LABORATORY MEASUREMENTS OF THE K-SHELL TRANSITION ENERGIES IN L-SHELL IONS OF SI AND S

The measurements presented here were carried out using the Lawrence Livermore National Laboratory (LLNL) electron beam ion traps, EBIT-I (Run-I) and SuperEBIT (Run-II). The details of their operation have been described elsewhere (Levine et al. 1988; Marrs et al. 1988, 1994; Beiersdorfer 2003, 2008). In brief, highly charged ions are produced, trapped, and excited by EBIT using a near mono-energetic electron beam and an electrostatic trap. Several methods have been developed to inject elements for study (Brown et al. 1986; Schneider et al. 1989; Elliott & Marrs 1995; Ullrich et al. 1998; Niles et al. 2006; Yamada et al. 2007; Magee et al. 2014). For the experiments described here, neutral sulfur and silicon were injected into the EBIT's trap region as gaseous ${\mathrm{SF}}_{6}$ and ${{\rm{C}}}_{10}{{\rm{H}}}_{30}{{\rm{O}}}_{3}{\mathrm{Si}}_{4}$, respectively, using a well-collimated ballistic gas injector. Once the neutral material intersects the electron beam, the molecules are broken apart and resulting atoms are collisionally ionized and trapped. To avoid the build up of high-Z material, such as tungsten and barium originating from the electron gun, the trap region is emptied and refilled periodically, on a timescale of tens of milliseconds.

The electron impact excitation energies of the K-shell transitions in the silicon and sulfur ions are ≳1.73 keV, while the ionization energies for the L-shell ions range from 166.8 eV for Ne-like Si v to 707.2 eV for Li-like S xiv (Cowan 1981). Hence, in order to excite the Kα lines the electron beam energy must be ∼3–10 times the ionization threshold. Under typical operating conditions at these energies, the charge state distribution would be dominated by lithium- and helium-like ions. In order to produce a significant amount of lower charge states at the high electron impact energies required for inner-shell excitation, several methods have been developed (Decaux & Beiersdorfer 1993; Schmidt et al. 2004). In the present experiment, the neutral gas injection pressure is set to values several orders of magnitudes larger than EBIT's base pressure of $\lesssim {10}^{-10}\,\mathrm{Torr}$, short refill cycle times and relatively low electron beam currents were employed. Together, these operating parameters yield a significant fraction of low charge states at high electron impact energy. The spectral signature of significant amounts of several L-shell ions can easily be seen in the X-ray spectra (see Figure 1). Note that the electron beam energies employed at these measurements were well away from any dielectronic recombination resonances of the respective measured elements, i.e., the emission lines originate entirely from electron impact excitation and inner-shell ionization, contrary to the laser experiments reported by Faenov et al. (1994).

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The spectrum of the X-ray radiation from the trapped ions is recorded with the 16 low-energy pixels of the EBIT Calorimeter Spectrometer (ECS; Porter et al. 2008a, 2008b, 2009a, 2009b), designed and built by the NASA/GSFC Calorimeter group. The ECS is the improved successor of the XRS/EBIT (Porter et al. 2004, 2008a), the engineering model of the Astro-E2/Suzaku calorimeter. The energy resolution of the ECS for these measurements was 4.5–5.0 eV, typical for the ECS. The spectra shown here are similar in quality to a spectrum measured with the Soft X-ray Spectrometer (SXS) system (Mitsuda et al. 2010) onboard the Astro-H/Hitomi X-ray observatory (Takahashi et al. 2010) or in the planned X-IFU instrument on Athena (Nandra et al. 2014; Ravera et al. 2014).

To assess the systematic errors in our measurement, we conducted a second experimental run using SuperEBIT (Run-II). SuperEBIT is the high-energy variant of EBIT-I used in Run-I and can achieve electron beam energies up to 250 keV (Beiersdorfer et al. 2003). SuperEBIT was used for Run-II because of beam time availability.

