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Issue
A&A
Volume 542, June 2012
Article Number A35
Number of page(s) 10
Section Atomic, molecular, and nuclear data
DOI https://doi.org/10.1051/0004-6361/201219215
Published online 01 June 2012

© ESO, 2012

1. Introduction

There are several reasons why the spectra of neutral sodium are of astrophysical importance. For instance,in studying the galactic fountain process (gas flows from the disk of galaxies produced by multiple supernova explosions which play an important role in formation of high, and intermediate-velocity clouds, see Spitoni et al. 2008), Na i is a good tracer for a neutral gas because of its low first ionization potential (5.1 eV). Na i absorption is expected to be observed in the inflow (the later) stage of the galactic fountain process when the gas is mostly neutral, and nearly absent during the outflow (the earlier) stage when the gas is believed to be almost fully ionized. The sodium enrichment of supergiant atmospheres is one of the long-standing problems in observational stellar astrophysics (Andrievsky et al. 2002). The overabundance of Na in the atmospheres of F, G, K supergiants is in a correlation with the stellar mass. The high probability of emissions of Na i at visible wavelengths makes its detection easy to use in studies of the exospheres (the outermost atmospheric layers) of some solar system bodies, e.g., Mercury (Mouawad et al. 2011), the Moon (Matta et al. 2009; Lee et al. 2011) and Io (Grava et al. 2010). Na i has also been identified in exoplanetary atmospheres (Jensen et al. 2011) through space-based, from onboard the Hubble Space Telescope (Charbonneau et al. 2002) and ground-based, the Hobby-Eberly Telescope (Redfield et al. 2008), observations.

The detection of neutral sodium in the aforementioned examples was performed at optical wavelengths. The sodium enrichment of the atmospheres of 48 supergiants and bright giants and its connection with stellar gravity was studied using two Na i lines, 6154 and 6160 Å (Andrievsky et al. 2002). The observations of time-variable Na i absorption features near the resonance doublet (D lines at 589 nm) in circumstellar matter are used for the investigation of evolution models of type Ia supernova progenitors (Sternberg et al. 2011). The Na i emission at the resonance doublet recorded by MESSENGER’s Mercury Atmospheric and Surface Composition Spectrometer (MASCS) was used to constrain models of Mercury’s sodium exosphere (Mouawad et al. 2011). The measured Na i absorption near the resonance doublet in the transmission spectrum of an extrasolar planet (Charbonneau et al. 2002) showed large discrepancies with models that used a solar abundance of atomic sodium in planetary atmosphere. The amount of absorption of Na i for other planets differs significantly (Redfield et al. 2008), which indicates that the two exoplanets may have significantly different atmospheric properties, in particular the temperature profiles of their atmospheres. A direct measurement of the effective temperature of the planetary atmospheres and confirmation of a thermal inversion therein could be provided by exploiting the enhanced contrast between stars and their planets in the infrared wavelengths (O’Donovan et al. 2010).

The infrared (IR) range is becoming more and more important in astronomical research. Recent research topics include studies of dust-obscured objects and interstellar clouds, cool objects such as dwarfs, disks or planets, and the extended atmospheres of evolved stars, including objects at cosmological distances from the Earth (Kerber et al. 2009). The great advantages of Fourier transform infrared spectroscopy (FTIR), such as its constant high resolution and energy throughput, have made the IR spectral region more accessible for laboratory spectral measurements (Nilsson 2009).

However, compared with the visible and ultraviolet ranges, fewer atomic and ionic lines are available in the IR spectral region (Ryde 2010). Atlases of stellar spectra often provide only a short list of identified lines (Lobel 2011), and modern laboratory-based spectral features for wavelengths longer than 1 micron are not available for most elements (Wahlgren 2011). The powerful capabilities of IR astronomy cannot be fully utilized without detailed spectroscopical information on atomic line features in the IR region, in particular, wavelengths and oscillator strengths (Biémont 1994; Grevesse & Noels 1994; Pickering 1999; Jorissen 2004; Johansson 2005; Pickering et al. 2011).

New laboratory spectra may identify spectral lines in the IR that could result in the discovery of new excited atomic levels that are difficult to compute accurately and must be determined solely from IR lines (Wahlgren 2011). Including additional energy levels, atomic transition lines and oscillator strengths will increase the reliability of astrophysical calculations such as stellar or planetary atmosphere models.

