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Article

Ab-Initio Calculations of Level Energies, Oscillator Strengths and Radiative Rates for E1 Transitions in Beryllium-Like Iron

by
Ahmed Abou El-Maaref
1,2,*,
Stefan Schippers
2 and
Alfred Müller
2
1
Physics Department, Faculty of Science, Al-Azhar University Assiut, 71524 Assiut, Egypt
2
Institut für Atom- und Molekülphysik, Justus-Liebig-Universität Giessen, D-35392 Giessen, Germany
*
Author to whom correspondence should be addressed.
Atoms 2015, 3(1), 2-52; https://doi.org/10.3390/atoms3010002
Submission received: 10 November 2014 / Accepted: 9 January 2015 / Published: 20 January 2015
(This article belongs to the Special Issue Atomic Data for Tungsten)
Versions Notes

Abstract

:
In the present work, energy levels, oscillator strengths, radiative rates and wavelengths of Be-like iron (Fe22+) from ab-initio calculations using the multiconfiguration Dirac-Hartree-Fock method are presented. These quantities have been calculated for a set of configurations in the general form 1s2 nl n′l′, where n = 2, 3 and n′ = 2, 3, 4, 5 and l = s, p, d and l′ = s, p, d, f, g. In addition, excitations of up to four electrons, including core-electron excitations, have been considered to improve the quality of the wave functions. This study comprises an extensive set of E1 transition rates between states with different J. The present results are compared with the available experimental and theoretical data.

1. Introduction

Accurate atomic data for iron ions are of interest in astrophysics, especially for the identification of solar spectra [1–4], as well as in the physics of controlled fusion [5] and plasma diagnostic [6]. From the astrophysical point of view, the importance of iron ions lies in the fact that iron is the cosmically most abundant heavy element beyond silicon [7]. The beryllium isoelectronic sequence including the Fe22+ ion has been studied using different theoretical approaches [8–21]. Most of the earlier calculations have produced results for one- or two-electron excitations to low-lying levels (up to n = 2 or 3). Excitation to high-lying levels was studied by Moribayashi and Kato [22], including configurations up to 2pnl (n ≤ 20, l = s, p, d) using Cowan’s code [23].
Recently, many theoretical calculations have been carried out for Fe22+ to meet the needs for accurate atomic structure data. Chidichimo et al. have calculated level energies for n ≤ 4, as well as wavelengths and weighted oscillator strengths using the Belfast R-matrix programs [24,25]. Del Zanna et al. [26] have compiled experimental observations of energy levels and wavelengths, and performed calculations of weighted oscillator strengths for Be-like iron using the non-relativistic SUPERSTRUCTURE program. Santos et al. [27] calculated probabilities for transitions from the 1s22s3p 3P0 level for selected beryllium-like ions, from Z = 5 to 92. They used the MCDF method including relativistic effects, QED (quantum-electrodynamics) effects, and correlations up to the 4f subshell, however, they neglected the Breit interaction. Jian-Hui et al. [28] have calculated energy levels, oscillator strengths, transition probabilities and wavelengths of Fe22+ using the MCDF method with the inclusion of vacuum polarization and Breit interaction. Charro et al. [29,30] have calculated some oscillator strengths of Be-like iron up to n = 2, 3 using the relativistic quantum defect orbital (RQDO) method and the MCDF method, but there were no Breit corrections included in the calculations. By using the FAC code Landi and Gu [31] calculated energy levels, oscillator strengths and transition probabilities for 166 fine-structure levels of Fe22+ belonging to the complexes 1s22lnl′, n = 2 – 5, l = s, p, d, f, g. In the present work an extensive set of configuration state functions (CSF) including subshell populations up to the 5g subshell is used. In addition, the Breit interaction and QED effects are incorporated, which have been neglected in most of the previous calculations. The present comprehensive treatment of the Fe22+ atomic structure aims at providing more accurate results than hitherto available.
For the present extensive atomic structure calculations of beryllium-like iron, Fe22+, we have used the multiconfiguration Dirac-Fock (MCDF) method [32] as implemented in the GRASP2K code [33]. Excitations from n = 3 to n = 4, 5 (doubly-excited levels) are included, and EOL (extended optimal level) type calculations have been performed. Wavelengths, energy levels, and E1 transition parameters (oscillator strengths, transition probabilities, and line strengths) have been computed for 182 fine-structure levels. The calculations have been divided into two main groups, with even and odd parity. The odd-parity group contains 90 levels while the even-parity group has 92 levels. The present calculations of oscillator strengths and radiative rates are generally in a good agreement with corresponding values in the NIST atomic data compilation [34]. The good agreement between our length and velocity gauge values provides some indication (although not a sufficient one) for the accuracy of the wave functions used in the present study.

2. Method of Calculation

Details of the MCDF method as implemented in the GRASP2K code can be found in References [32,33]. For the nuclear charge distribution within the 56Fe nucleus, we used the default Fermi distribution parameters suggested in GRASP2K. The initial estimate for the radial orbitals is generated by solving the Dirac equation in a Thomas-Fermi potential for a single reference configuration (i.e., the 2s2 level for even levels and the 2s2p level for odd levels) by allowing the single, double, triple, and quadruple excitations to active orbital sets with n = 2, 3, 4, 5. The self-consistent procedure (RSCF) including EOL type calculations (extended optimal levels) is done layer by layer, at each stage the outer orbitals are optimized. The EOL type calculations construct orbitals from an average energy functional in which the fine-structure levels are given the weight (2J + 1) [30]. This procedure is performed for every J-value separately. The splitting of the atomic levels into different groups has been found to be a useful compromise between two basic requirements in the atomic calculations, first, to get accurate wave functions for the radiative-rate calculations, and second, to keep the procedures manageable even with a large number of CSFs [35]. The same computational method has been applied to the even parity levels. The RSCF calculations were followed by relativistic configuration interaction (RCI) calculations including the Breit interaction Hamiltonian [36]. For the Breit interaction, we used the default low-frequency-limit approximation of the first-order perturbation theory, as implemented in the GRASP2K code. The GRASP2K procedure JJ2LSJ was used for the transformation of ASFs (atomic state functions) from a jj-coupled CSF basis into a LSJ-coupled CSF basis [37].
The beryllium-like iron atomic system has four electrons. In the ground state two electrons reside in the closed K-shell and the other two in the closed 2s subshell. In the first step of building the ground state wave function of the beryllium-like ion, only interactions between the two outer shell electrons were considered. In a second step the interaction with the atomic core was additionally considered since it is very important for the calculation of the wave functions of the excited states. The ground level of the Fe22+ ion is the 1s22s2 1S0 level, and the excited levels under consideration in this work belong to 1s2 nl n′l′ configurations, where n = 2, 3 and n′ = 2, 3, 4, 5 and l = s, p, d and l′ = s, p, d, f, g with different angular momenta and parities. The open K-shell states are already included in our calculations as admixing correlations, but not explicitly provided. We categorized these levels into groups having the same angular momentum and parity. For example the even parity states with J = 3 are represented by 57161 jj-coupled CSF. As shown in Table 1, the wave function expansions increase rapidly in size by increasing nl which means that we can get unpractically high numbers of CSFs for n > 5. The numbers of CSFs which are generated by quadruple excitations are shown in Table 1 which illustrates the degree of complexity of the present calculations.

