K-shell X-Ray Emission from Lithium-like Nitrogen N v

We present laboratory measurements of n = 3 → n = 1 N v X-ray emission lines situated near 26 Å. The lines are excited by electron-impact collisions and are shown to reach a combined intensity of about a fifth of the combined strong N v 1s2s2p 2 P 1/2,3/2 → 1s 22s 2 S 1/2 resonance lines, commonly labeled q and r, at 29.4 Å. In addition, we present new experimental data for the wavelength of the blended q and r lines at 29.4 Å, as well as for that of the blended inner-shell-excited N v lines u and v at 30.0 Å. All of these collisional N v lines need to be included in astrophysical emission models in order to properly account for flux from N v in the soft X-ray region. The measured wavelengths provide benchmarks for testing atomic structure calculations and excellent agreement is found with our calculations using the many-body perturbation theory method. We provide a complete listing of the N v energy levels with valence electrons in the n = 2, 3, and 4 shells calculated with this approach. The experimental and theoretical data, thus, provide accurate rest-frame wavelengths needed for velocity determinations based on high-resolution absorption features in spectra of warm absorbers in active galactic nuclei and other astrophysical objects.


Introduction
Depending on the temperature and thus the ionization balance, the K-shell emission lines from ionization stages lower than helium-like can be significant and dominate, for example, the spectral emission of the K-shell iron emission (Seely et al. 1986;Beiersdorfer et al. 1993;Gu et al. 2012).The emission from lower charge states drops as the atomic number of the emitting element drops because autoionization becomes increasingly competitive with X-ray emission.Nevertheless, even elements with atomic number Z as low as nitrogen (Z = 7) still exhibit significant X-ray flux from collisionally excited lithium-like ions.This emission needs to be taken into account when modeling astrophysical X-ray sources, even if these emission lines are blended and generally unresolved, such as the observations made with the Hitomi and soon with the XRISM X-ray observatories (Hell et al. 2013(Hell et al. , 2016(Hell et al. , 2020;;Hitomi Collaboration et al. 2016;Takahashi et al. 2018;Tashiro et al. 2020).
Moreover, the presence of lower ionization stages in warm absorbers surrounding active galactic nuclei can result in deep spectral absorption features, when observed with the powerful grating spectrometers aboard the Chandra and the XMM-Newton X-ray Observatories (Jansen & Parmar 2001;Weisskopf et al. 2002).More recently, such spectra were used to diagnose the C to N ratio in tidal disruptive events (Miller et al. 2015(Miller et al. , 2023)).These absorption features have become a tool for diagnosing flow velocities from the Doppler shift of a given absorption line (Kaastra et al. 2006(Kaastra et al. , 2011)).This means that the rest wavelength of a given transition must be known very accurately, which typically requires laboratory measurements, as demonstrated by measurements of the K-shell transitions from O VII, O VI, O V, and O IV (Schmidt et al. 2004;Gu et al. 2005;Beiersdorfer & Gu 2022).
In the following, we present laboratory measurements of the rest wavelengths of four prominent n = 2, 3 → n = 1 K-shell X-ray lines from N V.These lines are situated in the wavelength region between 25 and 30 Å, and are readily identified in our spectra produced by electron-impact excitation.Thus, they add to the plethora of so far unidentified or generally unresolved (weak) emission lines in spectra observed with Chandra and XMM-Newton, especially because spectral modeling codes, such as AtomDB V3.09 (Foster et al. 2017) andCHIANTI V10.1 (Del Zanna et al. 2021), do not currently include them in their list of collisionally excited lines.
Three of these emission features are newly identified in a collisionally excited spectrum.The wavelength of the fourth feature, which is the strongest X-ray line in N V corresponding to the 1s2s2p 2 P 1/2,3/2 → 1s 2 2s 2 S 1/2 transitions commonly labeled q and r, has been measured before (Nicolosi & Tondello 1977;Mack & Niehaus 1987;Beiersdorfer et al. 1999;Al Shorman et al. 2013).However, the measured wavelengths are in tension with the most recent calculations (Yerokhin et al. 2017), which are thought to be among the most accurate calculations so far.Our new measurement has the lowest uncertainty of any of the measurements and it is in excellent agreement with these recent calculations as well as with our own many-body perturbation theory (MBPT) calculations.
In addition to our measured values, we provide a complete listing of the N V energy levels with valence electrons in the n = 2, 3, and 4 shells.These energies were calculated with the Flexible Atomic Code (FAC; Gu 2008) using the configuration interaction (CI) method as well as the highly accurate MBPT approach.The present experimental and theoretical data, thus, provide accurate rest-frame wavelengths for spectral modeling using updated astrophysical databases.
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Measurements
Measurements were performed with Lawrence Livermore National Laboratory's EBIT-I ("ebit-one") electron beam ion trap, which has been in continuous use for spectroscopic measurements for over 35 yr (Beiersdorfer et al. 2003;Beiersdorfer 2003).We employ procedures very similar to those used by Schmidt et al. (2004), Gu et al. (2005), and Beiersdorfer & Gu (2022).
Nitrogen was introduced to EBIT-I in molecular form via a gas injector.The roughly 50 μm diameter electron beam operating at 8 keV dissociates and ionizes the nitrogen.Although bare nitrogen can be readily produced at this beam energy, the continuous injection of neutral N 2 ensures that lower charge states are also present at this beam energy.
