The Astrophysical Journal Supplement Series, 215:26 (14pp), 2014 December C 2014.
doi:10.1088/0067-0049/215/2/26
The American Astronomical Society. All rights reserved. Printed in the U.S.A.
SYSTEMATIC CALCULATIONS OF ENERGY LEVELS AND TRANSITION RATES OF C-LIKE IONS WITH Z = 13–36 K. Wang1 , D. F. Li1 , H. T. Liu1 , X. Y. Han1 , B. Duan1 , C. Y. Li1 , J. G. Li1 , X. L. Guo2,3 , C. Y. Chen2,3 , and J. Yan1,4 1
Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;
[email protected] Applied Ion Beam Physics Laboratory, Fudan University, Key Laboratory of the Ministry of Education, China 3 Shanghai EBIT Lab, Institute of Modern Physics, Department of Nuclear Science and Technology, Fudan University, Shanghai 200433, China 4 Center for Applied Physics and Technology, Peking University, Beijing 100871, China Received 2014 May 19; accepted 2014 September 11; published 2014 December 2 2
ABSTRACT Based on systematic calculations using a combined relativistic configuration interaction and a many-body perturbation theory (MBPT) approach, we provide a complete and consistent data set for 46 levels belonging to the 2s 2 2p2 , 2s2p3 , 2p4 , 2s 2 2p3s, 2s 2 2p3p, and 2s 2 2p3d configurations in C-like ions with 13 Z 36. The data set includes energy levels as well as electric dipole, magnetic dipole, electric quadrupole, and magnetic quadrupole transition properties. Extensive comparisons with available observed and calculated results are made and indicate that the present MBPT calculations are highly accurate. The present data set can be used reliably for many purposes, such as the line identification of observed spectra, and modeling and diagnostics of astrophysical and fusion plasmas. Key words: atomic data – atomic processes Online-only material: color figures, machine-readable tables
calculations have been carried out for radiative transition properties among the 46 levels of n = 2 and 3l complexes, which mainly include the works of Bhatia et al. (1987) and Bhatia & Doschek (1993), Zhang & Sampson (1997), Aggarwal (1998), Aggarwal et al. (1997, 2001, 2003). Compared with the results of Gu (2005a) and J¨onsson et al. (2011), for the n = 2 complex, all of the above-mentioned works for both n = 2 and 3l complexes are not satisfying because limited configuration interaction effects were considered in the calculations. For example, the level energies presented in Aggarwal el al.’s works, which were the best among the above-mentioned calculations involving the 3l complex, differ by up to 8% with the corresponding experimental values. Therefore, systematic and high quality calculations that involve levels beyond the n = 2 complex are in demand due to their importance in modeling astrophysical plasmas (Phillips et al. 1982; Acton et al. 1985; Raassen et al. 2002; Del Zanna & Woods 2013) and laboratory plasmas (Fawcett & Hayes 1975), as well as to provide a complete, accurate, and consistent data set for Databases such as NIST (Kramida et al. 2013) and CHIANTI (Dere et al. 1997; Landi et al. 2013). Recently, Ekman et al. (2014) reported calculated energies and radiative transition properties for 262 levels belonging to configurations (2s, 2p)4 , (2s, 2p)3 3l, and 2s 2 2p4l (with l = 0, 1, 2) in C-like ions in the range of 18 Z 30 by using a new release (J¨onsson et al. 2013) of the GRASP2K code (J¨onsson et al. 2007). Because the electron correlation effects were well considered through large configuration state function expansions, their calculations were highly accurate. However, Ekman et al. (2014) only reported radiative rates for electric dipole (E1) transitions. In some cases, especially when strong self-absorption effects exist, corresponding results for forbidden transitions, such as magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions, are also necessary for modeling and diagnostics of plasmas. In the present work, we report calculated energies, radiative E1, M1, E2, and M2 transition properties for 46 levels of the n = 2 and 3l complexes in the C-like ions with 13 Z 36,
1. INTRODUCTION Spectral lines of C-like ions in the ultraviolet (UV; 2000–4000 Å), far-ultraviolet (FUV; 1220–2000 Å), extremeultraviolet (EUV; 100–1220 Å), and X-ray ( 32. For this level, NIST recommended an energy of 59.289 eV because it is very close to our calculated value of 59.380 eV, but assigned it to the 1D2 level; our result for the 3P2 level is 115.974 eV. Therefore, this discrepancy arises from the different identifications.
http://sprg.ssl.berkeley.edu/∼mfgu/fac/
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The Astrophysical Journal Supplement Series, 215:26 (14pp), 2014 December
Wang et al.