3. Results and Discussion

The calculated total energies (in a.u.) and energy levels (in eV) are shown in ascending order in Table 2 where also comparisons with literature values [26,34,38,39] are included. Our calculated level energies for Fe22+ are in good agreement with the NIST levels [34]. The relative deviation is generally better than 1.0%, except for the levels (2); 1s22s2p(3P0) and (3); 1s22s2p(3P1), where the relative deviations from NIST energies are 1.16% and 1.21%, respectively. These deviations may be due to the limited numbers of CSFs in the calculations. However, including more correlations by adding 6l orbitals to the expansion would produce a number of CSFs greater than our computer memory can tolerate. As an illustration, the number of CSFs generated by quadruple (Q) excitation to 6l orbitals with JP = 2+ is 260,702. The energy of level 33, 1s22p3d(1D2), differs from the corresponding NIST [34] value by 0.13%, while the values by Del Zanna et al. [26] and the CHIANTI database [38] deviate from the NIST [34] value by 0.94% and 0.97%, respectively.
One might wonder whether quadruple excitations are really necessary. Two examples illustrate the improvement of the results when quadruple excitations are included. The first example is level 14, 1s22s3p(3P0), for which the present calculation gives an energy of 1124.70 eV which agrees to within less than 0.2% with the value 1126.47 eV recorded in the CHIANTI database [38]. If only triple excitations are included in the calculations the level energy drops to 1109.07 eV with an increase of the deviation from the CHIANTI energy by as much as 1.5%. The second example, that we want to mention, is level 21, 1s22p3s(3P0), which has a calculated energy of 1158.54 eV. This corresponds reasonably well to the NIST energy [34] 1152.40 eV with a relative difference of less than 0.55%. Again, when only triple excitations are considered, the level energy drops drastically, in this case to 1143.12 eV producing a difference in the resulting level energy of 15.42 eV and a relative deviation from the NIST energy of about 0.9%. Obviously, the agreement of the calculations with the CHIANTI and NIST databases becomes considerably better with the use of 4-electron excitations.
Dirac-Fock wave functions with a minimum number of radial functions are not sufficient to represent the occupied orbitals. Extra configurations have to be added to adequately represent electron correlations (i.e., mixing coefficients). These extra configurations are represented by CSFs and must have the same angular momentum and parity as the occupied orbital [40]. For instance, the level 1 s 2 2 s 2 p ( 3 P 0 − ) is represented by 0.996 of 1 s 2 2 s 2 p ( 3 P 0 − ) and 0.0660 of 1 s 2 2 s 3 p ( 3 P 0 − ). The mixing coefficients for the wave functions of some calculated levels are shown in Table 3. The most important contributions to the total wave function of a given level are those from the same configuration. For example, the configuration-mixed wave function for the 1s22p3p(3P0) level is represented as
| 1 s 2 2 p 3 p ( 3 P 0 ) 〉 = 0.9501 | 1 s 2 2 p 3 p ( 3 P 0 ) 〉 + 0.3 | 1 s 2 2 p 3 p ( 1 S 0 ) 〉 − 0.0697 | 1 s 2 2 s 3 s ( 1 S 0 ) 〉
where 0.9501, 0.3, and −0.0697 are the configuration mixing coefficients. Coefficients less than 0.05 were calculated but are not explicitly given. Expansion coefficients for several levels by Bhatia and Mason [10] are listed in Table 3 for comparison. Clearly, the present and the previous [10] results are very close to one another in the description of the configuration-interaction wave functions.
A comparison between the calculated wavelengths and other published experimental and theoretical values [1,2,8,24,26,28,29,34,41] is shown in Table 4. The accuracy of calculated wavelengths (in Å) relative to measurements [24,26,34] can be assessed from Table 4, where the agreement is within <0.2% for all available transitions such as 1–5; 2s2(1S0)−2s2p(1P1) with a calculated wavelength λ = 132.939 Å which deviates from the measurements [24,26,34] by about ±0.0248 Å and from the calculated wavelength of Reference [42] by about ±0.091 Å. In a few cases the agreement with measurements is slightly worse such as for the transitions 2–7, 3–6, 7–21, and 10–25 with λ =147.922, 172.469, 12.025, and 12.371 Å. In these cases the deviations from the measurements amount to 0.463%, 0.485%, 0.579%, and 0.451%, respectively, which are much greater than the experimental uncertainties. The deviations actually reflect the estimated errors in the wavelengths. In Table 6 many more Fe22+ transitions in the soft X-ray region are listed than in any of the previous studies. This will help with the identification of spectral lines of the solar corona [1,2]. In particular, our calculations presented in Table 6 provide comprehensive new data for Be-like Fe with λ in the range 8 to 17 Å and at 132.85 Å which are very important in the solar spectrum [3,4].
The calculated values of transition probabilities in s−1, oscillator strengths f, and line strengths S in a.u. (in both velocity and length forms) are listed in Table 6. A comparison between the present calculations of oscillator strengths (fL) and other published data [8,24,26,29,34,41] is presented in Table 4. Most of our calculations of oscillator strengths show a good agreement with the NIST [34] values, but in a few cases the relative differences reach tens of %. Actually, the NIST values are a compilation of experimental and theoretical data from previous works [8,41,43–47], and the estimated accuracies of most oscillator strengths and transition probabilities recorded in the NIST database [34] are quoted to be between 25% and 50%. For transitions 1–5, 2–7, and 3–6 the uncertainty of the NIST data is estimated to be ≤ 10%. The largest deviation in our calculations of oscillator strengths is found for the transition 3–23 where the deviation from NIST is 36%. Generally, this error is still acceptable for oscillator strengths as is shown in previous publications, where the fL values for the transition 1–49 in References [24,26] differ from the corresponding NIST [34] value by 35% and 33.25%, respectively, and for the line 5–48 the difference is 20% [26]. Our deviations for the same lines are about 6.75%, 12%, respectively. The transition 1–5 has an experimental fL-value of 0.15 [48] with an estimated accuracy of 10%. The agreement of our calculated value with this reference [48] is within 2%. In the study by Jian-Hui et al. [28], significant differences compared with the NIST database [34] are revealed for several fL values, where the deviations of the transitions 5–23, 5–27, and 7–36 are more than one order of magnitude, while our calculations agree with NIST [34] within about 17%, 21.5% and 2.8%, respectively. The precision of the theoretical calculations can be judged by the convergence between length and velocity gauge values of oscillator strengths. If exact wave functions are used then fL = fV [49], which is convincingly fulfilled by the approximate wave functions that are used in our calculations. The average deviation between fL and fV values is about 30%. There are several transitions with much larger deviations such as, the transitions 2–34, 2–47, 2–97, 3–48, 4–154, 11–116, 18–143, 93–149, 134–156, and 140–152. Comparisons between our transition probabilities and values from the NIST database [34] are available for some transitions. For instance, transitions 1–5, 1–13, and 1–15 in Table 6 have AL values of 1.91E+10, 4.99E+12 and 7.94E+12 s−1 while the values from the NIST database for these transitions are 2.0E+10, 4.9E+12 and 7.9E+12 s−1, respectively. A comparison between the present GRASP2K calculations of transition probabilities and other published data [28,41,42,50,51] is shown in Table 5.