Because of slight variations in performance, each pixel in the ECS array is calibrated separately. The energy scale for each pixel is determined by fitting 4th order polynomial functions to the measured pulse heights in volts space of known reference emission lines (Porter et al. 1997; Cottam et al. 2005); here, the X-ray line emission from K-shell transitions in He-like ions (Kα/line w: $1{\rm{s}}\,2{\rm{p}}\,{}^{1}{{\rm{P}}}_{1}\to 1{{\rm{s}}}^{2}\,{}^{1}{{\rm{S}}}_{0};$ Kβ: $1{\rm{s}}\,3{\rm{p}}\to 1{{\rm{s}}}^{2};$ Kγ: $1{\rm{s}}\,4{\rm{p}}\to 1{{\rm{s}}}^{2}$) and H-like ions (Lyα: $2{\rm{p}}\to 1{\rm{s}};$ Ly β: $3{\rm{p}}\to 1{\rm{s}}$). Specifically, for the Run-I measurement, the 1.7–1.9 keV band containing the lower charge states of silicon was calibrated with Kα, Lyα, Kβ, and Ly β lines of neon and silicon. For the 2.3–2.5 keV band containing the lower charge states of sulfur, Kα, Lyα, and Kβ of sulfur and Kα–Kγ of fluorine were used. For Run-II, Ne and S Kα, Lyα, and Kβ, and Si Kα–Kγ and Lyα were used to calibrate the silicon spectra, and Ne Kα, Lyα, and Kβ, Si and S Kα and Lyα, and Ar Kα were used to calibrate the sulfur spectra.

The reference wavelengths of the He-like systems used for calibration originate from Drake (1988) in case of the $1{\rm{s}}\,2{\rm{p}}\to 1{{\rm{s}}}^{2}$ resonance line labelled "w" in the notation of Gabriel (1972). The wavelengths for $1{\rm{s}}\,3{\rm{p}}\to 1{{\rm{s}}}^{2}$ Kβ and $1{\rm{s}}\,4{\rm{p}}\to 1{{\rm{s}}}^{2}$ Kγ Rydberg states were taken from Vainshtein & Safronova (1985) and corrected for the ground state of Drake (1988) according to Beiersdorfer et al. (1989). Values for the Lyman series in the H-like systems are from Garcia & Mack (1965). The wavelengths were converted to energy using $E={hc}{\lambda }^{-1}$ where ${hc}=12398.42\,\mathrm{eV}\,\mathring{\rm A}$ (with values for h, c and e from CODATA 2014, Mohr et al. 2015).

After calibration, the ECS events were binned to an energy grid of 0.5 eV. Figure 1 shows the summed Si and S spectra of all 16 low-energy ECS pixels for Run-I. To gauge the accuracy of the energy scale, the location of the H-like Lyα lines and the He-like line w of Si and S are determined from a simultaneous fit of the calibrated Run-I and Run-II spectra. The fitted values are then compared to the initial reference values. Table 1 shows the value from the comparison as well as from our FAC calculation, which is used as a guide for line identification (see below, Section 3.2). For silicon line w, the calibrated values are 0.16 eV lower than the reference values, for sulfur line w, they are 0.017 eV lower. For the S Lyα lines, the difference between theory and experiment is slightly larger, but still well below 0.5 eV (Table 1). Combining the uncertainties of the Lyα and w lines amounts to 0.13 eV for silicon and 0.23 eV for sulfur, which are taken as the systematic uncertainties. FAC results agree with Drake (1988) to within 0.2 eV in case of the transition energies in He-like ions, and within 0.03 eV for the transition energies in H-like ions.

