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Atoms 2018, 6(2), 25; doi:10.3390/atoms6020025

Article
Energy Levels and Radiative Rates for Transitions in F-like Sc XIII and Ne-like Sc XII and Y XXX
Astrophysics Research Centre, School of Mathematics and Physics, Queen’s University Belfast, Belfast BT7 1NN, Northern Ireland, UK
Received: 29 March 2018 / Accepted: 25 April 2018 / Published: 3 May 2018

Abstract

:
Energy levels, radiative rates and lifetimes are reported for F-like Sc XIII and Ne-like Sc XII and Y XXX for which the general-purpose relativistic atomic structure package (GRASP) has been adopted. For all three ions, limited data exist in the literature but comparisons have been made wherever possible to assess the accuracy of the calculations. In the present work, the lowest 102, 125 and 139 levels have been considered for the respective ions. Additionally, calculations have also been performed with the flexible atomic code (FAC) to (particularly) confirm the accuracy of energy levels.
Keywords:
rare earth elements; energy levels; radiative rates; lifetimes; F-like and Ne-like ions

1. Introduction

Atomic data for several parameters, including energy levels and radiative rates, are required for the diagnostics and modelling of plasmas. Often, the required data are not available experimentally and therefore it becomes necessary to obtain theoretical results. Consequently, a vast amount of theoretical data are available in the literature for a (very) wide range of ions. However, comparatively neglected are the rare earth elements (Sc, Y and those with 57 ≤ Z ≤ 71), although work on their ions is gradually picking momentum. In this paper, we report atomic data for F-like Sc XIII and Ne-like Sc XII and Y XXX.
The importance of Sc ions was realised early by Pryce [1], who speculated that their emission lines may be observed in the visible or near-visible regions of the coronal plasma. However, to the best of our knowledge, no lines of Sc XII or Sc XIII have been observed so far in the astrophysical plasmas. This may also be confirmed by the CHIANTI (http://www.chiantidatabase.org/) database, which stores data for all ions of astrophysical importance, but none for the Sc ions. Nevertheless, several lines of Sc XIII have been measured by Jupén et al. [2] in the laser-produced plasmas. Similarly, energy levels and radiative rates (A-values) have been determined for several ions of the F sequence of which the work by Jönsson et al. [3] is not only the latest, but also the most accurate because differences with the measurements are minimal for the energy levels. Unfortunately, they calculated data only for the lowest three levels of the 2s 2 2p 5 and 2s2p 6 configurations, which are not sufficient for modelling of plasmas because the data are required for a wider range of levels. Therefore, in this work, we cover a much wider range of levels, discussed in Section 2. We also note here that similar data for F-like Y XXXI are not considered here because results have already been reported in a separate paper [4].
Ne-like ions are of interest for the studies of astrophysical, lasing and fusion plasmas, and therefore many workers, such as [5,6,7,8,9,10], have reported data for a wide range of ions. However, for brevity, many of them have not reported data for Sc XII, although Hibbert et al. [9] have listed lifetimes ( τ ) for the lowest 27 levels of the 2s 2 2p 6 and 2s 2 2p 5 3 configurations. The only other results available for comparisons are those of Cogordan and Lunell [5] and Jönsson et al. [10], but are limited to the lowest 27 levels of the 2s 2 2p 6 and 2s 2 2p 5 3 configurations. Therefore, there is a clear need to expand the range of levels for this ion. Similarly, limited results are available in the literature for Y XXX, mainly by [5,6,7,8], whereas Nilsen and Scofield [11] and Silwal et al. [12] have measured wavelengths for a few transitions of this ion, which is of particular interest for the diagnostics of tokamak fusion plasmas, as it is one of the impurity elements. Therefore, our aim is to report a complete set of data for energies and lifetimes for a larger number of levels for all three above named ions and A-values for all transitions among their levels, not only for the dominant allowed electric dipole (E1) type, but also for electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2), which are not only required for complete and reliable plasma models, but are also useful for more accurate determination of lifetimes.

2. Energy Levels

As in our earlier work on several F-like [4,13] and Ne-like [14,15] ions, we adopt the fully relativistic GRASP (general-purpose relativistic atomic structure package) code of Grant et al. [16] to determine the atomic structure, and subsequently to calculate energy levels and A-values. However, this earlier version has been significantly revised by Dr. P.H. Norrington (one of the authors), and is currently hosted at the website: http://amdpp.phys.strath.ac.uk/UK_APAP/codes.html. Similarly, the option of extended average level (EAL), in which a weighted (proportional to 2j+1) trace of the Hamiltonian matrix is minimized, is used. This produces a compromise set of orbitals describing closely lying states with moderate accuracy. This also provides comparable results with other options such as average level (AL).
Since both Sc and Y are moderately heavy elements, both relativistic effects and configuration interaction (CI) are important for the determination of atomic structures. Our adopted version of the GRASP code is fully relativistic, as are the other ones, such as GRASP2K [17], but it cannot handle the inclusion of an extensive CI, or a very large number of configuration state functions (CSF). Therefore, we have also performed calculations with the Flexible Atomic Code (FAC) of Gu [18], hosted at the website https://www-amdis.iaea.org/FAC/. This is also a fully relativistic code and provides a variety of atomic parameters. Not only the code yields data, which, in most instances, are comparable to those generated with GRASP, but the inclusion of a very large CI is also possible with ease and efficiency. Therefore, these parallel calculations serve two purposes, i.e., firstly, the accuracy of the determined energy levels can be assessed, and this is necessary because similar results for a majority of levels are not available with which to compare, as already stated in Section 1, and secondly, the effect of larger CI (if any) can be quantified.

2.1. Sc XIII

With GRASP, we have performed a series of calculations with increasing CI, but mention here only three, namely (i) GRASP1, which includes 113 levels of the 2s 2 2p 5 , 2s2p 6 , 2s 2 2p 4 3, 2s2p 5 3, and 2p 6 3 (11) configurations; (ii) GRASP2, which includes a further eight of 2s 2 2p 4 4 and 2s2p 5 4, giving rise to additional 159 levels; and finally (iii) GRASP3, which includes 501 levels in total from 38 configurations, the additional ones being 2p 6 4, 2s 2 2p 4 5, 2s2p 5 5, and 2p 6 5. However, for brevity, we will discuss results from only our final calculations, but the effect of additional CI will be discussed with those from FAC.
As with GRASP, with FAC too we have performed a series of calculations, but focus on only three, i.e., (i) FAC1, which includes 113 levels as in GRASP1, (ii) FAC2, which includes 501 levels as in GRASP3, and finally (iii) FAC3, which includes in total 38 089 levels arising from all possible combinations of the (2*5) 3*2, 4*2, 5*2, 3*1 4*1, 3*1 5*1, and 4*1 5*1 configurations, plus those of FAC2. Although calculations have also been performed with even larger CI, these are not discussed here because the calculated energy levels show no appreciable differences, either in magnitude or orderings, i.e., the results have fully converged in FAC3. For brevity, for FAC calculations, we have used a short notation here (and elsewhere in the text) for describing configurations. As an example, 3*2 means 33 resulting in 3s3p, 3s3d, 3p3d, 3s 2 , 3p 2 , and 3d 2 .
Our calculated energies for the lowest 102 levels of Sc XIII are listed in Table 1. These levels mostly belong to the 2s 2 2p 5 , 2s2p 6 , 2s 2 2p 4 3, and 2s2p 5 3 configurations, and beyond these from others intermix, such as 2s 2 2p 4 4. However, energies for higher levels can be obtained from the author on request. Our energies calculated with GRASP, without and with the inclusion of Breit and QED (quantum electro-dynamic) effects, are listed in the table, along with all three calculations with the FAC, mentioned above. In addition, the experimental energies, compiled by the NIST (National Institute for Standards and Technology) team and available at the website http://www.nist.gov/pml/data/asd.cfm, are listed here along with the theoretical results of Jupén et al. [2], obtained from the Hartree–Fock Relativistic (HFR) code of Cowan—see [19]. However, these theoretical results have been adjusted with least square fitting with the available measurements for a few levels, and that is the reason that there are no appreciable differences for the levels in common with the NIST. We also note that, for two levels (40/41), the NIST and HFR energies are non differentiable, but not in any of our calculations with both codes.
The contributions of the Breit and QED effects on the energy levels of Sc XIII are not very significant, and are below 0.04 Ryd. However, these contributions have slightly lowered the energies and, subsequently, discrepancies with those of NIST have increased because comparatively there is a better match between the NIST and our energies obtained without them. Nevertheless, discrepancies between our results with GRASP (including the contributions from Breit and QED) and those of NIST are within 0.1 Ryd, and hence are highly satisfactory. Furthermore, there are no discrepancies in the level orderings between theory and measurements, and neither are there any ambiguities in level designations for this ion.
For most of the levels, there are no significant differences between the FAC1 and FAC2 energies, although the latter calculations include CI larger by more than a factor of four. However, for a few levels (such as 83 and 100), the differences are up to 0.04 Ryd, and energies in FAC2 are (mostly) lower. The same are the differences between the GRASP and FAC2 energies that include the same CI, but the latter ones are higher. Such small differences in energies between calculations with different codes are not uncommon and mainly arise due to the differences in algorithms, methodologies and formulations. Our FAC3 calculations include much larger CI and, as a result, the energies obtained are lower, by up to ~0.2 Ryd, in comparison to those from FAC2. This has resulted in a better agreement with the GRASP energies. Although the FAC3 energies should be comparatively more accurate, differences with our GRASP or NIST are up to 0.25 Ryd—see, for example, levels 45–49 and 56–58. Since the FAC3 energies are the lowest, we consider our results with GRASP to be comparatively more accurate, with agreement within 0.1 Ryd (0.3%) with those of NIST, except for level 3 (2s2p 6 2 S 1 / 2 ) for which the discrepancy is 2%, or 0.14 Ryd. For this level, the energy calculated by Jönsson et al. [10] is closer to that of NIST because not only have they included a significantly larger CI, but their methodology is also different. Similarly, combining CI with the many-body perturbation theory (MBPT) approach, Gu [20] calculated the energy 6.945 Ryd, which is lower than that of NIST by only 0.014 Ryd, a tenth of the difference we have.