4. Conclusions

In the present study, fine structure energy levels, oscillator strengths, line strengths, transition probabilities and wavelengths for transitions among levels belonging to Be-like iron are presented. We have used extensive CI wave functions based on large CSF expansions to produce 182 LSJ-coupling levels with various J-values. The self-consistent field approximation and the Breit interaction Hamiltonian as well as QED effects have been included in the calculations to improve the generated wave functions. The calculated energy levels and weighted oscillator strengths show a good agreement with both theoretical and experimental data from the literature. In addition, we have obtained some new and previously unpublished energy levels for this ion. Our results are useful for many applications such as controlled thermonuclear fusion, laser and plasma physics as well as astrophysics.

Author Contributions

Ahmed Abou El-Maaref suggested the main idea of the paper, performed the calculations, and wrote the great part of the manuscript. Alfred Müller and Stefan Schippers were involved in the discussion, particularly, of the astrophysical data needs, provided the required computer hardware, searched the literature and wrote parts of the manuscript.

Conflicts of Interest

The authors declare no conflict of interest.

Supplement

  • Supplementary File 1:

    Supplementary (XLSX, 127 KB)

    • References

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    Table
    Table 1. Number of configuration state functions (CSFs) used in the atomic state function expansion for the given angular momentum and parity (JP) considering only quadruple excitations.
    Table 1. Number of configuration state functions (CSFs) used in the atomic state function expansion for the given angular momentum and parity (JP) considering only quadruple excitations.
    J+3l4l5lJ−3l4l5l
    0211214913,5920180204013,302
    1436538436,6341460547636,894
    2534725052,4812516716852,238
    3380693057,1613392698857,354
    4228558853,5124222554053,342
    589365043,358590367243,466
    Table
    Table 2. Total energies Etotal (in a.u.) and energy levels (in eV) of Be-like iron (Fe22+). The sixth column lists the present energy levels, and the next 5-columns provide the energies from NIST database [34], the observed energies by Del Zanna et al. [26] and Gu et al. [39], and the calculated (Theor.) and observed (Exp.) values from the CHIANTI database [38].
    Table 2. Total energies Etotal (in a.u.) and energy levels (in eV) of Be-like iron (Fe22+). The sixth column lists the present energy levels, and the next 5-columns provide the energies from NIST database [34], the observed energies by Del Zanna et al. [26] and Gu et al. [39], and the calculated (Theor.) and observed (Exp.) values from the CHIANTI database [38].
    KeyConfigurationJParityEtotalPresentNISTReference [26]Reference [38]
    Theor.    		Reference [38]
    Exp.    		Reference [39]
    11s22s2(1S)0+−812.11233860.000.000.000.000.000.00
    21s22s2p(3P )0−−810.507486543.6743.168843.1642.8643.1343.219
    31s22s2p(3P )1−−810.405698646.4447.00554746.8346.9947.046
    41s22s2p(3P )2−−809.978432758.0758.493358.4958.1658.5158.538
    51s22s2p(1P )1−−808.684908593.2693.286993.2893.7893.3193.308
    61s22p2(3P )0+−807.7638371118.33118.541118.54118.27118.44118.599
    71s22p2(3P )1+−807.4272328127.49127.357127.35126.86127.26127.412
    81s22p2(3P )2+−807.2353664132.71132.874132.87132.87132.84132.937
    91s22p2(1D)2+−806.6250012149.31149.302149.3149.41149.42149.341
    101s22p2(1S)0+−805.6167768176.75176.38176.38176.93176.42176.383
    111s22s3s(3S)1+−771.58172731102.871102.721105.071105.841105.10
    121s22s3s(1S)0+−771.24256091112.11112.771114.731112.80
    131s22s3p(3P )1−−770.82414231123.481125.281125.261126.461125.20
    141s22s3p(3P )0−−770.7793891124.71126.471125.18
    151s22s3p(1P )1−−770.6797081127.411129.121129.161130.221129.20
    161s22s3p(3P )2−−770.65406031128.111129.721130.641129.69
    171s22s3d(3D)1+−770.26006641138.831140.531140.431141.791140.33
    181s22s3d(3D)2+−770.25352331139.011141.771140.631142.391140.96
    191s22s3d(3D)3+−770.17307421141.21142.141142.031143.351141.97
    201s22s3d(1D)2+−769.92898281147.841149.711149.621151.311149.65
    211s22p3s(3P )0−−769.53567861158.541152.431160.331159.01
    221s22p3s(3P )1−−769.4954221159.641162.561161.19
    231s22p3p(3D)1+−769.06718091171.291172.271173.741172.67
    241s22p3s(3P )2−−769.00060321173.11174.911175.291174.46
    251s22p3s(1P )1−−768.78649951178.931174.11180.151181.231180.19
    261s22p3p(3D)2+−768.77895361179.131180.831180.81181.791180.88
    271s22p3p(1P )1+−768.75628871179.751181.071181.941181.03
    281s22p3p(3P )0+−768.56501361184.961184.871183.43
    291s22p3d(3F )2−−768.50681321186.541189.091188.16
    301s22p3p(3P )1+−768.33344841191.261192.91192.22
    311s22p3d(3F )3−−768.2870931192.521193.351193.271194.451193.11
    321s22p3p(3D)3+−768.27759591192.781193.221193.121193.591193.56
    331s22p3d(1D)2−−768.25401911193.421194.961206.111206.611195.29
    341s22p3p(3S)1+−768.22405121194.231195.941195.17