Table 1 Level Energies (in eV) of the States in C-like Ions with Z = 13–36, as well as Level Designations in both the LSJ and jj Coupling Schemes, and their Mixing Coefficients Z
13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 ...
Key
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ...
Conf 2s 2 2p 2 2s 2 2p 2 2s 2 2p 2 2s 2 2p 2 2s 2 2p 2 2s2p 3 2s2p 3 2s2p 3 2s2p 3 2s2p 3 2s2p 3 2s2p 3 2s2p 3 2s2p 3 2s2p 3 2p 4 2p 4 2p 4 2p 4 2p 4 ...
LSJ 3P
0
3P
1
3P 2 1D 2 1S 0 5S 2 3D 3 3D 2 3D 1 3P 1 3P 2 3P 0 1D 2 3S 1 1P 1 3P 2 3P 1 3P 0 1D 2 1S 0
...
jj a,b,c
Jπ
2p − 2(0)0 2p − 1(1)12p + 1(3)2 2p + 2(4)4 2p − 1(1)12p + 1(3)4 2p + 2(0)0 2s + 1(1)12p − 1(1)22p + 2(4)4 2s + 1(1)12p − 1(1)22p + 2(4)6 2s + 1(1)12p − 1(1)02p + 2(4)4 2s + 1(1)12p − 1(1)22p + 2(4)2 2s + 1(1)12p − 1(1)22p + 2(0)2 2s + 1(1)12p + 3(3)4 2s + 1(1)12p − 1(1)02p + 2(0)0 2s + 1(1)12p − 1(1)22p + 2(4)4 2s + 1(1)12p − 1(1)22p + 2(4)2 2s + 1(1)12p + 3(3)2 2p + 2(4)4 2p − 1(1)12p + 3(3)2 2p + 4(0)0 2p − 1(1)12p + 3(3)4 2p + 2(0)0 ...
0e 1e 2e 2e 0e 2o 3o 2o 1o 1o 2o 0o 2o 1o 1o 2e 1e 0e 2e 0e ...
Energy
Mixing Coefficients
MBPTd
NISTe
jj
LSJf
0.00000E+00 2.12533E−01 5.47871E−01 5.77179E+00 1.19497E+01 1.66818E+01 3.24598E+01 3.24726E+01 3.24809E+01 3.82813E+01 3.82882E+01 3.82907E+01 4.91308E+01 5.00602E+01 5.50206E+01 7.52288E+01 7.56213E+01 7.57903E+01 8.00212E+01 9.13299E+01 ...
0.00000E+00 2.12000E−01 5.48000E−01 5.79300E+00 1.19300E+01 1.65940E+01 3.25060E+01 3.25170E+01 3.25250E+01 3.83250E+01 3.83250E+01 3.83250E+01 4.92240E+01 5.01140E+01 5.51200E+01 7.53950E+01 7.57770E+01 7.59420E+01 8.02560E+01 9.15610E+01 ...
−0.832 −0.989 −0.777 −0.777 0.819 −0.576 0.996 0.812 0.663 −0.813 −0.726 −0.996 0.811 −0.741 −0.610 −0.834 0.987 −0.787 0.833 −0.771 ...
−0.992(1) −0.992(2) −0.991(3) 0.991(4) 0.973(5) −0.999(6) 0.999(7) −0.998(8) −0.998(9) −0.999(10) −0.998(11) 0.999(12) 0.998(13) −0.997(14) −0.997(15) −0.991(16) 0.992(17) 0.992(18) −0.990(19) −0.972(20) ...