Na i at 7880 cm-1 (1.269 μm) first appears in early G spectral type stars and grows in strength toward later types (Wallace et al. 2000). The near-infrared line list (with oscillator strengths computed or obtained by fitting the solar spectrum) for Na i includes the 10 182–12 679 and 16 374–16 389 cm-1 (0.98186–0.78849 and 0.61056–0.60999 μm) ranges (Meléndez & Barbuy 1999). Some Na i lines are identified in the solar spectrum in Atmospheric Chemistry Experiment with a space-borne Fourier transform spectrometer (ACE-FTS), which has been performed onboard a SCISAT-1 satellite (Hase et al. 2010). The ACE solar atlas covers the 700–4430 cm-1 (14.3–2.26) range at a resolution of 0.02 cm-1. The measurements performed with FTS at the McMath-Pierce solar telescope (National Solar Observatory, Kitt Peak) cover the range 460–13600 cm-1 (22–0.74 μm), performed with some corrections to account for telluric absorption (Wallace et al. 1996). Parts of the IR range in 1200–1800 cm-1 (8–5.6 μm) have never been observed from the ground due to heavy contamination of the spectrum by telluric absorption lines. Such an infrared spectrum represents a great challenge for laboratory observations of new, unknown infrared atomic transitions involving the atomic levels with high orbital momentum (Civiš et al. 2011a) and their comparison with the available stellar (e.g., solar) spectra. An attempt to fill this gap for Na i is made in the present paper.

Since the middle of the past century, when the measurements of the Na i spectrum were performed by Risberg (1956) in the range of 0.737–1.14 μm (13 559–8767 cm-1) and by Johansson (1961) in the range of 1.2–3.0 μm (7885–4276 cm-1), only one neutral sodium IR line (4f–5g transition at 2472.622 cm-1 i.e. 4.04319 μm) has been reported (Litzen 1970). In this hollow-cathode measurement no lines with longer wavelengths were recorded, and no emissions from ng (with n > 5) nor nh-levels were observed. The energies of the ng and nh levels of Na i for 6 ≤ n ≤ 13 available in the NIST database (Ralchenko et al. 2010) or critical compilations (Sansonetti 2008) are calculated by extrapolation from the higher nh and ng levels with n ≥ 13 (Dyubko et al. 1997). They have never been measured experimentally. The f-values for the Na i transitions listed in the NIST database and critical compilations (Kelleher & Podobedova 2008) are taken from the very old measurements by Filippov & Prokofjew (1929) (taken before the rise of quantum mechanics) or from multi-configuration Dirac-Hartree-Fock calculations using the code by Froese Fischer (2002).

Here we report the results of an FTIR spectroscopy study of Na i transitions in four IR ranges: 1.4–2.5, 2.7–5.0, 5.9–9.1 and 11.1–14.3 μm. From the recorded spectra, we extracted the excitation energies of the 7h, 6h, and 6g states of Na i for which only theoretical predictions were previously avaible. In addition, we also calculated f-values for all transitions involving the observed Na i levels using quantum-defect theory (QDT) approximation. Comparisons with measured transition probabilities and oscillator strengths (Miculis & Meyer 2005; Nawaz et al. 1992) indicate that the QDT is a suitable approximation.

Table 1

Observed Na lines and their identification.

2. Methods

Transitions in the four IR spectra ranges defined previously can be observed using laser-induced breakdown spectroscopy (LIBS), which analyzes the light spectrum emitted from plasma created on the sample surface by laser pulses (laser ablation). Laser ablation is a versatile and sensitive probe for the detection and identification of trace substances. As such, this technique has many practical advantages over the conventional chemical analysis methods (Aragon & Aguilera 2008; Lednev & Pershin 2008) and is being used in a growing number of applications (Lee et al. 2004; Babánková et al. 2006; Gomes et al. 2004; Barthélemy et al. 2005; Aragon & Aguilera 2008). In this study, we combined LIBS with time-resolved Fourier-transform infrared (FTIR) spectroscopy to record IR emission spectra in seven spectral ranges: 800–1000, 1000–1300, 1200–1600, 1600–2000, 2000–3500, 4100–5000, and 5000–7700 cm-1 (12.5–10, 10–7.7, 8.33–6.25, 6.25–5.0, 5.0–2.85, 2.34–2.0, 2.0–1.3 μm). Note that measurements in the range below 1800 cm-1 (λ > 5.55 μm) are quite difficult because of the low sensitivity of the mercury-cadmium-telluride (MCT) detector and the high background (blackbody) radiation level. To our knowledge, there are no laboratory-measured spectra of alkali metals below 1800 cm-1. All the wavenumbers listed in the NIST database (Ralchenko et al. 2010) for the alkali metal atomic lines below 1800 cm-1 are Ritz wavenumbers (i.e., obtained by subtracting known energy level values, not from laboratory-measured spectra). Below we briefly describe the experimental setup used in the present work. For more details see our previous papers (Kawaguchi et al. 2008; Civiš et al. 2010; Civiš et al. 2011b).

The vapors of excited Na atoms are produced during the ablation of the salt (Na i) targets by a high-repetition rate (1.0 kHz) pulsed nanosecond ArF laser (ExciStar S-Industrial V2.0 1000, pulse length 12 ns, λ = 193 nm, output energy of 15 mJ, fluence about 2–20 J/cm2) inside a vacuum chamber (average pressure 10-2 Torr). The time resolution FTIR spectra were measured using the Bruker IFS 120 HR spectrometer. For the 2000–7700 cm-1 (1.3–5.0 μm) range we used a CaF2 beam splitter and an InSb detector, while for the 700–2000 cm-1 range, a KBr beam splitter and an HgCdTe (MCT) detector were used. The infrared emission (axial distance from the target approximately 10 mm) was focused into the spectrometer using a CaF2 or ZnSe lens (for 2000–7700 cm-1 (1.3–5.0 μm) or 700–2000 cm-1 (14.3–5.0 μm) respectively). The wavenumbers, line widths and their intensities (as well as the uncertainties for these quantities) are presented in Table 1.