    351s22p3p(3P )2+−768.2184991194.381195.71195.641196.421195.61
    361s22p3d(3D)1−−768.17173351195.661194.841198.031198.491197.51
    371s22p3p(1D)2+−767.92958581202.251203.761203.611204.211203.62
    381s22p3d(3D)2−−767.84570581204.531206.121194.871196.011204.91
    391s22p3d(3F )4−−767.80331021205.681205.091205.331206.13
    401s22p3d(3D)3−−767.70473961208.361208.721209.191209.81209.32
    411s22p3d(3P )1−−767.64263271210.051212.271211.77
    421s22p3d(3P )2−−767.6418391210.081209.221211.631212.181211.80
    431s22p3d(3P )0−−767.59052581211.471212.551212.07
    441s22p3p(1S)0+−767.52651031213.211214.111213.37
    451s22p3d(1F )3−−767.33473151218.431218.81218.611220.051218.89
    461s22p3d(1P )1−−767.32083211218.811218.521221.251220.56
    471s22s4s(3S)1+−757.69065611480.861484.441482.28
    481s22s4s(1S)0+−757.56024441484.41485.451485.41487.31485.43
    491s22s4p(3P )1−−757.38789631489.091490.791491.061492.461490.46
    501s22s4p(3P )0−−757.3700681489.581492.241490.73
    511s22s4p(3P )2−−757.32052431490.931493.931492.42
    521s22s4p(1P )1−−757.30727621491.291493.271493.231494.551493.23
    531s22s4d(3D)2+−757.16116151495.261497.111497.071498.771497.02
    541s22s4d(3D)1+−757.15478871495.441496.861496.831498.571497.25
    551s22s4d(3D)3+−757.10387531496.821497.851497.791499.151497.68
    561s22s4d(1D)2+−757.0516471498.241499.961499.931501.611499.97
    571s22s4f(3F )2−−757.0291911498.851502.111500.45
    581s22s4f(3F )3−−757.00299631499.571502.211500.55
    591s22s4f(1F )3−−756.97468351500.341503.031500.75
    601s22s4f(3F )4−−756.94562571501.131502.391501.37
    611s22p4s(3P )1−−755.80871741532.061535.311532.53
    621s22p4s(3P )0−−755.80242051532.241534.721533.18
    631s22p4p(3D)1+−755.60643841537.571540.471538.88
    641s22p4p(3D)2+−755.4826941540.941542.741543.871542.36
    651s22p4p(3P )1+−755.47678871541.11543.641542.64
    661s22p4d(3F )2−−755.37575011543.851546.681542.87
    671s22p4d(3P )2−−755.30043311545.91547.361548.61545.15
    681s22p4d(3F )3−−755.25864031547.031547.821547.71549.21547.27
    691s22p4d(3D)1−−755.25800341547.051548.311548.221549.881547.79
    701s22p4f(3G)4+−755.2419641547.491551.141548.74
    711s22p4s(3P )2−−755.2298471547.821550.31548.90
    721s22p4f(3F )2+−755.22962581547.821550.981549.08
    731s22p4f(3G)3+−755.22927621547.831550.571549.50
    741s22p4f(3D)3+−755.20931781548.371551.081549.62
    751s22p4s(1P )1−−755.20381211548.521551.121549.62
    761s22p4p(1P )1+−754.98001631554.611556.651549.66
    771s22p4p(3P )2+−754.95988151555.161560.571555.67
    781s22p4p(3D)3+−754.92580141556.091557.21557.121557.481556.78
    791s22p4p(3S)1+−754.9254251556.11558.151556.62
    801s22p4p(1D)2+−754.83947611558.441557.121557.521557.12
    811s22p4d(1D)2−−754.77489591560.21561.831561.791562.341559.90
    821s22p4p(1S)0+−754.72305681561.611564.051561.31
    831s22p4d(3D)3−−754.71344651561.871562.571562.541563.331561.67
    841s22p4d(3P )1−−754.70711091562.041564.061564.021564.281562.55
    851s22p4d(3P )2−−754.70100381562.211563.941563.91564.281563.46
    861s22p4d(3F )4−−754.69409711562.391562.341563.70
    871s22p4f(3F )4+−754.68170781562.731565.571563.66
    881s22p4d(3P )0−−754.67319931562.961564.421563.79
    891s22p4f(3F )2+−754.65111381563.56
    901s22p4f(1G)4+−754.64734171563.671566.631565.69
    911s22p4f(1F )3+−754.64499931563.731565.241564.31
    921s22p4f(3D)3+−754.61158141564.64
    931s22p4f(3D)1+−754.6039511564.851566.911566.04
    941s22p4f(1D)2+−754.59998271564.951566.071565.16
    951s22p4d(1P )1−−754.58935051565.241563.961567.361566.94
    961s22p4d(1F )3−−754.58418231565.381566.041565.881566.781566.04
    971s22s5s(3S)1+−751.3921811652.241653.77
    981s22s5s(1S)0+−751.32922551653.951655.941655.09
    991s22s5p(3P )1−−751.2466591656.21659.281657.83
    1001s22s5p(3P )0−−751.2213211656.891657.73
    1011s22s5p(3P )2−−751.20993551657.21658.66
    1021s22s5p(1P )1−−751.20113081657.441659.281659.281659.03
    1031s22s5d(3D)2+−751.13741521659.1716611661.341661.04
    1041s22s5d(3D)1+−751.1264861659.471657.541660.94
    1051s22s5d(1D)2+−751.08661581660.561666.11666.051662.22
    1061s22s5d(3D)1+−751.1264861659.471659.431660.94
    1071s22s5d(3D)3+−751.08607621660.571661.881661.771661.23
    1081s22s5g(3G)4+−751.08575871660.581662.95
    1091s22s5g(1G)4+−751.08265561660.661663.04
    1101s22s5f(3F )2−−751.06802621661.061662.78
    1111s22s5f(3F )3−−751.0414881661.781662.81
    1121s22s5f(1F )3−−751.02382411662.261663.23
    1131s22s5g(3G)3+−751.02182881662.321662.95
    1141s22s5g(3G)5+−751.02121891662.341663.02
    1151s22s5f(3F )4−−750.97866481663.491662.9
    1161s22p5s(3P )1−−749.5647711701.971703.76
    1171s22p5s(3P )0−−749.53899461702.671703.54
    1181s22p5p(3D)1+−749.45425691704.971706.64
    1191s22p5p(3P )0+−749.40062351706.431708.4
    1201s22p5p(3D)2+−749.39942271706.471708.39
    1211s22p5p(3P )1+−749.39054891706.711708.26
    1221s22p5d(3F )2−−749.34023951708.081709.85
    1231s22p5g(3H)5−−749.30269551709.11712.02
    1241s22p5d(3P )2−−749.29834721709.221710.88
    1251s22p5d(3D)1−−749.28674151709.531711.22