Table 1.  Calibration Results

Z	Line	FWHM	Line Energy (eV)			${\rm{\Delta }}{E}_{\mathrm{ref}}$	${\rm{\Delta }}{E}_{\mathrm{FAC}}$
		(eV)	Fit	Reference	FAC
Si	w	${4.36}_{-0.12}^{+0.08}$/4.92 ± 0.12	1864.84 ± 0.05	1864.9995	1864.812	−0.16	0.03
Si	Lyα	⋯	${2005.59}_{-0.20}^{+0.17}$	2005.494a	2005.516a	−0.10	0.07
S	w	4.55 ± 0.04/4.98 ± 0.14	2460.609 ± 0.018	2460.6255	2460.417	−0.017	0.191
S	Lyα1	⋯	${2622.97}_{-0.26}^{+0.18}$	2622.700	2622.730	$\phantom{-}0.27$	0.24
S	Lyα2	⋯	${2620.00}_{-0.34}^{+0.21}$	2619.701	2619.731	−0.30	0.27

Notes. Comparison between the fitted line centers (fit) of the He-like $1{\rm{s}}\,2{\rm{p}}\to 1{{\rm{s}}}^{2}$ line w with the reference value (reference) of Drake (1988) and of the H-like $2{\rm{p}}\to 1{\rm{s}}$ Lyα lines of Si and S with the values of Garcia & Mack (1965), which were used for calibration. The full width half maximum (FWHM) determined from line w (used as detector resolution throughout the fits) is listed for Run-I/Run-II. ${\rm{\Delta }}{E}_{i}$ gives the difference between the fit and the respective theoretical values. Listed uncertainties are purely statistical.

^aMean value of Lyα₁ and Lyα₂ weighted by their statistical weights.

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The fitted widths of the He-like lines of about 4.5–5.0 eV are consistent with the expected energy resolution of the ECS in this energy region.

In order to determine the transition energies of as many individual lines as the data allow, the spectra from Run-I and Run-II were fit simultaneously for each element, using the Interactive Spectral Interpretation System (ISIS; Houck & Denicola 2000; Houck 2002; Noble & Nowak 2008). The modeled energy range spans 1720–1880 eV for the Si spectra and 2290–2480 eV for the S spectra. The models for Run-I and Run-II consist of a sum of individual Gaussian lines, where the centers of these lines are tied between Run-I and Run-II, their widths are fixed to the respective resolution (Table 1), and their normalizations are left to vary freely. Fixing the line widths is valid because the natural line widths and the Doppler widths are small compared to the resolution of the calorimeter, no other line broadening mechanism is present in these experiments, and the energy resolution of the calorimeter is constant over these small energy ranges. In order to account for the flux above background found between the main peaks of the spectra, e.g., Figure 2, the models include a single second-order polynomial for each data set. A possible explanation for the presence of this continuum are weak unresolved lines (see Figure 5 in Section 3.3), low-energy spectral redistribution due to photon and electron escape events (Cottam et al. 2005), or some combination of both.

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In order to determine the number of Gaussian components required to describe the data, we test the statistical significance of each line. A Monte Carlo type simulation (see mc_sig of the Remeis ISISscripts), generates 10³ realizations of fake spectra based on the existing best-fit model: for each energy bin of the fake spectrum, it draws a random number from a Poisson distribution with the mean equal to the modeled value. These fake spectra are fitted with the model used to create them (model A) and with a model containing an additional Gaussian line (model B). Because of the increased number of degrees of freedom, the ${\chi }^{2}$ value for model B will be at least slightly better than the ${\chi }^{2}$ for model A. The additional line in model B is only accepted if the improvements, ${\rm{\Delta }}{\chi }_{\mathrm{fake},i}^{2}={\chi }_{{\rm{B}},i}^{2}-{\chi }_{{\rm{A}},i}^{2}$, of 99% of the simulated cases are smaller than the improvement in the real spectrum. Figure 2 shows the final distribution of the single Gaussian components for silicon and for sulfur. Tables 5 and 6 list the resulting line centers with their statistical 90% confidence limits.

As an additional consistency check for the accuracy of our results, in a second approach we allow for a constant shift of the Run-II data compared to the Run-I data. The derived constants of ${0.13}_{-0.05}^{+0.06}$ eV for Si and −0.12 ± 0.05 eV for S are consistent with our estimate of the systematic uncertainty of our calibration (Section 2.3).

