependence of the calculated energies by LANL is fitting well with the formula [68]:

(4)

Where, figures (1a-2b) show that, the NIST and CIV3 values of E2/Z decrease systematically vs 1/Z over all ions except for zinc ion, while the calculations of LANL fit well with the equation (4) over all ions including Zn.

Fig. 1a. The Z-dependence of the 3d2 3F3 energy level.

Fig. 1b. The Z-dependence of the 3d4s 3D1 energy level.

Fig. 2a. The Z-dependence of the 3d4p 3D1 energy level.

Fig. 2b. The Z-dependence of the 3d4d 3D1 energy level.

The fine structure parameter ζi depend on the angular momentum l > 0 and is given from:

(5)

Figure (3a) show that the CIV3 calculations of hyper fine structure parameter vary systematically with Z, except at Zn value which decreases rapidly. The ζ2/Z value was adjusted at 0.808 for the Zn ion to match the calculated energies by CIV3 with NIST, from the previous argument we think that the abnormal value of LANL calculations of the 3d2 3F3 energy level in Zn XI are accurate and may be an error has been occurred in the compilation process for the zinc data in the literature [43].

3.2. Oscillator Strengths and Radiative Rates

The configuration interaction calculations of radiative parameters (wavelengths, oscillator strengths, and transition probabilities) are given in Tables 4-7. In the present work, we have used two approximations to get better values for oscillator strengths and transition probabilities. First, the calculations using the non-relativistic configuration interaction method CIV3 including Breit-Pauli Hamiltonian. Second, the ab-initio calculations using the LANL atomic code based on Cowan’s method [64]. It obvious that for the listed data of oscillator strengths, the data produced from CIV3 calculations are so close to those from LANL calculations for the majority of transitions.

The accuracy of the results could be estimated by many ways such as, the comparison with the previous published theoretical calculations and experimental data, the use of dierent methods in the calculations, and/or the convergence between the length and velocity gauge forms [69]. In the present work we have used two dierent methods in the calculations, and compared the calculated data of oscillator strengths from the two methods with the available sources, and checked the agreement between length and velocity gauge values. The comparisons between CIV3 and LANL calculations of oscillator strengths and other literature have been accomplished in Table 8. Where the present calculations have been compared with the values of NIST [67] as well as with the cited values in the literature [20, 26, 34, 4446, 48, 49]. For most cited transitions in Table 8 our data either from CIV3 or from LANL are in a reasonable agreement with those of NIST and the literature, the deviation for some transitions reaches large values such as 3d4p(3D3) - 3d4d(3D3) in V IV ion, which deviates from NIST by as much as 99% but the average deviation for this ion lies within 10%. To avoid worse accuracies like that we should include a large number of correlations within the used configuration state list using CIV3 by adding the 7l and 8l correlations. Procedure like this needs high speed computer containing large memory (not available for us at the present time).

An important point should be mentioned here, that is the accuracy (D, E) of most of NIST-values for oscillator strengths are about 40% ≤ D ≤ 50% and E > 50% which means that our calculated results of most oscillator strengths are in the uncertainty range of NIST.

Table 7. Oscillator strengths, wavelengths, and transition probabilities for Ca-like Zn XI.