Notes. Note that only the 20 levels arising from the (1s 2 )2l 4 configurations in Al viii are shown here. a The number at the end or inside of the bracket is 2J . b s+ = s 1/2 , p− = p1/2 , p+ = p3/2 . 2 c The number after ± is the power of the corresponding configuration. For example, the jj configuration of level 6 is 2s 1/2 2p1/2 2p3/2 . d The present energies. e The observed energies from the NIST database (Kramida et al. 2013). f Mixing coefficient of the level (in brackets). (This table is available in its entirety in a machine-readable form in the online journal. A portion is shown here for guidance regarding its form and content.)
In fact, the LSJ designations for such levels are not very appropriate because the mixing among them is very strong, and thus jj designations are more suitable, as shown in Table 1. Note that the differences between the present results and observed values decrease smoothly along the isoelectronic sequence, while there a few irregularities exist. Theoretical results of J¨onsson et al. (2011) and Gu (2005a) show the similar irregularity behavior. Therefore, these irregularities may be caused by observation uncertainties. We hope that more precise measurements can verify this. For the 15 levels of configurations 2s2p3 and 2p4 in the n = 2 complex, the relative deviations between the present calculations and observed values are also within 0.2% for most of the levels, and within 0.5% for the remaining ones, but with four exceptions: 2s 1 2p3 5S2 in Ar xiii and Sc xvi, 2s 1 2p3 3D2 in Ni xxiii, and 2s 1 2p3 3P2 in Kr xxxi. For the 2s 1 2p3 3P2 level in Kr xxxi, the large discrepancy also arises from the different identifications, such as the above-mentioned 2s 2 2p23P2 level. For the other three cases, the deviations between the present MBPT energies and the observed ones are between 0.9% and 1.4%. Each of our calculated levels show good Z-dependent behavior and vary smoothly along the isoelectronic sequence. Considering the good agreements between the observed and present MBPT values for the three levels of other ions, we argue that the larger deviations may arise from measurement aspects. It can be seen from Figure 1 that early calculations of Aggarwal et al., using both the CIV3 code and the GRASP code,
are not as accurate as the more recent elaborate calculations of J¨onsson et al. (2011) and Gu (2005a), because the limited configuration interaction effects were considered in early works. Our results agree well with those of J¨onsson et al. (2011) and Gu (2005a). Quantitatively, because of more sufficient electron correlation effects considered in the present MBPT calculations by including more configurations in both the M and N spaces, our results are slightly better than those of Gu (2005a), especially for levels in the low Z ions as shown in Figure 1. Very recently, Ekman et al. (2014) reported the MCDHF/ RCI calculations of energies and transition properties for 262 levels belonging to 15 configurations (2s, 2p)4 , (2s, 2p)3 3l, and 2s 2 2p4l (l = 0, 1, 2) in C-like ions with 18 Z 30 by using a new release (J¨onsson et al. 2013) of the GRASP2K code (J¨onsson et al. 2007). The accuracy of their calculations is high enough to facilitate the identification of observed spectral lines. Comparisons of the present work, MCDHF/RCI calculations, NIST, and CHIANTI recommended values for the lowest 20 levels of n = 2 complex in Fe xxi show excellent agreement, i.e., the mean relative difference between calculations and NIST & CHIANTI observations are 0.022% and 0.025% for this work, 0.028% and 0.032% for the results of Ekman et al. (2014); plus the mean difference between the present work and MCDHF/ RCI calculations is 0.015% for all 46 levels belonging to the n = 2 and 3l complexes. There are 127 level energies recommended in the NIST database for 3l states in ions with 13 Z 36. Figure 2 3
The Astrophysical Journal Supplement Series, 215:26 (14pp), 2014 December
Fe xxi should mainly be caused by relatively larger observation uncertainties, especially in the NIST database.