To identify the lines associated with our measured spectra, we use FAC (Gu 2004b, 2008) to calculate the wavelengths of transitions in the involved ions and model the measured spectra. FAC is a compound package based on a fully relativistic ansatz via the Dirac equation which provides functions to calculate the atomic structure, bound–bound and bound-free processes, and includes a collisional ionization equilibrium code to estimate the line intensities for given plasma conditions (electron beam properties or plasma temperatures; Gu 2004a). The accuracy of FAC, determined from comparisons between FAC and experiments, is a few eV or 10–30 mÅ at ∼10 Å for energy levels (other than H-like) and 10%–20% for radiative transition rates and cross sections (Gu 2004a).

Our FAC calculations take into account radiative (de-)excitation, collisional (de-)excitation and ionization, autoionization, dielectronic recombination, and radiative recombination. At EBIT densities, the coronal limit applies, i.e., electron impact collisional excitation, inner-shell ionization, and subsequent radiative cascades are the main processes to populate upper states. At the electron beam energies used here, no emission from dielectronic recombination exists for the ions of interest and no X-rays from radiative recombination fall into our energy band. Although the main application for our results is photoionized plasmas, the collisional nature of EBIT does not compromise this task.

Our calculations include emission from all the $n\to 1$ transitions in Na-like to H-like silicon and sulfur, where $2\leqslant n\leqslant 5$, allowing interactions between all levels, including ${\rm{\Delta }}n=0$ transitions. For these limits, the calculation could be completed in a reasonable time. The contribution to the line strength from higher n transitions is negligible. Since the charge state distribution in EBIT depends on ionization and recombination processes, the level populations are estimated for all ions in a single calculation. The other plasma code parameters are the electron beam energy, which we assume to follow a Gaussian distribution with an energy spread of ∼40 eV (Beiersdorfer et al. 1992; Gu et al. 1999), and an electron density of ${10}^{12}\,{\mathrm{cm}}^{-3}$, which we estimate from beam current and energy. The relative abundances of the trapped ions are set to be 1. The simulation of the spectrum produced in the trap is therefore not self-consistent.

Figure 3 illustrates the resulting FAC simulations for silicon and sulfur, considering the presence of H- through Na-like ions. The line centers of transitions calculated by FAC are convolved with a Gaussian line with a FWHM of 4.6 eV, i.e., the resolution of the calorimeter (see Section 2.3).

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While the strongest K-shell line features from each charge state are easily resolved (Figures 1 and 3), identifying the transitions that contribute to each feature is accomplished by comparison to the FAC calculation as follows. For each feature we plot the data and individual model components and overlay them with the transitions obtained from FAC (Figures 9 and 10). Then we assume that for every Gaussian fit component the main contribution comes from the strongest FAC lines at this energy and identify the model component with these lines. The results are listed in Tables 5 (Si) and 6 (S). In each row the FAC lines are followed by the corresponding transitions as calculated by P08 (see Section 3.3 for details) and CHIANTI, if available. For most measured peaks, the distribution of the FAC lines agrees well enough with the measurements to allow a reliable identification. Both the Si and S spectra behave very similarly, so our description of the spectra here focuses on the contributions by iso-electronic sequence, for the most part not distinguishing in Z except in the rare cases where significant differences occur between the Si and S spectra.

The main Li-like, Be-like, and B-like features are each dominated by a single strong transition that is easily reproduced by the Gaussian components fitted to the spectra (see features labeled Li-2, Be-1, B-1 in Figures 9 and 10 panels (e)–(g)). Although there are a few weaker transitions surrounding these strong lines, they do not strongly affect the fitted line centers. Both the Be- and B-like features have a low-energy shoulder caused by weaker transitions that have a just large enough separation from the strong transition to be resolved. According to our FAC calculations, the Li-like ion also has a relatively strong transition that sits right between the Be-like lines. Although in the synthetic Si spectrum the Li-like line appears to have similar strength as the strong Be-like line, a comparison of Figure 3 to the measured Si spectrum shows that due to the incorrect assumption of charge balance entering our simulation, the synthetic spectra overestimate the Li-like features relative to the Be-like ones. Accordingly, despite this Li-like transition being unresolved in Si, it does not seem to affect the fitted line centers of the Be-like transitions Be-1 and Be-2 much (Figure 9, panel (f)). For S on the other hand (Figure 10, panel (f)), the Li-like transitions are attributed to their own Gaussian component (Be-2) while the weak Be-like line is assigned to a separate component (Be-3).