    1261s22p5f(3G)4+−749.28244521709.651712.13
    1271s22p5f(3F )2+−749.27335381709.91712.07
    1281s22p5f(3G)3+−749.26597551710.11711.84
    1291s22p5d(3F )3−−749.26539481710.111711.481711.07
    1301s22p5f(3D)3+−749.25556871710.381712.11
    1311s22p5g(3G)3−−749.23529511710.931711.97
    1321s22p5g(3H)4−−749.16842191712.751711.93
    1331s22p5g(3F )4−−749.16470461712.851712.05
    1341s22p5s(3P )2−−748.98716421717.681719.42
    1351s22p5s(1P )1−−748.97321181718.061719.89
    1361s22p5p(3D)2+−748.85243281721.35
    1371s22p5p(1P )1+−748.85117341721.381723.03
    1381s22p5p(3S)1+−748.82288751722.151723.76
    1391s22p5p(3D)3+−748.81087351722.481723.881723.55
    1401s22p5p(1D)2+−748.79366061722.951723.32
    1411s22p5d(1D)2−−748.74995921724.141726.111725.94
    1421s22p5p(1S)0+−748.72288711724.881726.27
    1431s22p5d(3P )1−−748.72205331724.91726.75
    1441s22p5d(3P )2−−748.71527481725.08
    1451s22p5f(3F )4+−748.71069541725.211727.69
    1461s22p5d(3D)3−−748.70693211725.311726.981726.34
    1471s22p5f(3F )2+−748.69493161725.64
    1481s22p5f(1G)4+−748.69062841725.751728.16
    1491s22p5d(3P )0−−748.68028541726.031726.82
    1501s22p5f(1F )3+−748.67213651726.261727.54
    1511s22p5f(1D)2+−748.67020541726.311727.89
    1521s22p5d(1P )1−−748.66837121726.361728.05
    1531s22p5g(3F )2−−748.66690931726.41728.1
    1541s22p5f(3D)1+−748.66518711726.451728.25
    1551s22p5d(3F )4−−748.6587631726.621725.99
    1561s22p5f(3D)3+−748.65641261726.68
    1571s22p5g(3G)3−−748.65442271726.74
    1581s22p5g(3G)5−−748.65113831726.831727.75
    1591s22p5d(1F )3−−748.64359731727.031728.961727.74
    1601s22p5g(1H)5−−748.64251231727.061727.95
    1611s22p5g(3F )3−−748.639941727.131728.18
    1621s22p5f(3G)5+−748.63225971727.341727.98
    1631s22p5g(3G)4−−748.5995931728.231727.87
    1641s22p5g(3F )4−−748.59224921728.43
    1651s22p4p(3P )0+−746.09265371796.45
    1661s23s2(1S)0+−729.76434032240.75
    1671s23s3p(3P )0−−729.37289512251.4
    1681s23s3p(3P )1−−729.36464072251.63
    1691s23s3p(3P )2−−729.24084852255
    1701s23s3p(1P )1−−728.82093552266.42
    1711s23s3d(1D)2+−728.79620862267.1
    1721s23s3d(3D)1+−728.67745712270.33
    1731s23s3d(3D)2+−728.6672052270.61
    1741s23s3d(3D)3+−728.6041822272.32
    1751s23p2(3P )0+−728.56770892273.31
    1761s23p2(3P )1+−728.51855342274.65
    1771s23p2(3P )2+−728.42709662277.14
    1781s23p3d(3F )2−−728.28117582281.11
    1791s23p3d(3F )3−−728.15454482284.56
    1801s23p3d(1D)2−−728.12388262285.39
    1811s23p2(1D)2+−728.04487652287.54
    1821s23p2(1S)0+−728.04354352287.58
    Table
    Table 3. The configuration mixing coefficients (> 0.05) for some levels in Fe22+. The number in the bra-kets refers to the level number (the key in Table 2).
    Table 3. The configuration mixing coefficients (> 0.05) for some levels in Fe22+. The number in the bra-kets refers to the level number (the key in Table 2).
    JP
    Configuration    		Present WorkReference [10]
    J = 0+
    1s22s2(1S)0.9772 |1⟩ + 0.2058 |10⟩0.98|1⟩ + 0.21 |10⟩
    1s22p2(3P)0.9663 |6⟩ + 0.2431 |10⟩ −0.075 |1⟩0.97 |6⟩ + 0.24 |10⟩ − 0.07 |1⟩
    1s22p2(1S)0.9465 |10⟩ − 0.2533 |6⟩ − 0.19241 |1⟩0.95 |10⟩ − 0.25 |6⟩ − 0.19 |1⟩
    1s22s3s(1S)0.9814 |12⟩ + 0.1688 |44⟩ − 0.0708|48⟩0.99 |12⟩ + 0.17 |44⟩
    1s22p3p(3P)0.9501 |28⟩ + 0.3 |44⟩ − 0.0697 |12⟩
    J = 1+
    1s22p2(3P)0.9992 |7⟩1.00 |7⟩
    1s22s3s(3S)0.9913 |11⟩ + 0.1301 |34⟩0.99 |11⟩ + 0.13 |34⟩
    1s22s3d(3D)0.9896 |17⟩ + 0.1399 |23⟩0.99 |17⟩ + 0.14 |23⟩
    1s22p3p(3D)0.8202 |36⟩ + 0.5328 |27 ⟩ − 0.1612 |34⟩ + 0.1265 |17⟩
    1s22p3p(1P)0.5302 |27⟩ + 0.5204 |34⟩ + 0.4903 |30⟩ + 0.4449 |23⟩
    J = 2+
    1s22p2(3P)0.8640 |8⟩ − 0.5014 |9⟩
    1s22p2(1D)0.8637 |9⟩ + 0.5016 |8⟩
    1s22s3d(3D)0.9903 |18⟩ − 0.1169 |26⟩
    1s22s3d(1D)0.9895 |20⟩ − 0.1180 |37⟩
    1s22p3d(3D)0.9169 |26⟩ − 0.2744 |37⟩ + 0.2595 |35⟩ + 0.1143 |18⟩
    J =3+
    1s22s3d(3D)0.9939 |19⟩ − 0.0943 |32⟩
    1s22p3p(3D)0.9948 |32⟩ + 0.0939 |19⟩
    1s22s4d(3D)0.9976 |55⟩
    1s22p4f(3G)0.8423 |73⟩ + 0.4515 |91⟩ + 0.2737 |89⟩
    J =4+
    1s22p4f(3G)0.6431 |70⟩ − 0.5492 |90⟩ + 0.5300 |87⟩
    1s22p4f(3F)0.8133 |87⟩ − 0.5656 |70⟩ + 0.1220 |90⟩
    1s22p4f(1G)0.8241 |90⟩ + 0.5122 |70⟩ + 0.2327 |87⟩
    1s22s5g(3G)0.8292 |108⟩ +0.5561 |109⟩
    J =5+
    1s22s5g(3G)0.9982 |114⟩
    1s22p5f(3G)0.9980 |162⟩
    J =0−
    1s22s2p(3P)0.9960 |2⟩ + 0.0660 |14⟩1.00|2⟩
    1s22s3p(3P)0.9908 |14⟩ − 0.0821 |43⟩
    1s22p3s(3P)0.9927 |21⟩ + 0.0714 |43⟩
    1s22p3d(3P)0.9918 |43⟩ + 0.0860 |14⟩
    J =1−
    1s22s2p(3P)0.9840 |3⟩ + 0.1564 |5⟩0.99 |3⟩ + 0.16 |5⟩
    1s22s2p(1P)0.9833 |5⟩ − 0.1568 |3⟩0.99 |5⟩ − 0.16 |3⟩
    1s22s3p(3P)0.7772 |13⟩ + 0.5935 |15⟩ − 0.1644 |25⟩0.80 |13⟩ + 0.58 |15⟩ − 0.16 |25⟩
    1s22s3p(1P)0.7411 |15⟩ − 0.6127 |13⟩ − 0.238 |25⟩0.76 |15⟩ − 0.59 |13⟩ − 0.24 |25⟩
    J =2−
    1s22s2p(3P)0.9965 |4⟩
    1s22s3p(3P)0.9890 |16⟩
    1s22p3s(3P)0.9843 |24⟩
    1s22p3d(3F)0.8727 |29⟩ + 0.4391 |33⟩ + 0.1375 |38⟩
    J =3−
    1s22p3d(3F)0.8829 |31⟩ + 0.3724 |40⟩ − 0.2776 |45⟩
    1s22p3d(3D)0.8737 |40⟩ − 0.4342 |31⟩ − 0.2094 |45⟩
    1s22p3d(1F)0.9344 |45⟩ + 0.3064 |40⟩ + 0.1649 |31⟩