Index UL. LL. λ fL fV fLANL AL L/V
1 3d2(3F2) 3d4p(3D1) 113.73 6.06E-02 5.97E-02 6.45E-02 5.21E+10 1.02
2   3d4p(3D2) 113.62 1.12E-02 1.11E-02 1.27E-02 5.81E+09 1.02
3   3d4p(3D3) 113.45 3.22E-04 3.15E-04 3.19E-03 1.19E+08 1.02
4   3d4p(3F2) 113.33 3.22E-02 3.15E-02 9.88E-03 1.67E+10 1.02
5   3d4p(3F3) 113.23 4.03E-03 3.93E-03 1.65E-03 1.50E+09 1.02
6   3d4f(3G3) 78.74 1.14E+00 1.34E+00 7.18E-01 8.76E+11 0.85
7   3d4f(3D1) 78.48 2.56E-02 2.99E-02 1.68E-02 4.63E+10 0.86
8   3d4f(3D2) 78.49 4.75E-03 5.53E-03 5.10E-03 5.14E+09 0.86
9   3d4f(3D3) 78.5 1.36E-04 1.58E-04 2.33E-02 1.05E+08 0.86
10 3d2(3F3) 3d4p(3D2) 113.85 6.43E-02 6.32E-02 5.48E-02 4.63E+10 1.02
11   3d4p(3D3) 113.68 8.05E-03 7.89E-03 3.75E-02 4.16E+09 1.02
12   3d4p(3F2) 113.56 2.88E-03 2.82E-03 1.71E-02 2.08E+09 1.02
13   3d4p(3F3) 113.46 3.05E-02 2.98E-02 6.13E-03 1.58E+10 1.02
14   3d4p(3F4) 113.33 2.92E-03 2.84E-03 3.42E-03 1.18E+09 1.03
15 3d2(3F4) 3d4p(3D3) 113.99 7.26E-02 7.11E-02 2.97E-02 4.79E+10 1.02
16   3d4p(3F3) 113.77 2.27E-03 2.22E-03 5.07E-02 1.51E+09 1.02
17   3d4p(3F4) 113.63 3.41E-02 3.32E-02 3.95E-02 1.76E+10 1.03
18   3d4f(3G4) 78.95 5.54E-02 6.52E-02 7.34E-02 5.93E+10 0.85
19   3d4f(3G5) 78.9 1.08E+00 1.27E+00 7.60E-01 9.51E+11 0.85
20   3d4f(3D3) 78.76 3.05E-02 3.57E-02 2.38E-02 4.22E+10 0.85
21 3d2(3P0) 3d4p(3D1) 117.56 2.78E-02 2.71E-02 4.43E-02 4.47E+09 1.02
22   3d4p(3P1) 116.09 8.44E-02 8.04E-02 7.22E-02 1.39E+10 1.05
23 3d2(3P1) 3d4p(3D1) 117.64 6.95E-03 6.79E-03 4.08E-03 3.35E+09 1.02
24   3d4p(3D2) 117.52 2.09E-02 2.03E-02 3.13E-02 6.05E+09 1.03
25   3d4p(3P1) 116.17 2.11E-02 2.01E-02 2.61E-02 1.04E+10 1.05
26   3d4p(3P0) 116.32 2.81E-02 2.69E-02 3.22E-02 4.16E+10 1.05
27   3d4p(3P2) 115.86 3.53E-02 3.34E-02 3.01E-02 1.05E+10 1.06
28 3d2(3P2) 3d4p(3P1) 116.31 2.11E-02 2.01E-02 1.23E-02 1.74E+10 1.05
29   3d4p(3P2) 116 6.36E-02 6.02E-02 7.29E-02 3.15E+10 1.06
30   3d4p(3D2) 117.67 4.18E-03 4.07E-03 1.85E-03 2.01E+09 1.03
31   3d4p(3D3) 117.49 2.34E-02 2.28E-02 9.23E-03 8.09E+09 1.03
32 3d2(1D2) 3d4p(1D2) 117.47 6.48E-02 6.33E-02 3.27E-02 3.13E+10 1.02
33   3d4p(1F3) 114.8 7.58E-03 7.07E-03 5.25E-03 2.74E+09 1.07
34   3d4p(1P1) 114.18 4.00E-02 3.69E-02 2.95E-02 3.41E+10 1.08
35   3d4f(1P1) 78.6 4.35E-02 4.99E-02 2.20E-02 7.82E+10 0.87
36 3d2(1G4) 3d4p(1F3) 116.53 1.09E-01 1.09E-01 1.22E-01 6.90E+10 1.01
37 3d4s(3D1) 3d4p(3P2) 892.33 2.59E-03 2.80E-03 5.80E-03 1.30E+07 0.93
38   3d4p(3P0) 920.16 5.02E-02 5.77E-02 8.93E-02 1.19E+09 0.87
39   3d4p(3P1) 910.84 3.81E-02 4.28E-02 1.06E-01 3.06E+08 0.89
40 3d4s(1D2) 3d4p(1P1) 887.63 9.38E-02 1.00E-01 1.57E-01 1.32E+09 0.94

Fig. 3a. The variation of fine structure parameter  with Z.

Fig. 3b. The Z-dependence of the oscillator strength for the transition 3d2 3P2 3d4p 3P2

For ions from nickel to zinc there are no data available at NIST online database. The present f-values of the Ni IX ion have been compared with those in reference [20] (see Table 8), the comparison shows that the ab-initio results from LANL are close to those in Ref. [20] than the data calculated by CIV3. The behavior of the oscillator strength of a given transition along an isoelectronic sequence can be illustrated using the formula [68]

(6)

The Z-dependence of oscillator strengths may be shown in the plot of oscillator strengths for the transition 3d2(3P2)-3d4p(3P2) versus the nuclear charge in figure (3b). The present calculations decrease with increasing Z, while the f-values by NIST [67] follow non-specific behavior with Z.

Another criterion is used to determine the accuracy of oscillator strengths, the precision of the theoretical oscillator strengths can be judged by the convergence between length and velocity gauge values. If exact wave functions are used then  [70,71]. For most of the present transitions the length and velocity gauge values are in a fairly good agreement, where the ratio L/V for most transitions are about one. The good agreement between  and  gives some indications (but not sucient) for the present calculations accuracy [72].

Table 8. Comparison between the present calculations of oscillator strengths for Ca-like ions and those in the literature, see explanation of tables.

Note:

a: The oscillator strengths from Ref. [20]

b: The oscillator strengths from Ref. [45]

c: The oscillator strengths from Ref. [48]

d: The oscillator strengths from Ref. [26]

e: The oscillator strengths from Ref. [44]

4. Conclusion

In the present study, configuration interaction calculations using CIV3 code and ab-initio calculations using the LANL code have been performed for Ca-like ions.An extensive calculations of energy levels, oscillator strengths, and radiative rates have been evaluated for configuration arrays including the 3d2, 3d4s, 3d4p, 3d4d, and 3d4f levels with dierent angular momenta and parity. The present calculations of energies and oscillator strengths have been compared with the available experimental and theoretical sources, and it show a reasonable agreement with the literature. The atomic structure data are useful for many applications such as the identification of the solar spectra, the plasma diagnostics, and the thermonuclear fusion researches. In this paper we mentioned some data we obtained, not all the data we calculated, Such as tables include energy levels for Ca like ions (Z=22-30) except Fe, ions and tables include oscillator strength for Co VIII, Ni IX, Cu X, Zn XI ions, also the table includes comparison our data with the other published literature.


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