2.2. Sc XII

As for Sc XIII, for Sc XII, we have also performed a series of calculations with both GRASP and FAC. Our final calculations with GRASP include 3948 levels from 64 configurations, namely 2s 2 2p 6 , 2s 2 2p 5 3 , 2s2p 6 3 , 2s 2 2p 5 4, 2s2p 6 4 , 2s 2 2p 5 5, 2s2p 6 5 , 2s 2 2p 5 6s/p/d, 2s 2 2p 5 7s/p/d, (2s 2 2p 4 ) 3s3p, 3s3d, 3p3d, 3s 2 , 3p 2 , 3d 2 , 3s4, 3s5, 3p4, 3p5, 3d4, and 3d5. Similarly, with FAC, we have performed mainly three sets of calculations, which are: (i) FAC1, which includes 3948 levels of the same configurations as in GRASP, (ii) FAC2, which includes 17 729 levels arising from all possible combinations of 2*8, (2*7) 3*1, 4*1, 5*1, 6*1, 7*1, (2*6) 3*2, 3*1 4*1, 3*1 5*1, 3*1 6*1, and 3*1 7*1, and finally (iii) FAC3, which includes a total of 93,437 levels, the additional ones arising from (2*6) 4*1 5*1, 4*1 6*1, 4*1 7*1, 5*1 6*1, 5*1 7*1, 6*1 7*1, and 2*5 3*3. These calculations are on the same lines as considered for some other Ne-like ions [14,15].
In Table 2, we list our final energies from both GRASP and FAC for the lowest 125 levels because, beyond these from other configurations intermix, particularly from 2s 2 2p 5 6. However, energies for higher levels can be obtained from the author on request. In general, energies obtained in FAC1 (not listed here but discussed below) are lower than of GRASP by ~0.1 Ryd, and both calculations include the same CI. This observation is similar to that noted earlier for Sc XIII. However, the FAC3 energies listed in Table 2 are lower than of GRASP by ~0.2 Ryd, i.e., the effect of additional CI (by more than a factor of 20) is about 0.1 Ryd. In addition, for a few levels, such as 79–84, there are some (minor) differences in energy orderings, but overall there are no (major) discrepancies between calculations with two different codes. This result was expected and has been noted earlier for several ions, including some Ne-like [14,15], although some authors, such as [21], have shown differences of up to ~2 Ryd, but their calculations are incorrect as discussed in [14,15] and further explained in [22,23]—see also [24] for many other examples of discrepancies. Although a good agreement between the two calculations in our work confirms the accuracy of the calculated energies, we discuss these further below.
As stated in Section 1, the only other energies available in the literature, but only for the lowest 27 levels, are by Cogordan and Lunell [5] and Jönsson et al. [10], who have also used (the different versions of) the GRASP code. Since experimental energies compiled by NIST are also available for a few levels of Sc XII, in Table 3, we compare different sets of energies for the lowest 37 levels, which belong to the 2s 2 2p 6 , 2s 2 2p 5 3, 2s2p 6 3, and 2s 2 2p 5 4s configurations. The FAC1 and FAC2 energies differ at most by 0.2 Ryd (see levels 29–33), which indicates a small effect of additional CI included in the latter. However, further inclusion of CI in FAC3 is not of any (great) advantage because differences with FAC2 are below 0.02 Ryd, i.e., the results have converged. However, energy differences between the FAC3 and NIST are the largest, and are up to 0.3 Ryd for several levels, and those from the former are invariably lower. Therefore, as for Sc XIII, energies calculated with FAC for Sc XII too are comparatively less accurate. On the other hand, our calculations (and those of Cogordan and Lunell [5]) with GRASP compare well with those of NIST because the differences are within ~0.1 Ryd (0.3%), with the measurements being (slightly) on the higher side. A notable exception is the level 15 (2s 2 2p 5 3p 1 S 0 ) for which the energy calculated by Cogordan and Lunell is (unusually) lower than our calculation by 0.14 Ryd. In all our calculations (with increasing CI) with the GRASP code, the energy obtained for this level is invariably higher, and the contributions of Breit and QED effects are only 0.02 Ryd. Therefore, the reason for this (comparatively) large difference is neither in the inclusion of (much) larger CI in our calculations nor in the modified version of the code adopted, but is due to the fact that they have treated this level separately in a different manner. Anyway, their calculated energy for this level is as much lower than NIST as ours is higher, and, therefore, the overall differences with measurements remain the same. Finally, the energies calculated by Jönsson et al. [10] are the most accurate because they have been able to produce results closer to those of NIST, for the same reasons as explained in Section 2.1 for Sc XIII.

2.3. Y XXX

For Y XXX, we have performed similar calculations with GRASP and FAC as for Sc XII, described in Section 2.2. In Table 4, we list our final results with both these codes for the lowest 139 levels, as beyond these is an intermix from other configurations, such as 2s 2 2p 5 6. However, energies for higher levels can be obtained from the author on request. As stated in Section 1, similar results for some levels are available in the literature by Zhang and Sampson [7] and Hagelstein and Jung [6], who have used the Dirac–Fock–Slater (DFS) and YODA codes, respectively. The GRASP results are listed with inclusion (GRASP1) and exclusion (GRASP2) of Breit and QED effects because Y XXX is a comparatively heavy ion, and their net effect is to lower the energies by a maximum of 0.4 Ryd. Their effect is comparatively more noticeable on higher levels than the lower ones, and the maximum is on the ground level, i.e., 5.60 Ryd (3.25 + 2.35). The DFS energies, available for 89 levels, are closer to the GRASP2 results, which indicates the neglect of higher order relativistic effects from the calculations. The other results from YODA, although for only the lowest 37 levels, are closer to GRASP1 and agree within 0.1 Ryd, which is highly satisfactory. However, as for the other two ions, the corresponding results with FAC are the lowest among those listed in Table 4, although differing by a maximum of 0.2 Ryd with GRASP1. Before drawing our conclusion, we make a few other comparisons below.
In Table 5, we compare our GRASP results with those of Cogordan and Lunell [5] and Quinet et al. [8], who have used the same code but of different versions. Also included in the table are our results from three calculations with FAC, with increasing CI. All three sets of energies agree within 0.2 Ryd (see level 29) and hence the differences are insignificant, i.e., <0.1%. Similarly, all calculations with GRASP agree within 0.1 Ryd and hence provide confidence in our results listed in Table 4. Since the FAC energies are the lowest, irrespective of the level of CI, these results are assessed to be comparatively less accurate, and therefore our results obtained with the GRASP should be considered to be more accurate, and perhaps the best available to date for a larger number of levels. Further accuracy of our energy levels can be confirmed by the measurements, which, unfortunately, are not yet available for the levels of Y XXX.

3. Radiative Rates

Our results for the A-values calculated with the GRASP code are listed in Table 6, Table 7 and Table 8 for the transitions in Sc XIII, Sc XII and Y XXX, respectively. For brevity, only resonance transitions, i.e., from the ground level, are listed here, but complete results for all transitions in ASCII format are available online as a supplementary material, and the indices for the lower (i) and upper (j) levels correspond to those listed in Table 1, Table 2 and Table 4, for the respective ions. Furthermore, for the E1 transitions, we list absorption oscillator strength ( f i j ) and line strength S (in atomic unit, 1 a.u. = 6.460 × 10 36 cm 2 esu 2 ) apart from the A-values, but only the latter parameter for other types of transitions, i.e., E2, M1 and M2. However, desired results for f- or S-values for these transitions can be easily obtained from the standard equations that have been listed in some of our earlier papers, but are also given below for a ready reference, i.e., for the electric dipole (E1) transitions
A j i = 2.0261 × 10 18 ω j λ j i 3 S E 1 and f i j = 303.75 λ j i ω i S E 1 ,
for the magnetic dipole (M1) transitions
A j i = 2.6974 × 10 13 ω j λ j i 3 S M 1 and f i j = 4.044 × 10 3 λ j i ω i S M 1 ,
for the electric quadrupole (E2) transitions
A j i = 1.1199 × 10 18 ω j λ j i 5 S E 2 and f i j = 167.89 λ j i 3 ω i S E 2 ,
and for the magnetic quadrupole (M2) transitions
A j i = 1.4910 × 10 13 ω j λ j i 5 S M 2 and f i j = 2.236 × 10 3 λ j i 3 ω i S M 2 .
We also note here that f- and A-values are related as
f i j = m c 8 π 2 e 2 λ j i 2 ω j ω i A j i = 1.49 × 10 16 λ j i 2 ω j ω i A j i ,
where m and e are the electron mass and charge, respectively, c is the velocity of light, λ j i is the transition wavelength in Å, and ω i and ω j are the statistical weights of the lower i and upper j levels, respectively. This relationship is the same irrespective of the type of a transition, and λ j i are also listed in Table 6, Table 7 and Table 8 for all possible transitions.
Assessing the accuracy of our calculated results for A-values (and other related parameters) is not straightforward. This is because no measurements are available for any transition of the ions concerned. However, limited theoretical results are available in the literature, which will perhaps be helpful for some accuracy assessments. For Sc XIII, Jönsson et al. [3] have listed A-values for the 1–3 E1 (4.635 × 10 10 s 1 ), 2–3 E1 (1.968 × 10 10 s 1 ), 1–2 M1 (9.773 × 10 2 s 1 ), and 1–2 E2 (3.849 × 10 2 s 1 ) transitions, which match very well (within 10%) with our corresponding results of 5.143 × 10 10 , 2.193 × 10 10 , 9.571 × 10 2 , and 3.849 × 10 2 s 1 , respectively. However, this direct comparison of A-values is very limited. Some further assessments of accuracy can be made by comparing the length and velocity forms (i.e., the Babushkin and Coulomb gauges in the relativistic terms) of the A-values, and their ratio (R) for all E1 transitions are listed in Table 6, Table 7 and Table 8. Ideally, R should be closer to unity, but, in practice, it is not, particularly for the weak(er) transitions. For many strong transitions with f ≥ 0.1, R is within 10% of unity as may be noted for the 1–49/52/55/56/59 transitions in Table 6. However, for 22 transitions (all with f ≤ 0.2), R is up to 2 and examples include 9–26/78, 10–25/79 and 25–50/89. Similarly, for a few very weak transitions, R can be up to several orders of magnitude, and some examples are: 3–18 (f = 5.9 × 10 6 , R = 164), 3–21 (f = 3.8 × 10 4 , R = 83) and 3–23 (f = 4.0 × 10 5 , R = 357). For such weak transitions, the modelling of plasmas is not affected and similar large values of R are often noted for almost all ions in any large calculation.
For Sc XII, A-values for all types of transitions, but only among the lowest 27 levels, have been reported by Jönsson et al. [10] and, therefore, in Table 9, we make comparisons for the E1 and E2 transitions from the lowest five to higher excited levels. Generally, for all E1 transitions, the agreement between the two calculations is within ~20%, which is highly satisfactory. However, for three weak transitions, namely 2–11 (f = 1.2 × 10 4 ), 3–13 (f = 1.2 × 10 4 ) and 5–9 (f = 4.4 × 10 5 ), discrepancies are up to a factor of two. As already stated above, accuracies for such weak transitions are often not reliable and hence any of the two calculations can be (in)correct. Similarly, for the comparatively weak E2 transitions, the two calculations agree within 20% for most, but discrepancies are up to a factor of two for four (2–24, 3–24, 3–25, and 5–20), whereas it is factor of four for one, i.e., 5–21 (f = 3.2 × 10 10 ). Similar comparisons for the M1 and M2 transitions are made in Table 10. There are no appreciable discrepancies for the M2 transitions (except for 1–25), but, for a few M1, the differences are up to two orders of magnitude, see in particular 2–18 for which our f = 9.7 × 10 13 . Such weak transitions (and discrepancies between different calculations) do not affect the modelling, or the subsequent calculations of lifetimes, τ = 1.0/ Σ i A j i , which includes contributions from all types of transitions, i.e., E1, E2, M1, and M2. This is further confirmed by comparing our results for τ , included in Table 6, Table 7 and Table 8, for the lowest 27 levels of Sc XII in Table 11, with those of Hibbert et al. [9] and Jönsson et al. [10], for which the agreements are within 10% for most levels.
For Y XXX, the only results available in the literature for comparison purposes are the f-values of Zhang and Sampson [7] for E1 transitions from the ground level and these are compared in Table 12. For a few weak transitions, the differences are large, in particular for 1–63 (2s 2 2p 6 1 S 0 – 2s 2 2p 5 4s 3 P 1 o ), a spin changing inter-combination transition, for which our f-value is very small (∼10 6 ), and subsequently the discrepancy is of three orders of magnitude. However, such comparisons are very limited and hence cannot be confidently relied upon. In conclusion, on the basis of the (whatever possible) comparisons have been made for all three ions, our experience on a wide range of other ions, including F-like [4,13] and Ne-like [14,15], and considering that we have included a large CI as well as relativistic effects in generating wavefunctions, we assess the accuracy of our radiative rates to be about 20%, for a majority of strong transitions with f ≥ 0.1.

4. Conclusions

In this paper, energy levels have been reported for three ions, namely F-like Sc XIII and Ne-like Sc XII and Y XXX. For the calculations, the GRASP code has been adopted and CI has been included among a large number of configurations. Additional calculations have also been performed with FAC, by including even larger CI. This was necessary for accuracy assessments [24] because the existing data available for these ions are very limited. Energies have been listed for the lowest 102, 125 and 139 levels of the respective ions, although calculations have been performed for much larger ranges. This is because beyond these levels is a mixing from other configurations. However, energies for higher levels can be obtained from the author on request. On the basis of a variety of comparisons, the listed energies (in general) are assessed to be accurate to better than 1% for most levels. However, this assessment of accuracy may change if laboratory measurements in the future become available for a larger number of levels.
Radiative rates are also presented for four types of transitions, namely E1, E2, M1, and M2. Again, very limited comparisons are possible because of the paucity of other available data. However, for the majority of strong transitions, the accuracy is assessed to be ~20%, which is primarily based on comparisons between the length and velocity forms. Any estimates of accuracy for particularly weak transitions with very small f-values will be unreliable. The calculated A-values have been used to determine lifetimes and have been listed for all levels. No measurements have so far been performed for any level of the three ions concerned, and theoretical results are available for only the lowest 27 levels of Sc XII, for which there are no (large) discrepancies. We hope our results listed for a large number of levels/transitions will be useful for the modelling and diagnostics of a variety of plasmas, fusion in particular.