    1s22s4f(3F)0.9807 |58⟩ + 0.1863 |59⟩
    J =4−
    1s223d(3F)0.9970 |39⟩
    1s22s4f(3F)0.9983 |60⟩
    1s22p4d(3F)0.9973 |86⟩
    J =5−
    1s22p5g(3G)0.8469 |158⟩ − 0.4368 |2p5g(3H)⟩ + 0.2964 |160⟩
    1s23d4f (3H)0.9974 |268⟩
    Table
    Table 4. Comparison between the present calculations of oscillator strengths fL (calc) and wavelengths (λcalc in Å) and other published data for some transitions in Be-like iron. LL. = lower level; UL. = upper level, λNIST denotes the Ritz wavelength from the NIST database spectra.
    Table 4. Comparison between the present calculations of oscillator strengths fL (calc) and wavelengths (λcalc in Å) and other published data for some transitions in Be-like iron. LL. = lower level; UL. = upper level, λNIST denotes the Ritz wavelength from the NIST database spectra.
    LL.UL.fL (calc)fL Reference [34,38]Other fL ValuesλcalcOther Values of λλobsλNIST
    151.52E−011.55E−0111.50E−01a, 1.55E−01b, 1.54E−01c132.939132.906a, 132.830d132.906132.910
    1132.73E−012.70E−0112.50E−01a, 2.50E−01b, 2.54E−01c11.03611.0063a, 11.018b, 11.017c11.01811.020
    1154.32E−014.30E−0114.10E−01a, 4.10E−01b, 4.14E−01c10.99710.9697a, 10.980b, 10.980c10.98010.980
    1229.82E−031.27E−0221.30E−02b, 2.11E−02c10.69110.6642, 10.6645b, 10.505c
    1365.97E−035.92E−0325.00E−03b, 5.91E−03c10.36910.3492, 10.3448b, 10.349c10.377
    1412.41E−042.32E−0422.00E−04b, 2.32E−04c10.24610.2332, 10.2272b, 10.227c
    1461.94E−021.90E−0221.70E−02b, 1.89E−02c10.17210.1522, 10.152b, 10.153c10.175
    1493.73E−024.00E−0212.60E−02a, 2.60E−02b, 3.60E−02d8.3268.3072a, 8.315b, 8.316d8.3178.320
    1521.55E−011.50E−0111.40E−01a, 1.40E−01b, 1.54E−01d8.3148.2956a, 8.303b, 8.303d8.3058.300
    1755.55E−044.65E−0423.00E−04b8.0077.9932, 7.9931b
    1846.79E−057.35E−0526.30E−05b7.9377.9272, 7.9258b7.927
    1955.44E−030.00E+0024.60E−03b7.9217.9272, 7.9102b
    11028.18E−026.30E−0216.30E−02d7.4807.480d7.4727.470
    276.21E−026.43E−0216.34E−02b, 6.43E−02e147.922147.254b, 146.900e147.240147.300
    2112.37E−022.70E−0212.47E−02c, 1.85E−02f11.70511.676c11.702
    2177.47E−017.50E−0117.51E−01c, 7.7E−01d, 6.58E−01f11.32011.299c, 11.298d, 11.285g11.29811.300
    2541.38E−011.40E−0111.30E−01a, 1.30E−01d8.5408.529a, 8.528d8.5298.530
    361.80E−021.85E−0211.83E−02a172.469173.318a173.310173.300
    3112.43E−022.70E−0212.48E−02c, 1.89E−02f11.74011.718c, 11.702g11.74811.740
    3171.82E−011.80E−0111.23E−01c, 1.65E−01f11.35011.338c, 11.366g11.338
    3233.14E−024.90E−0212.50E−01c11.02011.003c11.018
    3543.37E−023.50E−0213.23E−02a8.5608.551a8.550
    5232.48E−023.00E−0216.46E−06c11.50011.113c11.491
    5272.59E−023.30E−0211.06E−03c11.41011.033c11.398
    5484.17E−033.70E−0313.70E−03d8.9128.910d8.9068.910
    6361.27E+001.29E+0011.27E+00c, 1.29E+00d11.50811.486c, 11.489d11.51911.520
    6692.34E−012.30E−0112.40E−01a8.6788.672a8.6728.670
    7212.07E−021.70E−02112.02512.09512.100
    7369.15E−028.90E−0217.45E−04c11.60711.822c11.61411.610
    7845.02E−024.90E−0218.6438.6308.630
    10256.44E−025.50E−0212.11E−03c12.37112.579c12.42712.400
    10461.27E+001.29E+0011.28E+00c, 1.30E+00d11.89811.873c, 11.840d11.89811.900
    10751.53E−021.77E−0221.80E−02d9.0389.0222, 9.028d
    10952.37E−013.22E−0228.9298.9352, 8.920h
    1,2f -values and wavelengths from the NIST [34] and CHIANTI [38] databases, respectively;
    aExperimental observations (for λ) and benchmark calculations (for fL) by Del Zanna et al. [26];
    bR-matrix calculations by Chidichimo et al. [24,25];
    cMCDF calculations by Jian-Hui et al. [28];
    dCompilation of experimental and theoretical data by Fuhr et al. [41];
    eMCDF calculations by Cheng et al. [8];
    fRQDO calculations by Charro et al. [29];
    gMeasured wavelengths by Brown et al. [1];
    hMeasured wavelengths by Chen et al. [2]; λobs Observed wavelengths from NIST database [34]. Note: For numbers in this paper, aEb is a × 10b.
    Table
    Table 5. Comparison between the present calculations of transition probabilities (AL in s−1) and other references.
    Table 5. Comparison between the present calculations of transition probabilities (AL in s−1) and other references.
    Trans.PresentFuhr et al.*TheoreticalCHIANTI
    1–51.91E + 101.95E+101.93E+10a1.94E+10
    1–134.99E+124.90E+124.65E+12b4.57E+12
    1–157.94E+127.90E+127.64E+12b7.65E+12
    2–76.31E+096.59E+096.43E+09c6.49E+09
    2–544.19E+124.30E+121.23E+13d4.06E+12
    3–61.21E+101.23E+101.22E+10c1.22E+10
    3–542.97E+123.20E+122.97E+12d2.95E+12
    3–767.03E+118.30E+111.86E+12d4.87E+11
    6–696.91E+126.80E+122.10E+13d7.00E+12
    7–844.42E+124.40E+124.43E+12d4.41E+12
    *Compilation of experimental and theoretical data [41];
    aCalculated data by Cheng et al. [50];
    bCalculated data by Jian-Hui et al. [28];
    cCalculated data by Nussbaumer and Storey [42];
    dCalculated data by Wyart et al. [51]; CHIANTI: Compilation of experimental and theoretical data by the CHIANTI atomic database [38].
    Table