The transition rich spectra of the lower charge states C-like, O-like, and N-like are more complex as they have many transitions of similar strength rather than a distinct strong transition among a few weak ones (Figures 9 and 10, panels (b)–(d)). However, some of these transitions tend to cluster into groups. The separation of these groups is larger for the higher-Z element S, making it easier to partially resolve them. As discussed for iron by Decaux et al. (1997), starting around C-like ions the Kα line emission of the lower charge states probably has strong contributions from states excited through inner-shell ionization in addition to the collisionally excited states.

In the C-like ions (Figures 9 and 10, panel (d)), the strongest fitted component, C-2, is made up of the strongest calculated transitions at slightly lower energies than the component'(s) center and a few weaker transitions at and slightly above the fitted energy. The C-like feature also has a strong low-energy shoulder (C-3) from transitions similar in strength to the ones from the C-2 cluster, and a weaker high-energy shoulder (C-1) consisting of a C-like and two weak Li-like transitions.

The N-like transitions split into four main groups (Figures 9 and 10, panel (c)). They are accompanied by a Be-like transition in the low-energy tail of their spectral feature. Again, the larger spacing in S is beneficial, although in both Si and S this feature is modeled by three components. While N-1 coincides well with the first group of calculated transitions on the high-energy side for both components, the second group containing the other two of the strongest four transitions falls right between N-1 and N-2 in Si, but is clearly attributed to N-2 in S. N-2 also encompasses the third group of transitions, while N-3 contains the last group of N-like transitions and the mentioned Be-like transition.

The O-like peak is also described by three Gaussians (Figures 9 and 10, panel (b)). The strongest line calculated with FAC makes up the weaker component at high energies (O-1), while the main component (O-2) consists of a number of weaker transitions. A single O-like transition accounts for the low-energy shoulder (O-3).

The lowest energy peak (Figures 9 and 10, panel (a)) consists of a blend of K-shell transitions in F-like ions as well as emission from lower charge states (Figure 4). This is a result of the fact that, for charge states other than F-like, emission is dominated by innershell ionization followed by radiative decay in these cases and the effect of additional spectator electrons in $n\geqslant 3$ shell on these transition energies is relatively small. Additionally, owing to the open n = 3 shell, the M-shell ions have a more complex energy level structure—and, therefore, a multidue of transitions—in each of these charge states. The energy ranges covered by these transitions overlap severely (Figure 5). Specifically, the Kα transition energies from these charge states fall within a 3 eV energy band and are therefore unresolved (Figure 4). Consequently, although the F-like ion only has two distinct transitions, we cannot resolve this charge state individually from the transitions in M-shell ions in these low-Z elements. This last peak is modeled by two (Si) and three (S) Gaussian components, respectively. In both cases, we attribute the first, i.e., high-energy component (F-1) to a mixture of transissions in F-like and Ne-like ions. In case of the Si X-1 line at 1740.04 eV, however, there are no lines of considerable strength in our calculations that could be used for identification. We tentatively identify this line as a blend of Kα emission from very low charge states with more than 10 electrons. Similarly, although Table 6 lists weak transitions in Na-like S vi and B-like S xii for the lines F-2 and F-3, these lines probably also have a significant contribution from weak lines from near-neutral ions, as discussed for the case of silicon.

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Also notable is that for both Si and S, line z as calculated with FAC (Si: 1838.20 eV, S: 2429.075 eV) has a large offset (>1 eV) compared to the measured line center (Si: 1839.33 eV, S: 2430.380 eV). Our measurement is, however, consistent with the reference values reported by Drake (1988, Si: 1839.448 eV; S: 2430.347 eV).