Supplementary Materials

The data files are available online at http://www.mdpi.com/2218-2004/6/2/25/s1.

Conflicts of Interest

The author declares no conflict of interest with anyone.

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Table 1. Energies (in Ryd) and lifetimes ( τ , s) for the lowest 102 levels of Sc XIII. a ± ba × 10 ± b .
Table 1. Energies (in Ryd) and lifetimes ( τ , s) for the lowest 102 levels of Sc XIII. a ± ba × 10 ± b .
IndexConfigurationLevelNISTHFRGRASP1GRASP2FAC1FAC2FAC3 τ (GRASP2)
12s 2 2p 5 2 P 3 / 2 o 0.0000.00000.00000.00000.00000.00000.0000……..
22s 2 2p 5 2 P 1 / 2 o 0.3450.34580.35430.34300.34260.34240.34251.045-03
32s2p 6 2 S 1 / 2 6.9596.95887.10717.09787.11527.10217.08771.363-11
42s 2 2p 4 3s 4 P 5 / 2 32.01632.015531.929931.906731.941631.940431.79159.843-11
52s 2 2p 4 3s 4 P 3 / 2 32.17332.170332.089832.066632.106432.107331.94523.494-12
62s 2 2p 4 3s 4 P 1 / 2 32.32432.323532.236132.210432.244032.242932.09256.617-11
72s 2 2p 4 3s 2 P 3 / 2 32.39432.393732.315832.290632.337532.341932.16121.623-12
82s 2 2p 4 3s 2 P 1 / 2 32.57032.569632.494032.468432.521632.528232.33531.093-12
92s 2 2p 4 3s 2 D 5 / 2 32.98332.983332.929932.898432.916932.918832.77102.825-12
102s 2 2p 4 3s 2 D 3 / 2 32.99532.995132.940232.908832.928532.930832.78032.613-12
112s 2 2p 4 3p 4 P 5 / 2 o 33.591033.511233.486033.523133.516433.38134.776-10
122s 2 2p 4 3p 4 P 3 / 2 o 33.607033.524633.503233.540433.534133.39784.386-10
132s 2 2p 4 3p 4 P 1 / 2 o 33.724733.643933.620933.656433.648833.51354.412-10
142s 2 2p 4 3p 4 D 7 / 2 o 33.786933.714833.689133.726033.728333.57822.996-10
152s 2 2p 4 ( 3 P)3p 2 D 5 / 2 o 33.829733.756833.733133.752833.755433.61733.445-10
162s 2 2p 4 3s 2 S 1 / 2 33.88533.885133.772233.748033.775033.779133.65542.766-12
172s 2 2p 4 ( 3 P)3p 2 P 1 / 2 o 33.969233.906433.882333.915533.909433.76782.856-10
182s 2 2p 4 3p 4 D 3 / 2 o 33.988233.915133.889233.926433.928933.77293.208-10
192s 2 2p 4 3p 4 D 1 / 2 o 34.026033.951533.926533.963533.965833.81352.813-10
202s 2 2p 4 3p 4 D 5 / 2 o 34.080234.010433.982734.021134.024833.86243.175-10
212s 2 2p 4 ( 3 P)3p 2 P 3 / 2 o 34.122234.029534.000134.035934.029133.88192.730-10
222s 2 2p 4 3p 4 S 3 / 2 o 34.191334.120334.094934.135034.141233.98041.730-10
232s 2 2p 4 ( 3 P)3p 2 S 1 / 2 o 34.240834.173834.145534.182334.186134.02193.267-10
242s 2 2p 4 ( 3 P)3p 2 D 3 / 2 o 34.232734.179534.150534.191934.196834.02682.310-10
252s 2 2p 4 3p 2 F 5 / 2 o 34.595134.549134.517234.535734.538134.39733.788-10
262s 2 2p 4 3p 2 F 7 / 2 o 34.657134.614934.580334.597934.599834.46073.335-10
272s 2 2p 4 ( 1 D)3p 2 D 3 / 2 o 34.813434.766934.737534.757034.763534.61682.215-10
282s 2 2p 4 ( 1 D)3p 2 D 5 / 2 o 34.852434.808934.776534.796534.803734.65502.420-10
292s 2 2p 4 ( 1 D)3p 2 P 3 / 2 o 35.317535.238435.213535.291535.289535.06623.438-11
302s 2 2p 4 ( 1 D)3p 2 P 1 / 2 o 35.349935.273335.247935.319735.299635.12423.100-11
312s 2 2p 4 ( 1 S)3p 2 P 3 / 2 o 35.657235.559835.535335.555735.554635.44941.052-10
322s 2 2p 4 ( 1 S)3p 2 P 1 / 2 o 35.794235.687635.658535.727435.709635.54201.080-10
332s 2 2p 4 3d 4 D 7 / 2 35.768335.696735.667135.720035.701535.54181.979-10
342s 2 2p 4 3d 4 D 5 / 2 35.778535.705335.677835.745035.726735.54941.877-10
352s 2 2p 4 3d 4 D 3 / 2 35.820035.738335.713135.760535.743635.58247.254-11
362s 2 2p 4 3d 4 D 1 / 2 35.865435.785435.760235.808635.791935.62956.519-11
372s 2 2p 4 3d 4 F 9 / 2 35.948835.884735.855235.899135.889135.72681.705-10
382s 2 2p 4 3d 4 F 7 / 2 36.022535.966135.937535.973335.966835.79221.598-10
392s 2 2p 4 3d 4 P 1 / 2 36.10236.101736.032536.006536.038436.037435.86183.624-12
402s 2 2p 4 3d 4 F 5 / 2 36.16236.161836.101436.071536.110236.103535.92982.505-12
412s 2 2p 4 3d 4 P 3 / 2 36.16236.161836.103036.075736.110836.108335.93272.022-12
422s 2 2p 4 ( 3 P)3d 2 P 1 / 2 36.21536.214736.159236.132836.169436.161435.98642.918-12
432s 2 2p 4 3d 4 F 3 / 2 36.217136.170336.141536.183336.173736.00881.689-11
442s 2 2p 4 ( 3 P)3d 2 F 7 / 2 36.227136.171636.140436.176236.169035.99231.708-10
452s 2 2p 4 3d 4 P 5 / 2 36.25736.257536.197336.167236.202436.198536.02513.312-12
462s 2 2p 4 ( 3 P)3d 2 D 3 / 2 36.30736.306736.253036.225236.260436.253136.07677.388-13
472s 2 2p 4 ( 3 P)3d 2 F 5 / 2 36.33636.335936.284836.253736.284336.281636.09644.289-12
482s 2 2p 4 ( 3 P)3d 2 P 3 / 2 36.45336.453436.405136.372136.402236.395436.21861.771-12
492s 2 2p 4 ( 3 P)3d 2 D 5 / 2 36.49436.523636.457836.423036.457236.452736.26624.378-13
502s 2 2p 4 3d 2 G 7 / 2 36.766236.731036.693536.718536.705636.55691.725-10
512s 2 2p 4 3d 2 G 9 / 2 36.770236.736236.698036.721036.707636.56051.855-10
522s 2 2p 4 ( 1 D)3d 2 S 1 / 2 36.94536.944636.922636.887136.892636.895336.71961.683-13
532s 2 2p 4 ( 1 D)3d 2 F 5 / 2 36.97136.971036.944136.910536.920736.919936.75833.243-12
542s 2 2p 4 ( 1 D)3d 2 F 7 / 2 37.008636.980536.944236.952236.952636.78941.494-10
552s 2 2p 4 ( 1 D)3d 2 P 3 / 2 37.10337.104137.080837.047737.067637.069936.89501.329-13
562s 2 2p 4 ( 1 D)3d 2 D 5 / 2 37.10437.104137.101337.066337.087537.087436.89521.644-13
572s 2 2p 4 ( 1 D)3d 2 D 3 / 2 37.21937.188937.212537.174937.191337.193636.99721.723-13
582s 2 2p 4 ( 1 D)3d 2 P 1 / 2 37.218637.213837.173737.191437.194937.01321.250-13
592s 2 2p 4 ( 1 S)3d 2 D 5 / 2 37.81737.816737.729637.700737.698037.696137.58401.283-12
602s 2 2p 4 ( 1 S)3d 2 D 3 / 2 37.87337.873237.795537.763737.772337.770337.64583.332-13
612s2p 5 3s 4 P 5 / 2 o 38.202638.173638.225338.226238.10032.172-11
622s2p 5 3s 4 P 3 / 2 o 38.368338.335838.389038.389238.25881.090-11
632s2p 5 3s 4 P 1 / 2 o 38.511938.476338.527138.527538.39781.457-11
642s2p 5 ( 3 P)3s 2 P 3 / 2 o 38.657 38.707438.676738.762438.755238.57952.206-12
652s2p 5 ( 3 P)3s 2 P 1 / 2 o 38.858 38.912738.877938.962238.954838.77791.786-12
662s2p 5 3p 4 S 3 / 2 39.675939.645839.693939.690639.58852.118-11
672s2p 5 3p 4 D 7 / 2 39.907039.875439.925339.929439.81372.538-11
682s2p 5 3p 4 D 5 / 2 39.914239.884539.939539.943239.82076.173-12
692s2p 5 3p 4 D 3 / 2 40.005939.975240.029740.033339.91035.149-12
702s2p 5 ( 3 P)3p 2 D 5 / 2 40.097440.067240.122540.125839.99961.897-12
712s2p 5 3p 4 D 1 / 2 40.103040.070040.134840.136740.00401.119-11
722s2p 5 ( 3 P)3p 2 P 3 / 2 40.204940.170940.233040.237940.10081.138-12
732s2p 5 3p 4 P 5 / 2 40.245440.208340.269440.271840.13912.380-12
742s2p 5 3p 4 P 1 / 2 40.268340.233740.296540.295040.16448.976-12
752s2p 5 3p 4 P 3 / 2 40.272740.237540.302640.303440.16762.442-12
762s2p 5 ( 3 P)3p 2 P 1 / 2 40.332240.298040.361940.365440.22508.998-13
772s2p 5 ( 3 P)3p 2 D 3 / 2 40.425840.387440.450840.455840.31391.344-12
782s2p 5 ( 1 P)3s 2 P 3 / 2 o 40.685140.653640.680540.676140.53092.445-12
792s2p 5 ( 1 P)3s 2 P 1 / 2 o 40.703940.672440.701740.696940.54823.133-12
802s2p 5 ( 3 P)3p 2 S 1 / 2 40.775640.742440.812740.791640.65476.595-13
812s2p 5 3d 4 P 1 / 2 o 41.839741.809741.867941.852041.72372.127-11
822s2p 5 3d 4 P 3 / 2 o 41.881341.848541.908141.891541.76301.966-11
832s2p 5 3d 4 F 9 / 2 o 41.931041.895241.971541.939041.82413.837-11
842s2p 5 3d 4 P 5 / 2 o 41.956341.921041.982141.963941.83562.265-11
852s2p 5 3d 4 F 7 / 2 o 41.994241.958742.031441.999941.88243.677-11
862s2p 5 3d 4 F 5 / 2 o 42.077542.041442.113542.083041.96263.450-11
872s2p 5 3d 4 F 3 / 2 o 42.152142.116142.190542.158942.03871.909-11
882s2p 5 3d 4 D 7 / 2 o 42.212142.177042.240442.220442.08502.897-11
892s2p 5 ( 1 P)3p 2 D 3 / 2 42.273242.241842.267542.259442.12871.646-12
902s2p 5 3d 4 D 1 / 2 o 42.324342.288342.357242.331142.20354.572-12
912s2p 5 ( 1 P)3p 2 D 5 / 2 42.343642.309542.336342.326342.19621.957-12
922s2p 5 3d 4 D 5 / 2 o 42.349142.309542.374642.349742.22012.657-11
932s2p 5 3d 4 D 3 / 2 o 42.363342.324642.393742.370942.24017.444-12
942s2p 5 ( 3 P)3d 2 F 7 / 2 o 42.370042.330042.388842.366542.23082.915-11
952s2p 5 ( 3 P)3d 2 D 5 / 2 o 42.401942.365142.422442.407942.25852.755-11
962s2p 5 ( 1 P)3p 2 P 1 / 2 42.452242.421242.435842.441642.30882.255-12
972s2p 5 ( 1 P)3p 2 P 3 / 2 42.485942.453242.468842.472442.34072.618-12