    Table 6. Oscillator strengths f, wavelengths (in Å), transition probabilities A (in s−1) and line strengths S (in a.u.) for the transitions in Be-like iron. UL. = upper level; LL. = lower level, V and L indicate velocity and length forms.
    Table 6. Oscillator strengths f, wavelengths (in Å), transition probabilities A (in s−1) and line strengths S (in a.u.) for the transitions in Be-like iron. UL. = upper level; LL. = lower level, V and L indicate velocity and length forms.
    LL.UL.λALAVfLfVSL
    15132.9391.91E+101.55E+101.52E−011.23E−016.64E−02
    1311.0364.99E+125.30E+122.73E−012.90E−011.05E−02
    1510.9977.94E+127.44E+124.32E−014.05E−011.56E−02
    2210.6911.91E+112.61E+119.82E−031.34E−023.46E−04
    3610.3691.24E+111.20E+115.97E−035.80E−032.04E−04
    4110.2465.11E+094.79E+092.41E−042.26E−048.14E−06
    4610.1724.16E+114.21E+111.94E−021.96E−026.48E−04
    498.3261.20E+121.11E+123.73E−023.47E−021.02E−03
    528.3144.99E+124.69E+121.55E−011.46E−014.24E−03
    758.0071.92E+101.84E+105.55E−045.30E−041.46E−05
    847.9372.40E+092.33E+096.79E−056.60E−051.77E−06
    957.9211.93E+111.85E+115.44E−035.22E−031.42E−04
    997.4865.85E+114.64E+111.47E−021.17E−023.63E−04
    1027.4803.25E+122.53E+128.18E−026.38E−022.02E−03
    1437.1881.33E+091.09E+093.10E−052.52E−057.33E−07
    1527.1829.94E+108.45E+102.31E−031.96E−035.45E−05
    27147.9226.31E+094.59E+096.21E−024.52E−022.20E−02
    1111.7053.85E+113.32E+112.37E−022.04E−029.14E−04
    1711.3211.30E+131.30E+137.47E−017.51E−012.80E−02
    2310.9958.07E+111.05E+124.39E−025.70E−022.06E−03
    2710.9133.10E+123.23E+121.66E−011.73E−016.21E−03
    3010.8046.14E+114.51E+113.22E−022.37E−028.42E−04
    3410.7761.40E+117.15E+107.33E−033.74E−031.33E−04
    478.6271.89E+111.21E+116.34E−034.05E−031.15E−04
    548.5404.19E+124.09E+121.38E−011.34E−013.77E−03
    658.2998.30E+118.07E+112.57E−022.50E−026.83E−04
    768.2801.94E+121.85E+125.99E−025.69E−021.55E−03
    798.2062.26E+102.18E+106.85E−046.59E−041.78E−05
    978.1505.83E+072.45E+061.74E−067.33E−081.97E−09
    1187.4635.50E+114.57E+111.38E−021.14E−022.81E−04
    36172.4691.21E+107.63E+091.80E−021.13E−023.06E−02
    8143.7204.05E+095.31E+099.89E−031.30E−028.21E−02
    1111.7361.17E+129.64E+112.43E−021.99E−022.31E−03
    1711.3509.51E+129.42E+121.82E−011.80E−012.04E−02
    1811.3481.71E+131.70E+132.06E−022.05E−021.64E+00
    2011.2571.09E+111.05E+111.27E−041.23E−049.96E−03
    2311.0222.08E+121.72E+123.14E−022.59E−023.41E−03
    2610.9464.15E+123.70E+124.48E−034.00E−033.33E−01
    2710.9409.30E+111.02E+121.84E−022.01E−021.99E−03
    2810.8908.09E+127.40E+124.80E−024.37E−025.15E−03
    3010.8302.07E+122.10E+123.70E−023.75E−023.95E−03
    3710.7272.43E+112.40E+112.47E−042.44E−042.07E−02
    4410.6261.20E+119.83E+106.77E−045.53E−047.08E−05
    488.6225.54E+104.19E+102.06E−041.56E−041.75E−05
    538.5575.47E+125.63E+122.82E−032.90E−033.09E−01
    548.5562.97E+123.06E+123.37E−023.47E−022.84E−03
    568.5403.34E+103.45E+101.71E−051.77E−051.89E−03
    648.2962.37E+122.49E+121.12E−031.17E−031.28E−01
    658.2951.32E+121.46E+121.51E−021.67E−021.24E−03
    768.2217.03E+117.59E+117.83E−038.46E−036.41E−04
    798.2135.66E+115.50E+115.57E−035.41E−034.53E−04
    808.2002.80E+112.82E+111.27E−041.28E−041.42E−02
    828.1836.22E+115.96E+112.08E−032.00E−031.68E−04
    1037.6882.44E+122.70E+129.12E−041.01E−031.20E−01
    1057.6811.70E+101.87E+106.34E−066.99E−068.29E−04
    1187.4757.32E+119.19E+117.70E−039.67E−035.68E−04
    1207.4691.20E+121.41E+124.11E−044.83E−045.90E−02
    1217.4684.03E+115.03E+114.20E−035.24E−033.10E−04
    1377.4022.56E+112.53E+112.08E−032.06E−031.52E−04
    1407.3951.77E+111.91E+115.90E−056.35E−057.82E−03
    41111.8671.62E+122.01E+121.03E−011.27E−014.01E−03
    1711.4726.20E+116.25E+113.67E−023.70E−021.39E−03
    1811.4705.54E+125.57E+125.46E−015.49E−012.06E−02
    2011.3771.90E+102.02E+101.85E−031.96E−036.91E−05
    2910.9415.25E+114.16E+112.83E−022.24E−021.02E−03
    3410.9125.71E+125.72E+123.06E−013.06E−011.10E−02
    538.6271.81E+121.76E+121.01E−019.82E−022.86E−03
    548.6262.01E+111.98E+116.73E−036.62E−031.91E−04
    568.6091.70E+101.39E+109.47E−047.73E−042.68E−05
    768.2856.84E+116.82E+112.11E−022.11E−025.76E−04
    778.2822.29E+122.25E+121.18E−011.16E−013.21E−03
    798.2762.48E+122.22E+127.63E−026.85E−022.08E−03
    808.2637.17E+117.33E+113.67E−023.75E−029.98E−04
    937.7449.80E+108.90E+102.64E−032.40E−036.73E−05
    1037.7438.62E+117.82E+113.88E−023.52E−029.88E−04
    1047.7429.80E+108.94E+102.64E−032.41E−036.73E−05
    1057.7378.83E+097.77E+093.96E−043.49E−041.01E−05
    1217.5204.71E+114.21E+111.18E−021.05E−022.89E−04
    1367.4541.30E+121.15E+125.43E−024.79E−021.33E−03
    1377.4501.46E+121.11E+123.64E−022.78E−028.92E−04
    1407.4474.36E+114.02E+111.81E−021.67E−024.44E−04
    1547.4319.06E+092.61E+092.56E−057.36E−062.36E−06
    58314.3332.76E+083.49E+087.05E−038.91E−032.58E−02
    9221.1943.72E+094.43E+093.31E−023.94E−021.62E−01
    1711.8581.83E+111.84E+113.87E−033.89E−034.54E−04
    1811.8561.08E+111.08E+111.48E−041.48E−041.14E−02
    2011.7571.64E+131.61E+132.19E−022.15E−021.66E+00
    2311.5011.36E+121.25E+122.48E−022.28E−022.82E−03
    2611.4183.53E+114.32E+114.32E−045.28E−044.22E−02