The nitrogen K-shell emission was recorded using a highresolution grazing incidence spectrometer (Beiersdorfer et al. 2004(Beiersdorfer et al. , 2014)).This spectrometer consisted of a reflective grating with variable line spacing (average line spacing of 2400 grooves mm −1 ) and a radius of curvature of 44.3 m, which was set to an angle of incidence of 88°.5.The reflected X-rays were recorded with a two-dimensional charge-coupled device (CCD), which was cooled to −110°C.The CCD has 1340 × 1300 pixels, each having a nominal size of 20 μm × 20 μm.
The spectrometer records a wavelength interval of about 18.5 Å.This allowed us to see the three prominent lines in helium-like N VI: The 1s2p 1 P 1 → 1s 2 1 S 0 "resonance" line commonly labeled w, the 1s2p 3 P 1 → 1s 2 1 S 0 "intercombination" line labeled y, and the 1s2s 3 S 1 → 1s 2 1 S 0 "forbidden" line labeled z of helium-like N VI near 29 Å, as shown in Figure 1.In addition, we observed the 2p 3/2,1/2 → 1s Lyα lines of hydrogen-like N VII.We were also able to record the 1snp 1 P 1 → 1s 2 1 S 0 (n = 3-7) lines of helium-like N VI by shifting the spectrometer somewhat more to the shorter wavelength side.The wavelengths of these lines are known from theory (Garcia & Mack 1965;Drake 1988;Yerokhin & Surzhykov 2019) to within better than 1 mÅ, and they serve as our in situ calibration references.
The spectrum of the nitrogen emission lines in the 24 to 30.5 Å region shown in Figure 1 is dominated by the N VII and N VI lines.However, two well-resolved features of lithium-like N V can be seen near 26.0 and near 25.7 Å.These have been labeled A and B, respectively, in Figure 1.Following our earlier analysis of the O VI spectrum (Beiersdorfer & Gu 2022), we readily identify features A and B as 1s2s3p → 1s 2 2s transitions.Weaker features produced by 1s2s4p → 1s 2 2s transitions, one of which was identified in the the O VI spectrum (Beiersdorfer & Gu 2022), are expected, but in the case of N V the strongest of these is situated on the long-wavelength shoulder of Lyα 2 and we could not reliably discern it in our spectra.
The blend of the two resonance lines q and r dominates the N V emission.The combined intensity of the two 3p → 1s lines is about one-quarter to one-fifth of that of the q and r blend.The blend of u and v is much smaller, i.e., about 10% of the q and r blend.The absolute intensity of the N V lines of course depends on the charge balance, but it also reflects the fact that the fluorescence yield is diminished for lithium-like ions, because the upper levels of the N V lines can decay by autoionization, which does not produce X-ray photons.
We list the experimentally determined wavelengths of the four observed N V features in Table 1.We are aware of previous wavelength measurements only for the blend of lines q and r.These measurements were made by Nicolosi & Tondello (1977), Beiersdorfer et al. (1999), andAl Shorman et al. (2013).These results are presented graphically in Figure 2 for comparison with our measurement of that blend.For completeness, we note that we have omitted a fifth measurement made by Mack & Niehaus (1987) because it was made relative to the (calculated) ionization energy of N 4+ and thus does not provide an independent test of N V spectral theory.In any case, the uncertainties of this measurement are too high to make a difference in the subsequent discussions.Lyα 2 ) and the resonance, intercombination, and forbidden lines of N VI labeled w, y, and z.The intensities of these lines with the exception of the forbidden line extend well above the vertical cut-off.The N V features are labeled A (1s2s3p → 1s 2 2s), B (1s2s3p → 1s 2 2s), q + r (1s2s2p 2 P 3/2,1/2 → 1s 2 2s 2 S 1/2 ), and u + v (1s2s2p 4 P 3/2,1/2 → 1s 2 2s 2 S 1/2 ).

Calculated Energy Levels
We employed FAC (Gu 2008) to calculate the energy levels of N V and the associated transition energies.FAC is a relativistic CI atomic code, and energy levels are calculated by default in this approach.The results are shown in Table 2.However, it can also be used to calculate more accurate energy levels.In particular, we have used FAC to perform calculations that combine the CI method with the second-order MBPT  Upper Level  Vainshtein & Safronova (1980).i ATOMDB V3.0.9 line list (Foster et al. 2017).method (Gu 2004).The resulting energy levels with a valence electron as high as n = 4 are listed in Table 2.
The wavelengths produced by our calculations are given in Table 1 for comparison with our measurements.As seen from Table 1, the wavelengths produced by the MBPT calculation do indeed match the measured values more closely than those produced by the CI method alone.A second-order MBPT calculation had already been found earlier (Gu et al. 2005;Beiersdorfer & Gu 2022) to improve the accuracy of the predicted O VI wavelengths.
Various calculations exist that predict the wavelengths of the N V lines we measured.In particular, Vainshtein & Safronova (1978), Goryaev et al. (2017), andYerokhin et al. (2017) have calculated the wavelengths of the n = 2 → n = 1 N V transitions, while Vainshtein & Safronova (1980) and Goryaev et al. (2017) have calculated the n = 3 → n = 1 transitions.For comparison, we list these previous values in Table 1.
Among the available spectral databases, only AtomDB V3.09 (Liang & Badnell 2011;Foster et al. 2017) lists a few of the N V transitions we observed in our electron-impact excited spectra.The transition wavelengths given by AtomDB are reproduced in Table 1.By contrast, CHIANTI V10.1 (Del Zanna et al. 2021) does not give any N V K-shell transition wavelengths, nor does the Atomic Spectra Database V5.11 of the National Institute of Standards and Technology (Kramida et al. 2023).