982s2p 5 ( 3 P)3d 2 D 3 / 2 o 42.494642.458342.516042.501842.35072.525-12
992s2p 5 ( 3 P)3d 2 F 5 / 2 o 42.575742.534942.590742.575142.42462.676-11
1002s2p 5 ( 1 P)3p 2 S 1 / 2 42.674942.645642.749642.706242.51357.520-12
1012s2p 5 ( 3 P)3d 2 P 1 / 2 o 42.730742.696942.764242.744342.58881.981-13
1022s2p 5 ( 3 P)3d 2 P 3 / 2 o 42.916542.874742.929442.922142.76261.912-13
NIST: http://www.nist.gov/pml/data/asd.cfm; HFR: Earlier results of Jupén et al. [2]; GRASP1: Present results with the GRASP code for 501 level calculations without Breit and QED effects; GRASP2: Present results with the GRASP code for 501 level calculations with Breit and QED effects; FAC1: Present results with the FAC code for 113 level calculations; FAC2: Present results with the FAC code for 501 level calculations; FAC3: Present results with the FAC code for 38,089 level calculations.
Table 2. Energies (in Ryd) and lifetimes ( τ , s) for the lowest 125 levels of Sc XII. a ± ba × 10 ± b .
Table 2. Energies (in Ryd) and lifetimes ( τ , s) for the lowest 125 levels of Sc XII. a ± ba × 10 ± b .
IndexConfigurationLevelGRASPFAC τ (GRASP)
12s 2 2p 6 1 S 0 0.00000.0000……..
22s 2 2p 5 3s 3 P 2 o 29.385529.20664.462-05
32s 2 2p 5 3s 3 P 1 o 29.477129.29514.228-12
42s 2 2p 5 3s 3 P 0 o 29.727829.54221.530-03
52s 2 2p 5 3s 1 P 1 o 29.803329.61442.977-12
62s 2 2p 5 3p 3 S 1 30.905130.73625.161-10
72s 2 2p 5 3p 3 D 2 31.145530.97173.044-10
82s 2 2p 5 3p 3 D 3 31.157430.98462.805-10
92s 2 2p 5 3p 3 D 1 31.240131.06442.816-10
102s 2 2p 5 3p 3 P 2 31.307631.13312.276-10
112s 2 2p 5 3p 1 P 1 31.477231.29613.104-10
122s 2 2p 5 3p 3 P 0 31.483831.30592.131-10
132s 2 2p 5 3p 3 P 1 31.581531.40102.383-10
142s 2 2p 5 3p 1 D 2 31.580231.39912.559-10
152s 2 2p 5 3p 1 S 0 32.541332.31645.725-11
162s 2 2p 5 3d 3 P 0 o 33.312033.10181.287-10
172s 2 2p 5 3d 3 P 1 o 33.346133.13623.549-11
182s 2 2p 5 3d 3 P 2 o 33.415133.20431.303-10
192s 2 2p 5 3d 3 F 4 o 33.443633.23751.278-10
202s 2 2p 5 3d 3 F 3 o 33.487633.27371.190-10
212s 2 2p 5 3d 3 F 2 o 33.565533.34961.142-10
222s 2 2p 5 3d 3 D 3 o 33.614533.39531.166-10
232s 2 2p 5 3d 3 D 1 o 33.781733.55891.357-12
242s 2 2p 5 3d 1 D 2 o 33.848933.63211.131-10
252s 2 2p 5 3d 3 D 2 o 33.885833.65921.151-10
262s 2 2p 5 3d 1 F 3 o 33.893333.66651.194-10
272s 2 2p 5 3d 1 P 1 o 34.299134.05031.331-13
282s2p 6 3s 3 S 1 36.577036.46461.004-11
292s2p 6 3s 1 S 0 36.917736.78471.554-11
302s2p 6 3p 3 P 0 o 38.280638.18301.064-11
312s2p 6 3p 3 P 1 o 38.294938.19706.973-12
322s2p 6 3p 3 P 2 o 38.344038.24601.033-11
332s2p 6 3p 1 P 1 o 38.463538.36138.246-13
342s 2 2p 5 4s 3 P 2 o 39.422939.23859.358-12
352s 2 2p 5 4s 1 P 1 o 39.449239.26654.976-12
362s 2 2p 5 4s 3 P 0 o 39.763139.57179.131-12
372s 2 2p 5 4s 3 P 1 o 39.779039.58895.632-12
382s 2 2p 5 4p 3 S 1 40.044239.86281.232-11
392s 2 2p 5 4p 3 D 2 40.082539.90431.056-11
402s 2 2p 5 4p 3 D 3 40.082539.90371.075-11
412s 2 2p 5 4p 1 P 1 40.127939.94771.098-11
422s 2 2p 5 4p 3 P 2 40.149739.97011.169-11
432s 2 2p 5 4p 3 P 0 40.306940.12591.233-11
442s 2 2p 5 4p 3 D 1 40.385040.20851.079-11
452s 2 2p 5 4p 1 D 2 40.429840.25431.128-11
462s 2 2p 5 4p 3 P 1 40.462340.27561.186-11
472s2p 6 3d 3 D 3 40.546540.40812.170-11
482s2p 6 3d 3 D 1 40.561640.41262.323-11
492s2p 6 3d 3 D 2 40.561440.41362.152-11
502s 2 2p 5 4p 1 S 0 40.734440.55751.427-11
512s2p 6 3d 1 D 2 40.767640.61561.983-11
522s 2 2p 5 4d 3 P 0 o 40.889740.70587.852-12
532s 2 2p 5 4d 3 P 1 o 40.908040.72346.962-12
542s 2 2p 5 4d 3 F 4 o 40.932840.74697.748-12
552s 2 2p 5 4d 3 P 2 o 40.938840.75297.898-12
562s 2 2p 5 4d 3 F 3 o 40.952440.76487.871-12
572s 2 2p 5 4d 1 D 2 o 40.981940.79288.035-12
582s 2 2p 5 4d 3 D 3 o 40.996640.80768.035-12
592s 2 2p 5 4d 3 D 1 o 41.106340.91168.331-13
602s 2 2p 5 4f 3 G 5 41.282441.09183.184-12
612s 2 2p 5 4f 1 G 4 41.282941.09223.206-12
622s 2 2p 5 4d 3 F 2 o 41.291941.09867.908-12
632s 2 2p 5 4f 1 F 3 41.307841.11743.209-12
642s 2 2p 5 4d 3 D 2 o 41.309541.10623.215-12
652s 2 2p 5 4f 3 F 4 41.300641.11937.978-12
662s 2 2p 5 4d 1 F 3 o 41.312841.11777.893-12
672s 2 2p 5 4f 3 F 2 41.326241.13683.062-12
682s 2 2p 5 4f 3 F 3 41.328441.13882.968-12
692s 2 2p 5 4f 3 D 1 41.338641.14972.695-12
702s 2 2p 5 4f 3 D 2 41.338841.15022.801-12
712s 2 2p 5 4d 1 P 1 o 41.447041.24173.844-13
722s 2 2p 5 4f 3 G 3 41.635941.43883.193-12
732s 2 2p 5 4f 3 G 4 41.638341.44113.208-12
742s 2 2p 5 4f 1 D 2 41.661441.46473.059-12
752s 2 2p 5 4f 3 D 3 41.663841.46682.948-12
762s 2 2p 5 5s 3 P 2 o 43.619443.39631.163-11
772s 2 2p 5 5s 1 P 1 o 43.635343.41266.884-12
782s 2 2p 5 5p 3 S 1 43.929243.70801.432-11
792s 2 2p 5 5p 3 D 2 43.955643.73431.412-11
802s 2 2p 5 5p 3 D 3 43.958043.73621.455-11
812s 2 2p 5 5p 1 P 1 43.972743.75061.375-11
822s 2 2p 5 5s 3 P 0 o 43.963643.73321.161-11
832s 2 2p 5 5p 3 P 2 43.982043.76011.491-11
842s 2 2p 5 5s 3 P 1 o 43.971743.74167.711-12
852s 2 2p 5 5p 3 P 0 44.086443.86331.588-11
862s 2 2p 5 5p 3 D 1 44.293744.06421.381-11
872s 2 2p 5 5p 3 P 1 44.307644.07881.466-11
882s 2 2p 5 5p 1 D 2 44.313744.08491.454-11
892s 2 2p 5 5d 3 P 0 o 44.337344.11729.963-12
902s 2 2p 5 5d 3 P 1 o 44.347544.12679.039-12
912s 2 2p 5 5d 3 F 4 o 44.357844.13611.015-11
922s 2 2p 5 5d 3 P 2 o 44.362844.14081.013-11
932s 2 2p 5 5d 3 F 3 o 44.367644.14501.022-11
942s 2 2p 5 5d 1 D 2 o 44.381644.15771.038-11
952s 2 2p 5 5d 3 D 3 o 44.388344.16421.034-11
962s 2 2p 5 5p 1 S 0 44.408944.17971.608-11
972s 2 2p 5 5d 3 D 1 o 44.455544.22499.363-13
982s 2 2p 5 5f 3 D 1 44.533844.31695.510-12
992s 2 2p 5 5f 3 G 5 44.534244.31745.975-12
1002s 2 2p 5 5f 1 G 4 44.534844.31806.015-12
1012s 2 2p 5 5f 3 D 2 44.536344.31565.686-12
1022s 2 2p 5 5f 3 F 3 44.544044.31615.722-12
1032s 2 2p 5 5f 3 F 2 44.545844.31956.048-12
1042s 2 2p 5 5g 3 F 2 o 44.547044.32911.129-11
1052s 2 2p 5 5f 1 F 3 44.547044.32735.935-12
1062s 2 2p 5 5g 3 F 3 o 44.547544.32311.131-11
1072s 2 2p 5 5f 3 F 4 44.547944.32345.943-12
1082s 2 2p 5 5g 1 H 5 o 44.550944.31931.129-11
1092s 2 2p 5 5g 3 H 6 o 44.551344.31971.129-11
1102s 2 2p 5 5g 3 G 3 o 44.554544.33011.133-11
1112s 2 2p 5 5g 3 G 4 o 44.554844.32601.132-11
1122s 2 2p 5 5g 1 G 4 o 44.557544.33131.132-11
1132s 2 2p 5 5g 3 G 5 o 44.557944.32641.133-11
1142s 2 2p 5 5d 3 F 2 o 44.708444.47871.026-11
1152s 2 2p 5 5d 3 D 2 o 44.711344.48161.019-11
1162s 2 2p 5 5d 1 F 3 o 44.718944.48851.021-11
1172s 2 2p 5 5d 1 P 1 o 44.774844.53768.700-13
1182s 2 2p 5 5f 3 G 3 44.883144.65865.957-12
1192s 2 2p 5 5f 3 G 4 44.884644.65895.986-12
1202s 2 2p 5 5f 3 D 3 44.887044.65915.718-12
1212s 2 2p 5 5f 1 D 2 44.888444.66445.946-12
1222s 2 2p 5 5g 1 F 3 o 44.897344.66281.133-11
1232s 2 2p 5 5g 3 F 4 o 44.897744.65931.132-11
1242s 2 2p 5 5g 3 H 4 o 44.898244.66041.130-11
1252s 2 2p 5 5g 3 H 5 o 44.898744.65971.130-11
GRASP: Present results with the GRASP code for 3948 level calculations; FAC: Present results with the FAC code for 93,437 level calculations.
Table 3. Comparison of energies (in Ryd) for the lowest 37 levels of Sc XII.
Table 3. Comparison of energies (in Ryd) for the lowest 37 levels of Sc XII.
IndexConfigurationLevelFAC1FAC2FAC3GRASP1GRASP2GRASP3NIST
12s 2 2p 6 1 S 0 0.00000.00000.00000.00000.00000.00000.0000
22s 2 2p 5 3s 3 P 2 o 29.261929.212829.206629.404229.478729.385529.4811
32s 2 2p 5 3s 3 P 1 o 29.359229.301029.295129.500429.569529.477129.5720
42s 2 2p 5 3s 3 P 0 o 29.598229.548329.542229.746829.821529.727829.8233
52s 2 2p 5 3s 1 P 1 o 29.683129.620129.614429.829329.895629.803329.8970
62s 2 2p 5 3p 3 S 1 30.815630.743430.736230.921430.996730.905130.9960
72s 2 2p 5 3p 3 D 2 31.054630.977430.971731.159731.231731.145531.2312
82s 2 2p 5 3p 3 D 3 31.067830.990530.984631.170331.243431.157431.2431
92s 2 2p 5 3p 3 D 1 31.149031.070231.064431.253831.323531.240131.3234
102s 2 2p 5 3p 3 P 2 31.215731.138731.133131.323031.394231.307631.3940
112s 2 2p 5 3p 1 P 1 31.381731.301831.296131.490631.560631.477231.5598
122s 2 2p 5 3p 3 P 0 31.388531.311731.305931.498831.567831.483831.5681