For completeness and to provide a test for the accuracy of the Kα line energies employed by XSTAR, we compare our measurements and our FAC calculations to those of P08. Note that the calculated transition wavelengths listed by P08 have been empirically shifted by P08 for ions with $3\leqslant N\leqslant 9$, where N is the number of electrons. A qualitative comparison between the results obtained with FAC and the lines published by P08 is displayed in Figure 5 for silicon. Since the P08 data do not provide luminosities, the line distributions are shown via their radiative transition rates (Einstein A). P08 only list $2{\ell }\to 1{\rm{s}}$ transitions. We therefore also filter for these lines calculated with FAC. The transitions with a spectator electron in a higher n shell blend strongly with Kα transitions of the next ionization state, but according to the FAC calculations, their contribution to the Kα line strength is negligible (Figure 3).

As expected, the positions of the He-like lines agree very well. For lower ionization states, the general distribution of the lines is still similar, but the predicted energy separation of some line features does not agree. For example, there are two O-like Si vii lines around 1750 eV (Figure 5), specifically the transitions 1s²2s2p⁵ ${}^{1}{{\rm{P}}}_{1}^{{\rm{o}}}$—1s2s2p⁶ ${}^{1}{{\rm{S}}}_{0}$ and 1s²2s²2p⁴ ${}^{1}{{\rm{S}}}_{0}$—1s2s²2p⁵ ${}^{1}{{\rm{P}}}_{1}^{{\rm{o}}}$ (P08) respectively ${(1{{\rm{s}}}^{2}2{{\rm{s}}}_{1/2}2{{\rm{p}}}_{1/2}^{2}{(2{{\rm{p}}}_{3/2}^{3})}_{3/2})}_{1}$—${(1{{\rm{s}}}_{1/2}2{{\rm{s}}}_{1/2}2{{\rm{p}}}_{1/2}^{2}2{{\rm{p}}}_{3/2}^{4})}_{0}$ and 1${{\rm{s}}}^{2}$ 2${{\rm{s}}}^{2}$ 2${{\rm{p}}}_{1/2}^{2}$ ${(2{{\rm{p}}}_{3/2}^{2})}_{0}$— ${(1{{\rm{s}}}_{1/2}2{{\rm{s}}}^{2}2{{\rm{p}}}_{1/2}^{2}{(2{{\rm{p}}}_{3/2}^{3})}_{3/2})}_{1}$ (FAC), for which the ratio of the transition probabilities is approximately the same in both calculations (P08: 0.21; FAC: 0.20). The separation of their line energies, however, is almost twice as large in FAC (2.32 eV) as in P08 (1.33 eV). The most outstanding difference is that in the P08 calculations the two F-like spectral lines at ∼1741 eV have distinctly lower energies than the Ne-like lines, although the Ne-like iso-electronic sequence has an electron more than the F-like ions. This behavior is in contrast to the FAC calculations where the F-like lines have higher energies.

Comparing FAC (jj-coupling) and P08 (LS-coupling) is not trivial since the two calculations are based on different coupling schemes. It is therefore necessary to translate one scheme into the other. The calculations are in sufficient agreement such that most lines can be identified through a comparison of the line lists instead of resorting to a complicated formal mapping between both schemes (see, e.g., Calvert & Tuttle 1979; Dyall 1986). We do this comparison by first sorting the levels of both calculations according to energy and then matching the levels in order of increasing energy. The match is cross-checked via the total angular momentum J, which is the only good quantum number common between the two coupling schemes and therefore should be identical between them. In cases where J does not match between two assigned levels, LS-coupling multiplets can be rearranged for their Js to fit the jj-coupling partners. This is possible because within these multiplets the differences between the calculated level energies are smaller than the estimated uncertainty of the calculations and, in most cases, smaller than the energy differences between P08 and FAC results.

As an example, Table 2 lists the sorted energy levels of Li-like Si xii for both FAC and P08. Figure 6 shows a comparison of their total angular momenta. The energy differences between the levels from different calculations are within their stated accuracy of at least 2 eV. The levels with IDs 14 and 15 are mismatched in their J. These levels belong to the doublet ${}^{2}{\rm{D}}$, with a fine structure splitting of roughly 0.1 eV. This difference is small compared to the ∼0.4 eV between FAC and P08. For practical purposes we therefore assume that FAC level 14 corresponds to P08 level 15 and vice versa. The results are listed in Tables 5 and 6.