    2711.4111.49E+121.33E+122.59E−022.31E−022.92E−03
    2811.3572.43E+112.48E+111.57E−031.60E−031.76E−04
    3011.2923.38E+123.13E+125.97E−025.53E−026.66E−03
    3411.2613.36E+113.02E+115.73E−035.15E−036.38E−04
    3511.2602.04E+122.23E+122.39E−032.61E−032.12E−01
    3711.1806.84E+127.63E+127.86E−038.77E−037.15E−01
    4411.0707.53E+127.26E+124.60E−024.43E−025.04E−03
    478.9359.40E+091.23E+101.47E−041.93E−041.30E−05
    488.9121.05E+128.33E+114.17E−033.31E−033.66E−04
    538.8431.44E+101.43E+108.18E−068.15E−068.40E−04
    548.8426.54E+106.63E+107.77E−047.87E−046.79E−05
    568.8256.25E+126.36E+123.53E−033.59E−033.71E−01
    648.5644.47E+114.62E+112.31E−042.39E−042.54E−02
    658.5632.83E+113.53E+113.90E−034.86E−033.29E−04
    768.4841.63E+121.95E+122.10E−022.51E−021.76E−03
    778.4818.04E+118.28E+114.04E−044.15E−044.46E−02
    798.4764.64E+115.68E+116.10E−037.47E−035.12E−04
    808.4622.28E+122.35E+121.14E−031.17E−031.26E−01
    828.4442.28E+122.74E+128.13E−039.77E−036.77E−04
    898.4321.07E+101.23E+105.28E−066.09E−066.58E−04
    938.4255.95E+075.63E+076.00E−075.68E−074.98E−08
    948.4251.73E+102.16E+108.52E−061.06E−051.15E−03
    1037.9183.17E+093.51E+091.29E−061.43E−061.65E−04
    1057.9113.11E+123.31E+121.27E−031.35E−031.55E−01
    1207.6863.01E+113.50E+111.12E−041.31E−041.55E−02
    1217.6841.09E+111.89E+111.67E−032.90E−031.27E−04
    1367.6153.96E+114.61E+111.44E−041.68E−042.01E−02
    1407.6081.09E+121.27E+123.96E−044.60E−045.51E−02
    62211.9061.09E+129.02E+116.93E−025.75E−022.72E−03
    2511.6904.03E+103.58E+102.48E−032.20E−039.53E−05
    3611.5082.14E+132.12E+131.27E+001.26E+004.83E−02
    4111.3573.10E+103.25E+101.80E−031.89E−036.73E−05
    4611.2664.43E+114.54E+112.53E−022.59E−029.37E−04
    698.6786.91E+125.51E+122.34E−011.87E−015.33E−03
    758.6691.23E+111.11E+114.16E−033.76E−031.19E−04
    848.5882.26E+091.95E+097.49E−056.45E−052.12E−06
    958.5695.62E+115.11E+111.86E−021.69E−025.23E−04
    1527.7103.35E+113.09E+118.95E−038.27E−032.27E−04
    72112.0252.87E+122.54E+122.07E−021.83E−022.18E−03
    2212.0125.70E+114.96E+111.42E−021.23E−021.46E−03
    2411.8571.01E+121.13E+123.56E−023.98E−024.66E−03
    2511.7921.20E+111.04E+112.89E−032.51E−032.92E−04
    2911.7072.44E+112.45E+118.34E−038.39E−039.70E−04
    3311.6311.27E+131.27E+134.29E−014.29E−014.93E−02
    3611.6074.53E+124.52E+129.15E−029.13E−021.05E−02
    3811.5111.08E+131.08E+133.57E−013.57E−014.06E−02
    4111.4531.17E+131.17E+132.30E−012.30E−012.60E−02
    4211.4522.07E+122.07E+126.79E−026.77E−027.66E−03
    4311.4381.60E+131.62E+131.04E−011.06E−011.19E−02
    4611.3612.51E+112.51E+114.87E−034.87E−035.46E−04
    529.0911.59E+071.60E+071.95E−071.96E−071.76E−08
    579.0419.09E+068.81E+061.86E−071.80E−071.61E−08
    668.7546.74E+106.59E+101.29E−031.26E−031.09E−04
    678.7415.40E+125.61E+121.03E−011.07E−019.24E−03
    698.7341.24E+121.22E+121.45E−021.42E−021.23E−03
    718.7296.18E+114.94E+111.18E−029.40E−038.10E−04
    818.6542.27E+122.30E+124.25E−024.30E−023.67E−03
    848.6434.42E+124.37E+125.02E−024.97E−024.23E−03
    858.6429.54E+119.80E+111.78E−021.83E−021.56E−03
    888.6375.66E+125.52E+122.11E−022.06E−021.75E−03
    958.6231.44E+111.41E+111.64E−031.60E−031.36E−04
    1227.8444.79E+105.17E+107.36E−047.94E−046.15E−05
    1247.8382.83E+123.14E+124.34E−024.82E−023.73E−03
    1257.8375.53E+114.95E+115.70E−035.10E−033.94E−04
    1417.7659.50E+111.05E+121.43E−021.58E−021.21E−03
    1437.7612.29E+122.05E+122.30E−022.06E−021.58E−03
    1447.7614.79E+115.35E+117.21E−038.05E−036.17E−04
    1497.7563.10E+122.84E+129.33E−038.53E−036.54E−04
    1527.7549.19E+108.10E+109.42E−048.30E−046.35E−05
    1537.7543.56E+083.92E+085.34E−065.89E−064.51E−07
    82212.0731.29E+121.36E+123.35E−033.55E−038.94E−02
    2411.9171.97E+121.77E+122.10E−011.88E−018.22E−03
    2511.8511.11E+111.02E+112.73E−042.51E−046.42E−03
    2911.7651.60E+121.60E+121.66E−011.66E−016.41E−03
    3111.6996.84E+126.88E+129.82E−019.88E−013.78E−02
    3311.6891.55E+121.56E+121.59E−011.60E−016.12E−03
    3611.6641.84E+111.82E+114.31E−044.29E−041.12E−02
    3811.5672.15E+122.16E+122.16E−012.17E−018.21E−03
    4011.5262.30E+132.31E+133.21E+003.23E+001.22E−01
    4111.5085.61E+125.61E+121.27E−021.27E−023.34E−01
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    MDPI and ACS Style

    El-Maaref, A.A.; Schippers, S.; Müller, A. Ab-Initio Calculations of Level Energies, Oscillator Strengths and Radiative Rates for E1 Transitions in Beryllium-Like Iron. Atoms 2015, 3, 2-52. https://doi.org/10.3390/atoms3010002

    AMA Style

    El-Maaref AA, Schippers S, Müller A. Ab-Initio Calculations of Level Energies, Oscillator Strengths and Radiative Rates for E1 Transitions in Beryllium-Like Iron. Atoms. 2015; 3(1):2-52. https://doi.org/10.3390/atoms3010002

    Chicago/Turabian Style

    El-Maaref, Ahmed Abou, Stefan Schippers, and Alfred Müller. 2015. "Ab-Initio Calculations of Level Energies, Oscillator Strengths and Radiative Rates for E1 Transitions in Beryllium-Like Iron" Atoms 3, no. 1: 2-52. https://doi.org/10.3390/atoms3010002

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