132s 2 2p 5 3p 3 P 1 31.485231.406731.401031.596031.666831.581531.6662
142s 2 2p 5 3p 1 D 2 31.483131.404631.399131.595231.666931.580231.6662
152s 2 2p 5 3p 1 S 0 32.402132.333232.316432.401732.489032.541332.4845
162s 2 2p 5 3d 3 P 0 o 33.185233.108533.101833.319133.396033.3120
172s 2 2p 5 3d 3 P 1 o 33.220033.142933.136233.353433.428733.346133.4302
182s 2 2p 5 3d 3 P 2 o 33.288933.211033.204333.422933.496633.415133.4980
192s 2 2p 5 3d 3 F 4 o 33.318733.244533.237533.455633.522233.443633.5237
202s 2 2p 5 3d 3 F 3 o 33.357733.280733.273733.500833.563633.487633.5650
212s 2 2p 5 3d 3 F 2 o 33.435633.356533.349633.577233.639633.565533.6413
222s 2 2p 5 3d 3 D 3 o 33.484433.402033.395333.627433.687433.614533.6887
232s 2 2p 5 3d 3 D 1 o 33.648033.566033.558933.794033.851733.781733.8510
242s 2 2p 5 3d 1 D 2 o 33.718833.638933.632133.860533.922733.848933.9238
252s 2 2p 5 3d 3 D 2 o 33.748733.665833.659233.845833.959833.885833.9608
262s 2 2p 5 3d 1 F 3 o 33.754933.673233.666533.906233.967433.893333.9682
272s 2 2p 5 3d 1 P 1 o 34.144634.060634.050334.300934.335534.299134.3300
282s2p 6 3s 3 S 1 36.626836.476036.4646 36.5770
292s2p 6 3s 1 S 0 36.995736.799336.7847 36.9177
302s2p 6 3p 3 P 0 o 38.336638.194438.1830 38.2806
312s2p 6 3p 3 P 1 o 38.350738.208438.1970 38.294938.2550
322s2p 6 3p 3 P 2 o 38.398138.257538.2460 38.3440
332s2p 6 3p 1 P 1 o 38.528038.372138.3613 38.463538.4100
342s 2 2p 5 4s 3 P 2 o 39.320039.261039.2385 39.422939.5248
352s 2 2p 5 4s 1 P 1 o 39.346339.289239.2665 39.449239.5430
362s 2 2p 5 4s 3 P 0 o 39.653839.595039.5717 39.7631
372s 2 2p 5 4s 3 P 1 o 39.670239.612339.5889 39.779039.9030
FAC1: Present results with the FAC code for 3948 level calculations; FAC2: Present results with the FAC code for 17,729 level calculations; FAC3: Present results with the FAC code for 93,437 level calculations; GRASP1: Earlier results of Cogordan and Lunell [5] with the GRASP code; GRASP2: Earlier results of Jönsson et al. [10] with the GRASP code; GRASP3: Present results with the GRASP code for 3948 level calculations; NIST: http://www.nist.gov/pml/data/asd.cfm.
Table 4. Energies (in Ryd) and lifetimes ( τ , s) for the lowest 139 levels of Y XXX. a ± ba × 10 ± b .
Table 4. Energies (in Ryd) and lifetimes ( τ , s) for the lowest 139 levels of Y XXX. a ± ba × 10 ± b .
IndexConfigurationLevelGRASP1GRASP2FACDFSYODA τ (GRASP1)
12s 2 2p 6 1 S 0 0.00000.00000.00000.00000.0000........
22s 2 2p 5 3s 3 P 2 o 146.6987146.8657146.5497146.8576146.80478.827-08
32s 2 2p 5 3s 1 P 1 o 146.9606147.1241146.8078147.1295147.06781.283-13
42s 2 2p 5 3p 3 S 1 150.9658151.1208150.8223151.0984151.03741.067-10
52s 2 2p 5 3p 3 D 2 151.1804151.3472151.0345151.3336151.24764.442-11
62s 2 2p 5 3p 3 D 3 152.4685152.6663152.3230152.6493152.54054.083-11
72s 2 2p 5 3p 1 P 1 152.4932152.6816152.3437152.6640152.56474.749-11
82s 2 2p 5 3s 3 P 0 o 152.4791152.7338152.3099152.7375152.61321.805-07
92s 2 2p 5 3s 3 P 1 o 152.6077152.8713152.4363152.8771152.74331.889-13
102s 2 2p 5 3p 3 P 2 152.8584153.0399152.7116153.0314152.92932.449-11
112s 2 2p 5 3p 3 P 0 154.2837154.4569154.1154154.4647154.36691.989-11
122s 2 2p 5 3p 3 D 1 156.8517157.1167156.6846157.1106156.94751.010-10
132s 2 2p 5 3d 3 P 0 o 157.6799157.8546157.5000157.8309157.74713.221-11
142s 2 2p 5 3d 3 P 1 o 157.8890158.0863157.7075158.0661157.95733.807-12
152s 2 2p 5 3d 3 F 3 o 158.1738158.3932157.9895158.3822158.24472.864-11
162s 2 2p 5 3d 3 D 2 o 158.2712158.4762158.0866158.4557158.33953.116-11
172s 2 2p 5 3d 3 F 4 o 158.2876158.5230158.1143158.5071158.34614.574-11
182s 2 2p 5 3p 3 P 1 158.3146158.5880158.1492158.5806158.41603.794-11
192s 2 2p 5 3p 1 D 2 158.4251158.7151158.2578158.7129158.52622.562-11
202s 2 2p 5 3d 1 D 2 o 158.5283158.7396158.3391158.7202158.60043.485-11
212s 2 2p 5 3p 1 S 0 158.6252158.8512158.4291158.8893158.73421.943-11
222s 2 2p 5 3d 3 D 3 o 158.8049159.0240158.6145159.0142158.88124.014-11
232s 2 2p 5 3d 3 D 1 o 159.7700159.9925159.5589159.9991159.86838.547-15
242s 2 2p 5 3d 3 F 2 o 163.9104164.2167163.7151164.2106164.00772.803-11
252s 2 2p 5 3d 3 P 2 o 164.2275164.5414164.0182164.5340164.32454.173-11
262s 2 2p 5 3d 1 F 3 o 164.3548164.6758164.1453164.6736164.44954.267-11
272s 2 2p 5 3d 1 P 1 o 164.8886165.2049164.6642165.2175164.99927.820-15
282s2p 6 3s 3 S 1 167.5933167.8473167.5051167.8635167.67902.216-12
292s2p 6 3s 1 S 0 168.4649168.7070168.3525168.7381168.55003.028-12
302s2p 6 3p 3 P 0 o 171.9546172.1943171.8826172.2072172.00732.413-12
312s2p 6 3p 3 P 1 o 172.0393172.2913171.9655172.3028172.09181.180-13
322s2p 6 3p 3 P 2 o 173.3963173.6725173.3240173.6846173.45602.304-12
332s2p 6 3p 1 P 1 o 173.6114173.8890173.5349173.9051173.66693.951-14
342s2p 6 3d 3 D 1 178.8170179.0985178.7101179.1014178.88092.685-12
352s2p 6 3d 3 D 2 178.8986179.1968178.7914179.1970178.96322.541-12
362s2p 6 3d 3 D 3 179.1053179.4192178.9983179.4248179.16242.585-12
372s2p 6 3d 1 D 2 179.7476180.0497179.6257180.0789179.82101.706-12
382s 2 2p 5 4s 3 P 2 o 199.3165199.5290199.1716199.5414 3.442-13
392s 2 2p 5 4s 1 P 1 o 199.4034199.6142199.2606199.6296 1.803-13
402s 2 2p 5 4p 3 S 1 201.0886201.2950200.9476201.3053 3.072-13
412s 2 2p 5 4p 3 D 2 201.1477201.3587201.0071201.3641 3.033-13
422s 2 2p 5 4p 3 D 3 201.6754201.8994201.5336201.9080 3.378-13
432s 2 2p 5 4p 1 P 1 201.6926201.9130201.5496201.9227 3.317-13
442s 2 2p 5 4p 3 P 2 201.8149202.0323201.6736202.0403 3.445-13
452s 2 2p 5 4p 1 S 0 202.4018202.6089202.2643202.6210 3.651-13
462s 2 2p 5 4d 3 P 0 o 203.6528203.8698203.5107203.8851 1.740-13
472s 2 2p 5 4d 3 P 1 o 203.7330203.9577203.5899203.9733 1.709-13
482s 2 2p 5 4d 3 F 3 o 203.8229204.0551203.6770204.0615 1.763-13
492s 2 2p 5 4d 3 D 2 o 203.8692204.0950203.7236204.1056 1.763-13
502s 2 2p 5 4d 3 F 4 o 203.8863204.1251203.7419204.1350 1.740-13
512s 2 2p 5 4d 1 D 2 o 203.9686204.1992203.8208204.2085 1.754-13
522s 2 2p 5 4d 3 D 3 o 204.0699204.3017203.9220204.3114 1.762-13
532s 2 2p 5 4d 1 P 1 o 204.4392204.6729204.2800204.6789 1.619-14
542s 2 2p 5 4f 3 D 1 205.0260205.2616204.8713205.2816 8.126-14
552s 2 2p 5 4f 3 G 4 205.0516205.2961204.8970205.3184 8.452-14
562s 2 2p 5 4f 3 D 2 205.0755205.3135204.9208205.3331 8.218-14
572s 2 2p 5 4f 3 G 5 205.0973205.3419204.9425205.3625 8.462-14
582s 2 2p 5 4f 3 F 3 205.1329205.3729204.9787205.3919 8.392-14
592s 2 2p 5 4f 1 D 2 205.1513205.3899204.9965205.4139 8.569-14
602s 2 2p 5 4f 1 F 3 205.1659205.4060205.0108205.4246 8.382-14
612s 2 2p 5 4s 3 P 0 o 205.1153205.4217204.9493205.4433 3.427-13
622s 2 2p 5 4f 3 F 4 205.1953205.4368205.0410205.4580 8.490-14
632s 2 2p 5 4s 3 P 1 o 205.1705205.4783205.0058205.5021 3.381-13
642s 2 2p 5 4p 3 D 1 206.9038207.2126206.7408207.2293 2.999-13
652s 2 2p 5 4p 3 P 0 207.3845207.6802207.2255207.7071 3.224-13
662s 2 2p 5 4p 3 P 1 207.4992207.8124207.3363207.8320 3.411-13
672s 2 2p 5 4p 1 D 2 207.5333207.8527207.3708207.8688 3.384-13
682s 2 2p 5 4d 3 F 2 o 209.5980209.9242209.4319209.9488 1.763-13
692s 2 2p 5 4d 3 P 2 o 209.7364210.0653209.5701210.0884 1.744-13
702s 2 2p 5 4d 1 F 3 o 209.7832210.1147209.6157210.1325 1.750-13
712s 2 2p 5 4d 3 D 1 o 209.9192210.2458209.7448210.2648 2.381-14
722s 2 2p 5 4f 3 G 3 210.8816211.2201210.7060211.2571 8.423-14
732s 2 2p 5 4f 3 F 2 210.9115211.2487210.7362211.2791 8.427-14
742s 2 2p 5 4f 1 G 4 210.9436211.2829210.7674211.3159 8.492-14
752s 2 2p 5 4f 3 D 3 210.9487211.2869210.7725211.3159 8.335-14
762s2p 6 4s 3 S 1 219.9878220.2881219.9299220.3194 2.957-13
772s2p 6 4s 1 S 0 220.3037220.5991220.2466220.6134 3.127-13
782s2p 6 4p 3 P 0 o 221.8067222.1002221.7550222.1201 2.714-13
792s2p 6 4p 3 P 1 o 221.8169222.1140221.7623222.1495 1.018-13
802s2p 6 4p 3 P 2 o 222.2897222.5686222.1888222.7228 3.191-13
812s2p 6 4p 1 P 1 o 222.4682222.7721222.4021222.7963 5.936-14
822s 2 2p 5 5s 1 P 1 o 222.6048222.8365222.4369 2.513-13
832s 2 2p 5 5s 3 P 2 o 222.6489222.9041222.5133 4.010-13
842s 2 2p 5 5p 3 S 1 223.4433223.6654223.2605 3.891-13
852s 2 2p 5 5p 3 D 2 223.4497223.6750223.2688 3.711-13