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Table 2.  Comparison of the FAC and P08 Energy Levels of Li-like Si

Level	FAC/jj-coupling			P08/LS-coupling
ID	label	$2J$	E (eV)	label	2J	E (eV)
0	1${{\rm{s}}}^{2}$ 2${{\rm{s}}}_{1/2}$	1	0.0000	1s22s ${}^{2}{{\rm{S}}}_{1/2}$	1	0.0000
1	1${{\rm{s}}}^{2}$ 2${{\rm{p}}}_{1/2}^{}$	1	24.2019	1s22p ${}^{2}{{\rm{P}}}_{1/2}^{{\rm{o}}}$	1	23.8072
2	1${{\rm{s}}}^{2}$ 2${{\rm{p}}}_{3/2}^{}$	3	25.1920	1s22p ${}^{2}{{\rm{P}}}_{3/2}^{{\rm{o}}}$	3	24.8172
3	1${{\rm{s}}}_{1/2}$ 2${{\rm{s}}}^{2}$	1	1819.3742	1s2s2 ${}^{2}{{\rm{S}}}_{1/2}$	1	1819.7636
4	$((1{{\rm{s}}}_{1/2}\,2{{\rm{s}}}_{1/2}{)}_{1}^{}\,2{{\rm{p}}}_{1/2}^{}{)}_{1/2}^{}$	1	1825.5977	1s(${}^{2}{\rm{S}}$)2s2p(${}^{3}{{\rm{P}}}^{{\rm{o}}}$) ${}^{4}{{\rm{P}}}_{1/2}^{{\rm{o}}}$	1	1825.6379
5	$((1{{\rm{s}}}_{1/2}\,2{{\rm{s}}}_{1/2}{)}_{1}^{}\,2{{\rm{p}}}_{1/2}^{}{)}_{3/2}^{}$	3	1825.8735	1s(${}^{2}{\rm{S}}$)2s2p(${}^{3}{{\rm{P}}}^{{\rm{o}}}$) ${}^{4}{{\rm{P}}}_{3/2}^{{\rm{o}}}$	3	1826.0523
6	$((1{{\rm{s}}}_{1/2}\,2{{\rm{s}}}_{1/2}{)}_{1}^{}\,2{{\rm{p}}}_{3/2}^{}{)}_{5/2}^{}$	5	1826.5509	1s(${}^{2}{\rm{S}}$)2s2p(${}^{3}{{\rm{P}}}^{{\rm{o}}}$) ${}^{4}{{\rm{P}}}_{5/2}^{{\rm{o}}}$	5	1826.7783
7	$((1{{\rm{s}}}_{1/2}\,2{{\rm{s}}}_{1/2}{)}_{0}^{}\,2{{\rm{p}}}_{1/2}^{}{)}_{1/2}^{}$	1	1844.2892	1s(${}^{2}{\rm{S}}$)2s2p(${}^{3}{{\rm{P}}}^{{\rm{o}}}$) ${}^{2}{{\rm{P}}}_{1/2}^{{\rm{o}}}$	1	1844.7912
8	$((1{{\rm{s}}}_{1/2}\,2{{\rm{s}}}_{1/2}{)}_{0}^{}\,2{{\rm{p}}}_{3/2}^{}{)}_{3/2}^{}$	3	1844.8632	1s(${}^{2}{\rm{S}}$)2s2p(${}^{3}{{\rm{P}}}^{{\rm{o}}}$) ${}^{2}{{\rm{P}}}_{3/2}^{{\rm{o}}}$	3	1845.3252
9	$(1{{\rm{s}}}_{1/2}(2{{\rm{p}}}_{1/2}^{2}{)}_{0}^{}{)}_{1/2}^{}$	1	1851.4807	1s(${}^{2}{\rm{S}}$)2p2(${}^{3}{\rm{P}}$) ${}^{4}{{\rm{P}}}_{1/2}$	1	1851.1741
10	$((1{{\rm{s}}}_{1/2}\,2{{\rm{p}}}_{1/2}^{}{)}_{0}^{}\,2{{\rm{p}}}_{3/2}^{}{)}_{3/2}^{}$	3	1851.8761	1s(${}^{2}{\rm{S}}$)2p2(${}^{3}{\rm{P}}$) ${}^{4}{{\rm{P}}}_{3/2}$	3	1851.6101