Table 2 Wavelengths (λ, in Å), Line Strengths (S, in Atomic Unit), Absorption Oscillator Strengths (f, Dimensionless), and Transition Rates (A, in s−1 ) for Transitions in C-like Ions with Z = 13–36 Z 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 ...
i−j
Type
λ
S
f
A
1–2 1–3 1–4 1–6 1–8 1–9 1–10 1–11 1–13 1–14 1–15 1–16 1–17 1–19 1–22 1–23 1–24 1–25 1–26 1–27 1–29 1–31 1–32 1–33 1–35 1–37 1–39 1–40 1–42 1–43 1–46 ...
M1 E2 E2 M2 M2 E1 E1 M2 M2 E1 E1 E2 M1 E2 E1 M2 E1 M1 M1 E2 M1 M1 E2 E2 M2 M2 E1 M2 M2 E1 E1 ...
5.83364E+04 2.26302E+04 2.14810E+03 7.43230E+02 3.81811E+02 3.81714E+02 3.23877E+02 3.23818E+02 2.52355E+02 2.47670E+02 2.25341E+02 1.64809E+02 1.63954E+02 1.54939E+02 7.58037E+01 7.55998E+01 7.49929E+01 7.23292E+01 7.19856E+01 7.19157E+01 7.14068E+01 7.11048E+01 7.10303E+01 7.00744E+01 6.81540E+01 6.80032E+01 6.74233E+01 6.73973E+01 6.71657E+01 6.71237E+01 6.63134E+01 ...
1.973E+00 3.113E−02 5.600E−05 2.293E+00 1.882E+00 1.007E−01 8.339E−02 3.676E−01 1.109E+00 7.954E−02 5.150E−06 3.861E−03 5.265E−10 2.021E−07 1.657E−02 7.041E−02 2.067E−04 3.209E−07 3.145E−07 4.676E−02 3.064E−06 1.164E−06 1.018E−02 3.112E−05 1.654E−03 1.598E+00 2.161E−01 5.317E−01 1.907E−01 2.010E−02 6.280E−04 ...
1.368E−07 4.510E−13 9.486E−13 1.249E−11 7.558E−11 8.015E−02 7.821E−02 2.420E−11 1.543E−10 9.756E−02 6.943E−06 1.448E−07 1.299E−14 9.125E−12 6.640E−02 3.643E−10 8.370E−04 1.794E−11 1.767E−11 2.111E−05 1.735E−10 6.619E−11 4.772E−06 1.519E−08 1.168E−11 1.136E−08 9.737E−01 3.882E−09 1.407E−09 9.098E−02 2.877E−03 ...
8.937E−02 1.175E−06 2.743E−04 3.016E−02 6.916E−01 1.223E+09 1.658E+09 3.079E−01 3.232E+00 3.536E+09 3.040E+05 7.113E+03 1.074E−03 5.071E−01 2.569E+10 8.502E+01 3.309E+08 7.625E+00 7.581E+00 5.444E+06 7.566E+01 2.911E+01 1.262E+06 4.126E+03 3.354E+00 3.277E+03 4.762E+11 1.140E+03 4.161E+02 4.490E+10 1.454E+09 ...
Wang et al.
3.2. Radiative Rates In an individual C-like ion, there are 70 E1 transitions among the n = 2 levels, consisting of 36 resonance E1 (ΔS = 0, ΔL 1, and dipole-allowed) transitions and 34 intercombination E1 (spin-changed and dipole-allowed) transitions. Figure 3 compares the present E1 A values and those from J¨onsson et al. (2011) for C-like ions with 13 Z 28. For the 576 resonance transitions, the two sets of data agree within 5%, except for the relatively weak one (8%), 2s2p3 3D2 − 2s 2 2p2 3P2 in Mn xx. The differences arise from different electron correlation effects included in the calculations, and the weak transitions are usually more sensitive to cancellation among mixing coefficients. For the 544 intercombination transitions, which are even more sensitive to correlation effects, the two sets of data agree within 5% for 504 lines, differing by over 10% for 16 lines, which are relatively weak. However, for a majority of weak transitions (Avalues