862s 2 2p 5 5p 3 D 3 223.7106223.9432223.5300 4.028-13
872s 2 2p 5 5p 1 P 1 223.7394223.9689223.5557 4.095-13
882s 2 2p 5 5p 3 P 2 223.7892224.0166223.6064 4.206-13
892s 2 2p 5 5p 1 S 0 224.0789224.2965223.8943 4.332-13
902s2p 6 4d 3 D 1 224.4288224.7380224.3693224.7881 1.733-13
912s2p 6 4d 3 D 2 224.4779224.7928224.4184224.8249 1.720-13
922s2p 6 4d 3 D 3 224.5842224.9046224.5246224.9278 1.703-13
932s 2 2p 5 5d 3 P 0 o 224.6993224.9276224.5216 2.400-13
942s 2 2p 5 5d 3 P 1 o 224.7374224.9689224.5588 2.383-13
952s 2 2p 5 5d 3 F 3 o 224.7747225.0091224.5944 2.405-13
962s 2 2p 5 5d 3 D 2 o 224.7997225.0306224.6191 2.418-13
972s 2 2p 5 5d 3 F 4 o 224.8111225.0491224.6317 2.401-13
982s 2 2p 5 5d 1 D 2 o 224.8502225.0839224.6686 2.407-13
992s2p 6 4d 1 D 2 224.7977225.1145224.7342225.1336 1.696-13
1002s 2 2p 5 5d 3 D 3 o 224.8972225.1308224.7150 2.409-13
1012s 2 2p 5 5d 1 P 1 o 225.0872225.3180224.8959 3.097-14
1022s 2 2p 5 5g 3 F 2 o 225.3178225.5788225.1566 2.050-13
1032s 2 2p 5 5g 3 F 3 o 225.3502225.6094225.1846 2.157-13
1042s 2 2p 5 5f 3 G 4 225.3857225.6287225.2042 1.608-13
1052s 2 2p 5 5f 3 D 1 225.3960225.6370225.2177 1.486-13
1062s 2 2p 5 5f 3 G 5 225.4076225.6509225.2261 1.611-13
1072s 2 2p 5 5f 3 D 2 225.4161225.6579225.2372 1.515-13
1082s 2 2p 5 5f 3 F 3 225.4264225.6673225.2451 1.586-13
1092s 2 2p 5 5g 3 G 3 o 225.4225225.6782225.2485 2.272-13
1102s 2 2p 5 5f 1 D 2 225.4457225.6869225.2651 1.602-13
1112s 2 2p 5 5g 3 G 4 o 225.4377225.6930225.2631 2.281-13
1122s 2 2p 5 5f 1 F 3 225.4515225.6938225.2713 1.551-13
1132s 2 2p 5 5f 3 F 4 225.4566225.6982225.2750 1.603-13
1142s 2 2p 5 5g 1 H 5 o 225.4899225.7330225.2931 2.882-13
1152s 2 2p 5 5g 3 H 6 o 225.5069225.7498225.3100 2.889-13
1162s 2 2p 5 5g 1 G 4 o 225.5151225.7571225.3186 2.882-13
1172s 2 2p 5 5g 3 G 5 o 225.5310225.7730225.3345 2.892-13
1182s2p 6 4f 3 F 3 o 225.7962226.1104225.7044226.0597 8.881-14
1192s2p 6 4f 3 F 4 o 225.8311226.1473225.7417226.1111 8.798-14
1202s2p 6 4f 3 F 2 o 225.8669226.1719225.7639226.0523 9.089-14
1212s2p 6 4f 1 F 3 o 225.9203226.2297225.8217226.1332 8.967-14
1222s 2 2p 5 5s 3 P 0 o 228.3506228.6719228.1423 4.345-13
1232s 2 2p 5 5s 3 P 1 o 228.3696228.6922228.1616 3.699-13
1242s 2 2p 5 5p 3 D 1 229.2465229.5683229.2483 3.776-13
1252s 2 2p 5 5p 3 P 0 229.4556229.7686229.0393 3.932-13
1262s 2 2p 5 5p 3 P 1 229.5449229.8690229.3380 4.238-13
1272s 2 2p 5 5p 1 D 2 229.5601229.8870229.3535 4.207-13
1282s 2 2p 5 5d 3 F 2 o 230.5663230.8966230.3626 2.415-13
1292s 2 2p 5 5d 3 P 2 o 230.6384230.9698230.4346 2.397-13
1302s 2 2p 5 5d 1 F 3 o 230.6603230.9929230.4558 2.407-13
1312s 2 2p 5 5d 3 D 1 o 230.7145231.0425230.5047 4.944-14
1322s 2 2p 5 5f 3 G 3 231.2020231.5406230.9968 1.599-13
1332s 2 2p 5 5f 3 F 2 231.2205231.5584231.0153 1.598-13
1342s 2 2p 5 5f 1 G 4 231.2348231.5740231.0291 1.612-13
1352s 2 2p 5 5f 3 D 3 231.2366231.5751231.0308 1.576-13
1362s 2 2p 5 5g 3 H 4 o 231.3059231.6452231.0853 2.883-13
1372s 2 2p 5 5g 1 F 3 o 231.3132231.6521231.0928 2.839-13
1382s 2 2p 5 5g 3 H 5 o 231.3233231.6626231.1026 2.891-13
1392s 2 2p 5 5g 3 F 4 o 231.3301231.6691231.1097 2.844-13
GRASP1: Present results with the GRASP code for 3948 level calculations including Breit and QED effects; GRASP2: Present results with the GRASP code for 3948 level calculations excluding Breit and QED effects; FAC: Present results with the FAC code for 93,437 level calculations; DFS: Earlier results of Zhang and Sampson [7]; YODA: Earlier results of Hagelstein and Jung [6].
Table 5. Comparison of energies (in Ryd) for the lowest 37 levels of Y XXX.
Table 5. Comparison of energies (in Ryd) for the lowest 37 levels of Y XXX.
IndexConfigurationLevelFAC1FAC2FAC3GRASP1GRASP2GRASP3
12s 2 2p 6 1 S 0 0.00000.00000.00000.00000.00000.0000
22s 2 2p 5 3s 3 P 2 o 146.6164146.5697146.5497146.7014 146.6987
32s 2 2p 5 3s 1 P 1 o 146.8884146.8272146.8078146.9787 146.9606
42s 2 2p 5 3p 3 S 1 150.9125150.8425150.8223150.9653151.0112150.9658
52s 2 2p 5 3p 3 D 2 151.1260151.0538151.0345151.1747 151.1804
62s 2 2p 5 3p 3 D 3 152.4161152.3427152.3230152.4651152.5129152.4685
72s 2 2p 5 3p 1 P 1 152.4397152.3634152.3437152.4908152.5414152.4932
82s 2 2p 5 3s 3 P 0 o 152.3800152.3298152.3099152.4813152.5560152.4791
92s 2 2p 5 3s 3 P 1 o 152.5137152.4558152.4363152.6247 152.6077
102s 2 2p 5 3p 3 P 2 152.8034152.7307152.7116152.8575 152.8584
112s 2 2p 5 3p 3 P 0 154.2124154.1432154.1154154.2961154.3980154.2837
122s 2 2p 5 3p 3 D 1 156.7825156.7041156.6846156.8470156.9004156.8517
132s 2 2p 5 3d 3 P 0 o 157.5915157.5213157.5000157.6708157.7660157.6799
142s 2 2p 5 3d 3 P 1 o 157.8001157.7287157.7075157.8813 157.8890
152s 2 2p 5 3d 3 F 3 o 158.0818158.0112157.9895158.1763158.2056158.1738
162s 2 2p 5 3d 3 D 2 o 158.1807158.1077158.0866158.2663158.2950158.2712
172s 2 2p 5 3d 3 F 4 o 158.2009158.1363158.1143158.2879158.3356158.2876
182s 2 2p 5 3p 3 P 1 158.2446158.1690158.1492158.3102158.3604158.3146
192s 2 2p 5 3p 1 D 2 158.3547158.2770158.2578158.4209 158.4251
202s 2 2p 5 3d 1 D 2 o 158.4372158.3602158.3391158.5266158.5801158.5283
212s 2 2p 5 3p 1 S 0 158.5336158.4648158.4291158.5319158.5608158.6252
222s 2 2p 5 3d 3 D 3 o 158.7122158.6354158.6145158.8041158.8350158.8049
232s 2 2p 5 3d 3 D 1 o 159.6610159.5862159.5589159.7764 159.7700
242s 2 2p 5 3d 3 F 2 o 163.8100163.7367163.7151163.9070163.9513163.9104
252s 2 2p 5 3d 3 P 2 o 164.1176164.0390164.0182164.2192164.2507164.2275
262s 2 2p 5 3d 1 F 3 o 164.2434164.1664164.1453164.3523164.3840164.3548
272s 2 2p 5 3d 1 P 1 o 164.7694164.6913164.6642164.8795 164.8886
282s2p 6 3s 3 S 1 167.6548167.5336167.5051 167.5933
292s2p 6 3s 1 S 0 168.5527168.3882168.3525 168.4649
302s2p 6 3p 3 P 0 o 172.0201171.9109171.8826 171.9546
312s2p 6 3p 3 P 1 o 172.1062171.9936171.9655 172.0393
322s2p 6 3p 3 P 2 o 173.4597173.3526173.3240 173.3963
332s2p 6 3p 1 P 1 o 173.6801173.5627173.5349 173.6114
342s2p 6 3d 3 D 1 178.8518178.7405178.7101 178.8170
352s2p 6 3d 3 D 2 178.9334178.8218178.7914 178.8986
362s2p 6 3d 3 D 3 179.1391179.0286178.9983 179.1053
372s2p 6 3d 1 D 2 179.7807179.6561179.6257 179.7476
FAC1: Present results with the FAC code for 3948 level calculations; FAC2: Present results with the FAC code for 17 729 level calculations; FAC3: Present results with the FAC code for 93 437 level calculations; GRASP1: Earlier results of Cogordan and Lunell [5] with the GRASP code; GRASP2: Earlier results of Quinet et al. [8] with the GRASP code; GRASP3: Present results with the GRASP code for 3948 level calculations.
Table 6. Transition wavelengths ( λ i j in Å), radiative rates (A j i in s 1 ), oscillator strengths (f i j , dimensionless), and line strengths (S, in atomic units) for electric dipole (E1), and A j i for E2, M1 and M2 transitions in Sc XIII. The last column gives the ratio R of the velocity and length forms of A(E1). a ± ba × 10 ± b .
Table 6. Transition wavelengths ( λ i j in Å), radiative rates (A j i in s 1 ), oscillator strengths (f i j , dimensionless), and line strengths (S, in atomic units) for electric dipole (E1), and A j i for E2, M1 and M2 transitions in Sc XIII. The last column gives the ratio R of the velocity and length forms of A(E1). a ± ba × 10 ± b .
ij λ ij A ji E 1 f ij E 1 S E 1 A ji E 2 A ij M 1 A M 2 R
122.656 + 030.000 + 000.000 + 000.000 + 003.849 − 029.570 + 020.000 + 000.0 + 00
131.284 + 025.143 + 106.354 − 021.074 − 010.000 + 000.000 + 004.272 + 028.4 − 01
142.856 + 011.016 + 101.863 − 037.009 − 040.000 + 000.000 + 004.296 + 049.3 − 01
152.842 + 012.717 + 113.290 − 021.231 − 020.000 + 000.000 + 007.041 + 039.4 − 01
162.829 + 011.706 + 091.023 − 043.812 − 050.000 + 000.000 + 001.414 + 041.1 + 00
172.822 + 015.591 + 116.676 − 022.481 − 020.000 + 000.000 + 001.737 + 039.4 − 01
182.807 + 013.941 + 112.327 − 028.601 − 030.000 + 000.000 + 001.264 + 049.5 − 01
192.770 + 013.539 + 116.107 − 022.228 − 020.000 + 000.000 + 001.063 + 049.3 − 01
1102.769 + 011.897 + 092.181 − 047.952 − 050.000 + 000.000 + 003.051 + 038.7 − 01