11	$(1{{\rm{s}}}_{1/2}(2{{\rm{p}}}_{3/2}^{2}{)}_{2}^{}{)}_{5/2}^{}$	5	1852.4077	1s(${}^{2}{\rm{S}}$)2p2(${}^{3}{\rm{P}}$) ${}^{4}{{\rm{P}}}_{5/2}$	5	1852.2880
12	$((1{{\rm{s}}}_{1/2}\,2{{\rm{s}}}_{1/2}{)}_{1}^{}\,2{{\rm{p}}}_{3/2}^{}{)}_{1/2}^{}$	1	1853.9104	1s(${}^{2}{\rm{S}}$)2s2p(${}^{1}{{\rm{P}}}^{{\rm{o}}}$) ${}^{2}{{\rm{P}}}_{1/2}^{{\rm{o}}}$	1	1853.8947
13	$((1{{\rm{s}}}_{1/2}\,2{{\rm{s}}}_{1/2}{)}_{0}^{}\,2{{\rm{p}}}_{3/2}^{}{)}_{3/2}^{}$	3	1854.0850	1s(${}^{2}{\rm{S}}$)2s2p(${}^{1}{{\rm{P}}}^{{\rm{o}}}$) ${}^{2}{{\rm{P}}}_{3/2}^{{\rm{o}}}$	3	1854.2217
14	$((1{{\rm{s}}}_{1/2}\,2{{\rm{p}}}_{1/2}^{}{)}_{1}^{}\,2{{\rm{p}}}_{3/2}^{}{)}_{5/2}^{}$	5	1864.3543	1s(${}^{2}{\rm{S}}$)2p2(${}^{1}{\rm{D}}$) ${}^{2}{{\rm{D}}}_{3/2}$	3	1863.9732
15	$((1{{\rm{s}}}_{1/2}\,2{{\rm{p}}}_{1/2}^{}{)}_{0}^{}\,2{{\rm{p}}}_{3/2}^{}{)}_{3/2}^{}$	3	1864.4771	1s(${}^{2}{\rm{S}}$)2p2(${}^{1}{\rm{D}}$) ${}^{2}{{\rm{D}}}_{5/2}$	5	1864.0761
16	$((1{{\rm{s}}}_{1/2}\,2{{\rm{p}}}_{1/2}^{}{)}_{1}^{}\,2{{\rm{p}}}_{3/2}^{}{)}_{1/2}^{}$	1	1867.1243	1s(${}^{2}{\rm{S}}$)2p2(${}^{3}{\rm{P}}$) ${}^{2}{{\rm{P}}}_{1/2}$	1	1866.9400
17	$(1{{\rm{s}}}_{1/2}(2{{\rm{p}}}_{3/2}^{2}{)}_{2}^{}{)}_{3/2}^{}$	3	1868.0803	1s(${}^{2}{\rm{S}}$)2p2(${}^{3}{\rm{P}}$) ${}^{2}{{\rm{P}}}_{3/2}$	3	1867.8849
18	$(1{{\rm{s}}}_{1/2}(2{{\rm{p}}}_{3/2}^{2}{)}_{0}^{}{)}_{1/2}^{}$	1	1881.3194	1s(${}^{2}{\rm{S}}$)2p2(${}^{1}{\rm{S}}$) ${}^{2}{{\rm{S}}}_{1/2}$	1	1881.2095

Note. With the exception of levels 14 and 15 (marked in bold), which have to be swapped either in FAC or in P08 in order for the total angular momentum to match the LS- and jj-coupling notations, this table can be used to match the LS- and jj-coupling notations. The level IDs are the same as in Figure 6.

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