Discussion
Comparing the theoretical predictions in Table 1 with the measured values shows that our CI calculations can differ by as much as 100 mÅ, while our MBPT results are in very good agreement, typically differing by no more than 2 mÅ.We note that for comparison purposes we use a wavelength average that is weighted by the oscillator strengths for the components making up features A and B.
The weighted value of the calculation by Vainshtein & Safronova (1980) reproduces our measured value for feature A to within 5 mÅ, while that calculated by Goryaev et al. (2017) differs by about 7 mÅ, albeit with the opposite sign.The values given in AtomDB differ by more than 25 mÅ for feature A. The measured wavelength for feature B is reproduced within a few mÅ by our MBPT calculations, by the results presented by Goryaev et al. (2017), and by the wavelengths given in AtomDB.
The strongest feature in the N V K-shell emission spectrum is the blend of lines q and r, as we have already pointed out.Our measured value of 29.4316 ± 0.0015 Å is the most precise of its kind, as shown in Figure 2. It agrees with the oldest such measurement made by Nicolosi & Tondello (1977) using a laserproduced plasma.It also agrees very well with the weighted average of the theoretical values provided by our MBPT calculation and the CI calculation by Yerokhin et al. (2017), which was augmented by QED energies, as shown in Figure 2.However, it differs significantly with two earlier measurements.The first measurement was made by Beiersdorfer et al. (1999) using one of the Livermore electron beam ion traps.The second measurement was made using photoionization on the SOLEIL synchrotron facility by Al Shorman et al. (2013).
Although the Livermore electron beam ion trap measurement reported in 1999 employed a lower-resolution grazingincidence spectrometer than the one we employed for the present measurements, the line was observed in third, fourth, fifth, and sixth order in eight separate measurements.However, the data obtained in the fifth order of reflection had been excluded from the average value reported by Beiersdorfer et al. (1999) because the intensity of the q + r feature was about twice as large as that seen in the other orders and thus deemed to be blended with an undetermined line.Ironically, the average value of the eight measurements carried out in the fifth order is 29.4357 ± 0.0024 Å, which agrees within uncertainty limits with our present result of 29.4316 ± 0.0015 Å as well as the value of 29.434 ± 0.003 Å reported by Nicolosi & Tondello (1977) and shown in Figure 2. Despite a reexamination of the 1999 analysis prompted by A. Kramida (2024, private communication), we find no scientifically valid reason to discount the published result of 1999.
The second measurement that disagrees with our present measurement (Al Shorman et al. 2013) lends support to our earlier 1999 measurement, as seen in Figure 2. The reported uncertainties of that 2013 measurement are competitive with those of our present measurement.This means that there is an unresolved discrepancy of 10-15 mÅ between the two sets of measurements.However, given that our MBPT calculations agree with all other present measurements (e.ġ., A, B, and u + v) to within 2 mÅ, we must assume that MBPT is also good to within 2 mÅ in the case of the q + r feature.This implies that the 1999 and 2013 measurements are outliers.To prove this, however, would require a measurement with 1 order of magnitude lower uncertainties than any of the measurements shown in Figure 2.
In summary, our experiments clearly show that N V K-shell transitions provide a nonnegligible flux to the collisionally excited soft X-ray emission of nitrogen, and they should be included in spectral models.Given that our current measurements validate our MBPT calculations of the N V energy levels, we suggest that those data, as provided in Table 2, should be incorporated into the CHIANTI and AtomDB databases in order to augment the values available from measurement.

Figure 2 .
Figure 2. Comparison of measured values of the blend of the N V lines q + r with the theoretical values of Yerokhin et al. (2017) and AtomDB (Liang & Badnell 2011; Foster et al. 2017) (dashed lines) and that from our MBPT calculation (dotted line).The experimental values are from Nicolosi & Tondello (1977), Beiersdorfer et al. (1999), Al Shorman et al. (2013), and our present result.

Table 1
Line Identifications and Wavelength Comparisons of Measured and Predicted K-shell Lines of N V Present measurement; numbers in parentheses are uncertainties in tenths of mÅ.b Present calculation of the theoretical absorption oscillator strength of the transition with FAC.

Table 2 N
V Level Energies Calculated with the Flexible Atomic Code Using the Configuration Interaction (CI) Method as Well as Many-body Perturbation Theory (MBPT)