1112.721 + 010.000 + 000.000 + 000.000 + 001.377 + 061.238 + 030.000 + 000.0 + 00
1122.720 + 010.000 + 000.000 + 000.000 + 001.759 + 071.803 + 040.000 + 000.0 + 00
1132.710 + 010.000 + 000.000 + 000.000 + 003.160 + 079.887 + 030.000 + 000.0 + 00
1142.705 + 010.000 + 000.000 + 000.000 + 007.016 + 060.000 + 000.000 + 000.0 + 00
1152.701 + 010.000 + 000.000 + 000.000 + 001.986 + 082.216 + 030.000 + 000.0 + 00
1162.700 + 011.483 + 118.105 − 032.882 − 030.000 + 000.000 + 003.201 + 041.0 + 00
1172.690 + 010.000 + 000.000 + 000.000 + 001.302 + 085.680 + 030.000 + 000.0 + 00
1182.689 + 010.000 + 000.000 + 000.000 + 002.984 + 072.450 + 010.000 + 000.0 + 00
1192.686 + 010.000 + 000.000 + 000.000 + 001.118 + 042.589 + 030.000 + 000.0 + 00
1202.682 + 010.000 + 000.000 + 000.000 + 001.456 + 086.430 + 030.000 + 000.0 + 00
1212.680 + 010.000 + 000.000 + 000.000 + 002.498 + 082.819 + 000.000 + 000.0 + 00
1222.673 + 010.000 + 000.000 + 000.000 + 008.681 + 063.929 + 030.000 + 000.0 + 00
1232.669 + 010.000 + 000.000 + 000.000 + 007.119 + 072.847 + 030.000 + 000.0 + 00
1242.668 + 010.000 + 000.000 + 000.000 + 005.727 + 076.973 + 030.000 + 000.0 + 00
1252.640 + 010.000 + 000.000 + 000.000 + 001.702 + 072.971 + 020.000 + 000.0 + 00
1262.635 + 010.000 + 000.000 + 000.000 + 001.932 + 080.000 + 000.000 + 000.0 + 00
1272.623 + 010.000 + 000.000 + 000.000 + 001.504 + 079.730 + 030.000 + 000.0 + 00
1282.620 + 010.000 + 000.000 + 000.000 + 005.473 + 079.653 + 030.000 + 000.0 + 00
1292.588 + 010.000 + 000.000 + 000.000 + 002.103 + 074.039 + 020.000 + 000.0 + 00
1302.585 + 010.000 + 000.000 + 000.000 + 001.236 + 081.065 + 040.000 + 000.0 + 00
1312.564 + 010.000 + 000.000 + 000.000 + 001.784 + 071.429 + 030.000 + 000.0 + 00
1322.556 + 010.000 + 000.000 + 000.000 + 002.357 + 058.866 + 020.000 + 000.0 + 00
1332.555 + 010.000 + 000.000 + 000.000 + 000.000 + 000.000 + 007.415 + 050.0 + 00
1342.554 + 014.054 + 075.948 − 062.001 − 060.000 + 000.000 + 004.591 + 036.6 − 01
1352.552 + 012.277 + 092.223 − 047.468 − 050.000 + 000.000 + 001.059 + 049.6 − 01
1362.548 + 019.740 + 084.741 − 051.591 − 050.000 + 000.000 + 001.489 + 051.0 + 00
1382.536 + 010.000 + 000.000 + 000.000 + 000.000 + 000.000 + 001.461 + 050.0 + 00
1392.531 + 012.690 + 111.292 − 024.304 − 030.000 + 000.000 + 002.884 + 059.1 − 01
1402.526 + 013.929 + 115.638 − 021.876 − 020.000 + 000.000 + 003.032 + 049.5 − 01
1412.526 + 013.991 + 113.818 − 021.270 − 020.000 + 000.000 + 008.862 + 049.3 − 01
1422.522 + 012.258 + 111.077 − 023.576 − 030.000 + 000.000 + 008.113 + 059.3 − 01
1432.521 + 012.046 + 101.950 − 036.474 − 040.000 + 000.000 + 008.295 + 029.5 − 01
1442.522 + 010.000 + 000.000 + 000.000 + 000.000 + 000.000 + 003.590 + 030.0 + 00
1452.520 + 012.956 + 114.221 − 021.400 − 020.000 + 000.000 + 003.244 + 059.5 − 01
1462.516 + 017.467 + 117.084 − 022.347 − 020.000 + 000.000 + 001.225 + 059.4 − 01
1472.514 + 012.270 + 113.226 − 021.068 − 020.000 + 000.000 + 002.500 + 039.5 − 01
1482.505 + 017.205 + 106.781 − 032.237 − 030.000 + 000.000 + 009.144 + 049.3 − 01
1492.502 + 012.278 + 123.207 − 011.057 − 010.000 + 000.000 + 004.764 + 039.5 − 01
1502.483 + 010.000 + 000.000 + 000.000 + 000.000 + 000.000 + 009.072 + 030.0 + 00
1522.470 + 014.834 + 122.212 − 017.195 − 020.000 + 000.000 + 003.265 + 059.0 − 01
1532.469 + 013.016 + 114.134 − 021.344 − 020.000 + 000.000 + 006.072 + 049.6 − 01
1542.467 + 010.000 + 000.000 + 000.000 + 000.000 + 000.000 + 003.246 + 040.0 + 00
1552.460 + 016.680 + 126.059 − 011.963 − 010.000 + 000.000 + 002.424 + 059.2 − 01
1562.458 + 016.076 + 128.259 − 012.674 − 010.000 + 000.000 + 001.651 + 049.6 − 01
1572.451 + 017.517 + 116.772 − 022.186 − 020.000 + 000.000 + 007.996 + 049.6 − 01
1582.451 + 011.608 + 127.245 − 022.339 − 020.000 + 000.000 + 009.940 + 049.2 − 01
1592.417 + 017.732 + 111.016 − 013.233 − 020.000 + 000.000 + 001.510 + 059.6 − 01
1602.413 + 016.649 + 105.804 − 031.844 − 030.000 + 000.000 + 001.598 + 021.0 + 00
1612.387 + 010.000 + 000.000 + 000.000 + 002.093 + 022.304 + 030.000 + 000.0 + 00
1622.377 + 010.000 + 000.000 + 000.000 + 006.929 + 046.434 + 020.000 + 000.0 + 00
1632.368 + 010.000 + 000.000 + 000.000 + 005.313 + 041.568 + 020.000 + 000.0 + 00
1642.356 + 010.000 + 000.000 + 000.000 + 001.346 + 066.397 + 010.000 + 000.0 + 00
1652.344 + 010.000 + 000.000 + 000.000 + 002.864 + 062.384 + 020.000 + 000.0 + 00
1662.299 + 016.378 + 075.052 − 061.529 − 060.000 + 000.000 + 003.535 + 045.4 − 01
1672.285 + 010.000 + 000.000 + 000.000 + 000.000 + 000.000 + 001.067 + 050.0 + 00
1682.285 + 011.207 + 111.417 − 024.262 − 030.000 + 000.000 + 007.639 + 011.0 + 00
1692.280 + 011.445 + 111.126 − 023.379 − 030.000 + 000.000 + 001.961 + 049.5 − 01
1702.274 + 014.807 + 115.591 − 021.675 − 020.000 + 000.000 + 007.822 + 041.0 + 00
1712.274 + 012.117 + 108.206 − 042.457 − 040.000 + 000.000 + 008.406 + 019.3 − 01
1722.268 + 017.750 + 115.979 − 021.786 − 020.000 + 000.000 + 001.618 + 049.5 − 01
1732.266 + 013.728 + 114.306 − 021.285 − 020.000 + 000.000 + 002.096 + 041.0 + 00
1742.265 + 013.029 + 101.165 − 033.473 − 040.000 + 000.000 + 002.006 + 049.8 − 01
1752.265 + 012.244 + 111.726 − 025.147 − 030.000 + 000.000 + 006.875 + 039.9 − 01
1762.261 + 017.117 + 112.728 − 028.124 − 030.000 + 000.000 + 008.459 + 039.6 − 01
1772.256 + 011.087 + 108.295 − 042.465 − 040.000 + 000.000 + 004.842 + 037.4 − 01
1782.242 + 010.000 + 000.000 + 000.000 + 003.231 + 037.871 + 020.000 + 000.0 + 00
1792.241 + 010.000 + 000.000 + 000.000 + 001.042 + 051.739 + 030.000 + 000.0 + 00
1802.237 + 016.381 + 112.393 − 027.047 − 030.000 + 000.000 + 005.659 + 031.0 + 00
1812.180 + 010.000 + 000.000 + 000.000 + 002.445 + 042.086 + 020.000 + 000.0 + 00
1822.177 + 010.000 + 000.000 + 000.000 + 008.185 + 051.952 + 010.000 + 000.0 + 00
1842.174 + 010.000 + 000.000 + 000.000 + 007.207 + 061.597 + 010.000 + 000.0 + 00
1852.172 + 010.000 + 000.000 + 000.000 + 004.140 + 070.000 + 000.000 + 000.0 + 00
1862.167 + 010.000 + 000.000 + 000.000 + 009.654 + 071.069 + 020.000 + 000.0 + 00
1872.164 + 010.000 + 000.000 + 000.000 + 005.051 + 077.469 + 010.000 + 000.0 + 00
1882.161 + 010.000 + 000.000 + 000.000 + 006.636 + 080.000 + 000.000 + 000.0 + 00
1892.157 + 019.573 + 106.679 − 031.898 − 030.000 + 000.000 + 003.241 + 031.0 + 00
1902.155 + 010.000 + 000.000 + 000.000 + 001.414 + 073.011 + 010.000 + 000.0 + 00
1912.154 + 013.598 + 113.754 − 021.065 − 020.000 + 000.000 + 004.381 + 049.5 − 01
1922.154 + 010.000 + 000.000 + 000.000 + 001.498 + 074.910 + 000.000 + 000.0 + 00
1932.153 + 010.000 + 000.000 + 000.000 + 009.335 + 061.958 + 010.000 + 000.0 + 00
1942.153 + 010.000 + 000.000 + 000.000 + 001.171 + 090.000 + 000.000 + 000.0 + 00
1952.151 + 010.000 + 000.000 + 000.000 + 001.606 + 091.808 − 010.000 + 000.0 + 00
1962.148 + 016.229 + 102.155 − 036.095 − 040.000 + 000.000 + 001.887 + 041.3 + 00
1972.147 + 011.437 + 119.927 − 032.806 − 030.000 + 000.000 + 004.044 + 041.3 + 00
1982.146 + 010.000 + 000.000 + 000.000 + 001.386 + 096.283 + 000.000 + 000.0 + 00
1992.142 + 010.000 + 000.000 + 000.000 + 008.041 + 072.817 + 010.000 + 000.0 + 00
11002.137 + 019.936 + 093.401 − 049.570 − 050.000 + 000.000 + 006.580 + 043.2 − 01
11012.134 + 010.000 + 000.000 + 000.000 + 002.070 + 092.749 + 010.000 + 000.0 + 00
11022.125 + 010.000 + 000.000 + 000.000 + 004.964 + 084.492 + 000.000 + 000.0 + 00
Table 7. Transition wavelengths ( λ i j in Å), radiative rates (A j i in s 1 ), oscillator strengths (f i j , dimensionless), and line strengths (S, in atomic units) for electric dipole (E1), and A j i for E2, M1 and M2 transitions in Sc XII. The last column gives the ratio R of the velocity and length forms of A(E1). a ± ba × 10 ± b .
Table 7. Transition wavelengths ( λ i j in Å), radiative rates (A j i in s 1 ), oscillator strengths (f i j , dimensionless), and line strengths (S, in atomic units) for electric dipole (E1), and A j i for E2, M1 and M2 transitions in Sc XII. The last column gives the ratio R of the velocity and length forms of A(E1). a ± ba × 10 ± b .
ij λ ij A ji E 1 f ij E 1 S E 1 A ji E 2 A ij M 1 A M 2 R
123.101 + 010.000 + 000.000 + 000.000 + 000.000 + 000.000 + 002.241 + 040.0 + 00
133.091 + 012.365 + 111.017 − 011.035 − 020.000 + 000.000 + 000.000 + 009.4 − 01
153.058 + 013.359 + 111.412 − 011.422 − 020.000 + 000.000 + 000.000 + 009.4 − 01
162.949 + 010.000 + 000.000 + 000.000 + 000.000 + 008.085 + 030.000 + 000.0 + 00
172.926 + 010.000 + 000.000 + 000.000 + 007.312 + 070.000 + 000.000 + 000.0 + 00
192.917 + 010.000 + 000.000 + 000.000 + 000.000 + 001.521 + 030.000 + 000.0 + 00
1102.911 + 010.000 + 000.000 + 000.000 + 009.485 + 070.000 + 000.000 + 000.0 + 00
1112.895 + 010.000 + 000.000 + 000.000 + 000.000 + 004.143 + 000.000 + 000.0 + 00
1132.885 + 010.000 + 000.000 + 000.000 + 000.000 + 001.699 + 040.000 + 000.0 + 00
1142.886 + 010.000 + 000.000 + 000.000 + 001.167 + 080.000 + 000.000 + 000.0 + 00
1172.733 + 012.044 + 106.865 − 036.176 − 040.000 + 000.000 + 000.000 + 009.8 − 01
1182.727 + 010.000 + 000.000 + 000.000 + 000.000 + 000.000 + 005.992 + 050.0 + 00
1212.715 + 010.000 + 000.000 + 000.000 + 000.000 + 000.000 + 006.530 + 040.0 + 00
1232.698 + 017.276 + 112.381 − 012.115 − 020.000 + 000.000 + 000.000 + 009.8 − 01
1242.692 + 010.000 + 000.000 + 000.000 + 000.000 + 000.000 + 006.344 + 040.0 + 00
1252.689 + 010.000 + 000.000 + 000.000 + 000.000 + 000.000 + 001.704 + 030.0 + 00
1272.657 + 017.503 + 122.382 + 002.084 − 010.000 + 000.000 + 000.000 + 009.8 − 01
1282.491 + 010.000 + 000.000 + 000.000 + 000.000 + 001.295 + 030.000 + 000.0 + 00
1312.380 + 014.824 + 101.229 − 029.625 − 040.000 + 000.000 + 000.000 + 009.9 − 01
1322.377 + 010.000 + 000.000 + 000.000 + 000.000 + 000.000 + 008.775 + 040.0 + 00
1332.369 + 011.114 + 122.813 − 012.194 − 020.000 + 000.000 + 000.000 + 001.0 + 00
1342.311 + 010.000 + 000.000 + 000.000 + 000.000 + 000.000 + 006.187 + 030.0 + 00
1352.310 + 018.909 + 102.138 − 021.626 − 030.000 + 000.000 + 000.000 + 008.2 − 01
1372.291 + 016.570 + 101.551 − 021.170 − 030.000 + 000.000 + 000.000 + 008.3 − 01
1382.276 + 010.000 + 000.000 + 000.000 + 000.000 + 006.454 + 030.000 + 000.0 + 00
1392.274 + 010.000 + 000.000 + 000.000 + 008.428 + 070.000 + 000.000 + 000.0 + 00
1412.271 + 010.000 + 000.000 + 000.000 + 000.000 + 001.889 + 020.000 + 000.0 + 00
1422.270 + 010.000 + 000.000 + 000.000 + 008.206 + 070.000 + 000.000 + 000.0 + 00
1442.257 + 010.000 + 000.000 + 000.000 + 000.000 + 004.896 + 010.000 + 000.0 + 00
1452.254 + 010.000 + 000.000 + 000.000 + 001.516 + 080.000 + 000.000 + 000.0 + 00
1462.252 + 010.000 + 000.000 + 000.000 + 000.000 + 006.392 + 030.000 + 000.0 + 00
1482.247 + 010.000 + 000.000 + 000.000 + 000.000 + 001.968 + 010.000 + 000.0 + 00
1492.247 + 010.000 + 000.000 + 000.000 + 002.945 + 070.000 + 000.000 + 000.0 + 00
1512.235 + 010.000 + 000.000 + 000.000 + 002.082 + 090.000 + 000.000 + 000.0 + 00
1532.228 + 011.660 + 103.704 − 032.717 − 040.000 + 000.000 + 000.000 + 009.5 − 01
1552.226 + 010.000 + 000.000 + 000.000 + 000.000 + 000.000 + 003.037 + 050.0 + 00
1572.224 + 010.000 + 000.000 + 000.000 + 000.000 + 000.000 + 005.724 + 040.0 + 00
1592.217 + 011.081 + 122.389 − 011.744 − 020.000 + 000.000 + 000.000 + 009.5 − 01
1622.207 + 010.000 + 000.000 + 000.000 + 000.000 + 000.000 + 001.861 + 040.0 + 00
1652.206 + 010.000 + 000.000 + 000.000 + 000.000 + 000.000 + 002.348 + 040.0 + 00
1672.205 + 010.000 + 000.000 + 000.000 + 002.607 + 070.000 + 000.000 + 000.0 + 00
1692.204 + 010.000 + 000.000 + 000.000 + 000.000 + 003.594 − 020.000 + 000.0 + 00
1702.204 + 010.000 + 000.000 + 000.000 + 003.388 + 070.000 + 000.000 + 000.0 + 00
1712.199 + 012.487 + 125.406 − 013.913 − 020.000 + 000.000 + 000.000 + 009.5 − 01
1742.187 + 010.000 + 000.000 + 000.000 + 007.572 + 070.000 + 000.000 + 000.0 + 00
1762.089 + 010.000 + 000.000 + 000.000 + 000.000 + 000.000 + 007.937 + 030.0 + 00
1772.088 + 015.646 + 101.108 − 027.614 − 040.000 + 000.000 + 000.000 + 007.1 − 01
1782.074 + 010.000 + 000.000 + 000.000 + 000.000 + 003.896 + 030.000 + 000.0 + 00
1792.073 + 010.000 + 000.000 + 000.000 + 002.839 + 070.000 + 000.000 + 000.0 + 00
1812.072 + 010.000 + 000.000 + 000.000 + 000.000 + 001.077 + 020.000 + 000.0 + 00
1832.072 + 010.000 + 000.000 + 000.000 + 002.467 + 070.000 + 000.000 + 000.0 + 00
1842.072 + 014.167 + 108.049 − 035.491 − 040.000 + 000.000 + 000.000 + 007.3 − 01
1862.057 + 010.000 + 000.000 + 000.000 + 000.000 + 001.494 + 020.000 + 000.0 + 00
1872.057 + 010.000 + 000.000 + 000.000 + 000.000 + 002.694 + 030.000 + 000.0 + 00
1882.056 + 010.000 + 000.000 + 000.000 + 003.006 + 070.000 + 000.000 + 000.0 + 00
1902.055 + 011.092 + 102.073 − 031.402 − 040.000 + 000.000 + 000.000 + 009.2 − 01
1922.054 + 010.000 + 000.000 + 000.000 + 000.000 + 000.000 + 001.693 + 050.0 + 00
1942.053 + 010.000 + 000.000 + 000.000 + 000.000 + 000.000 + 003.708 + 040.0 + 00
1972.050 + 019.711 + 111.835 − 011.238 − 020.000 + 000.000 + 000.000 + 009.2 − 01
1982.046 + 010.000 + 000.000 + 000.000 + 000.000 + 001.006 + 010.000 + 000.0 + 00
11012.046 + 010.000 + 000.000 + 000.000 + 007.876 + 070.000 + 000.000 + 000.0 + 00
11032.046 + 010.000 + 000.000 + 000.000 + 001.535 + 080.000 + 000.000 + 000.0 + 00
11042.046 + 010.000 + 000.000 + 000.000 + 000.000 + 000.000 + 006.763 − 010.0 + 00
11142.038 + 010.000 + 000.000 + 000.000 + 000.000 + 000.000 + 007.163 + 030.0 + 00
11152.038 + 010.000 + 000.000 + 000.000 + 000.000 + 000.000 + 002.434 + 040.0 + 00
11172.035 + 011.052 + 121.960 − 011.313 − 020.000 + 000.000 + 000.000 + 009.2 − 01
11212.030 + 010.000 + 000.000 + 000.000 + 001.136 + 080.000 + 000.000 + 000.0 + 00
Table 8. Transition wavelengths ( λ i j in Å), radiative rates (A j i in s 1 ), oscillator strengths (f i j , dimensionless), and line strengths (S, in atomic units) for electric dipole (E1), and A j i for E2, M1 and M2 transitions in Y XXX. The last column gives the ratio R of the velocity and length forms of A(E1). a ± ba × 10 ± b .
Table 8. Transition wavelengths ( λ i j in Å), radiative rates (A j i in s 1 ), oscillator strengths (f i j , dimensionless), and line strengths (S, in atomic units) for electric dipole (E1), and A j i for E2, M1 and M2 transitions in Y XXX. The last column gives the ratio R of the velocity and length forms of A(E1). a ± ba × 10 ± b .
ij λ ij A ji E 1 f ij E 1 S E 1 A ji E 2 A ij M 1 A M 2 R
126.212 + 000.000 + 000.000 + 000.000 + 000.000 + 000.000 + 001.133 + 070.0 + 00
136.201 + 007.791 + 121.347 − 012.750 − 030.000 + 000.000 + 000.000 + 009.8 − 01
146.036 + 000.000 + 000.000 + 000.000 + 000.000 + 002.716 + 070.000 + 000.0 + 00
156.028 + 000.000 + 000.000 + 000.000 + 001.212 + 100.000 + 000.000 + 000.0 + 00
175.976 + 000.000 + 000.000 + 000.000 + 000.000 + 002.612 + 060.000 + 000.0 + 00
195.971 + 005.295 + 128.492 − 021.669 − 030.000 + 000.000 + 000.000 + 009.8 − 01
1105.962 + 000.000 + 000.000 + 000.000 + 001.207 + 100.000 + 000.000 + 000.0 + 00
1125.810 + 000.000 + 000.000 + 000.000 + 000.000 + 009.393 + 050.000 + 000.0 + 00
1145.772 + 002.314 + 113.467 − 036.588 − 050.000 + 000.000 + 000.000 + 009.9 − 01
1165.758 + 000.000 + 000.000 + 000.000 + 000.000 + 000.000 + 001.542 + 080.0 + 00
1185.756 + 000.000 + 000.000 + 000.000 + 000.000 + 001.680 + 070.000 + 000.0 + 00
1195.752 + 000.000 + 000.000 + 000.000 + 001.360 + 100.000 + 000.000 + 000.0 + 00
1205.748 + 000.000 + 000.000 + 000.000 + 000.000 + 000.000 + 002.417 + 080.0 + 00
1235.704 + 001.170 + 141.711 + 003.213 − 020.000 + 000.000 + 000.000 + 009.9 − 01
1245.560 + 000.000 + 000.000 + 000.000 + 000.000 + 000.000 + 001.046 + 070.0 + 00
1255.549 + 000.000 + 000.000 + 000.000 + 000.000 + 000.000 + 005.876 + 070.0 + 00
1275.527 + 001.278 + 141.756 + 003.195 − 020.000 + 000.000 + 000.000 + 009.9 − 01
1285.437 + 000.000 + 000.000 + 000.000 + 000.000 + 002.951 + 060.000 + 000.0 + 00
1315.297 + 008.047 + 121.015 − 011.771 − 030.000 + 000.000 + 000.000 + 001.0 + 00
1325.255 + 000.000 + 000.000 + 000.000 + 000.000 + 000.000 + 005.146 + 070.0 + 00
1335.249 + 002.487 + 133.082 − 01