For data sampling, we used the so-called 1/3-sampling (Civiš et al. 2010), where the scanner velocity was set to produce a 3 kHz He–Ne laser interference signal, and the ArF laser oscillation was triggered at one third of the He-Ne frequency. Measurements were performed with a resolution of 0.017 cm-1, and three scans were needed to complete the interferogram. The resolution of 0.017 cm-1 allows us to collect 64 time-shifted interferograms. At higher resolutions, the number of interferograms was reduced to 30. Higher spectral resolution requires a longer scanning time, an increase in the number of laser pulses (the lifetime of the ArF excimer laser is limited by the total number of pulses) and a reduction of the entrance aperture of the spectrometer (fewer photons on the detector).

Usually, 3 to 30 scans were coadded to obtain a reasonable signal-noise ratio. The acquired spectrograms were post-zero filled by a factor of 2 and analyzed using a commercial software routine (Bruker OPUS Ver.3.1) (OPUS 2010). Finally, the spectra were corrected by subtracting the blackbody background spectrum.

Using a time-resolved scheme is essential, because the emission intensities of the spectra lines are dependent on the time delay after the ArF laser pulse shot. The time profiles of the emission lines have maxima at different delay times τ ≃ 10...20   μs after a laser shot. This non-monotonic decay of the emission intensity could be due to a complex combination of the repopulation of the atomic Na states by collisional cascade (Civiš et al. 2010) and the transfer processes in ablation products (Khalil & Sreenivasan 2005; Kawaguchi et al. 2008).

For an optically thin plasma at local thermal equilibrium (LTE), the emission transition from an upper state k to a lower state i has the intensity Iki proportional to the transition probability Aki and to the transition wavenumber νki: Iki~gkAkiνkiexp(−EkkBT),\begin{equation} \label{Eq:Boltzmann} I_{ki}\sim{g_k A_{ki}}{\nu_{ki}} \exp\left(-\frac{E_k}{k_\mathrm{B}T}\right), \end{equation}(1)where kB is the Boltzmann constant, T is the excitation temperature, Ek and gk being the energy and the degeneracy factor of the upper state, respectively. Since at the low pressures, used in our experiment the atom concentration is low, we can consider our plasma to be optically thin. However, in the same conditions some deviations from LTE conditions can occur, see Giacomo et al. (2001), but the Boltzmann distribution of the atomic populations remains valid according to Qi et al. (2007), although with different temperatures of electrons and atoms, see Giacomo et al. (2001). This means that even if the observed line intensities slightly deviate from the proportionality to the A-values, they should describe the qualitative picture of the relative line intensities well enough to assign the lines. The dipole matrix elements required to determine Aki were calculated using the single-channel quantum defect theory (QDT) (Chernov et al. 2000, 2005a).

3. Results and discussion

A list of the observed lines with their parameters and identification is presented in Table 1. The measurements were performed in the seven spectral ranges mentioned in Sect. 2. Only lines within the same spectral range have intensities with the same scale. Eighteen lines in Table 1 have not previously been measured in laboratories. Also, note that we have resolved the fine structure of the 3d–4f transition, see Fig. 1.

thumbnail Fig. 1

Resolved fine structure of the 3d–4f transition.

Table 1 also contains the wavenumbers of some Na i lines as measured in laboratories (Litzen 1970; Johansson 1961), by a ground-based (McMath-Pierce solar telescope at Kitt Peak; Wallace et al. 1996) and space-based (ACE; Hase et al. 2010) Fourier transform spectrometers. The uncertainty of ACE peak picking is 0.001 cm-1, which is less than our technique. The accuracy of the National Solar Observatory wavenumbers (Wallace et al. 1996) can be evaluated from the resolving power R = 300   000; the uncertainty Δν = 0.008–0.015 cm-1 for ν = 2400–4500 cm-1 (4.16–2.22 μm) is somewhat greater than uncertainties given in Table 1. However, for several lines our uncertainties are better than previous laboratory measurements, 0.005 cm-1 in (Johansson 1961) and 0.01 cm-1 in (Litzen 1970). Our wavenumbers agree with these laboratory measurements within the uncertainties, but the measurements do not always coincide with the wavenumbers listed in the ACE and NSO atlases.

The ACE-FTS spectral data are represented as three data lists. The second data list (according to Hase et al. 2010) contains the set of wavenumbers and transitions specified in the graphic ACE atlas pages. A simple analysis shows that the Na i line wavenumbers encountered in data list 2 are simply the Ritz wavenumbers obtained from the Na i level energies stored in the NIST database (Ralchenko et al. 2010). The first data list is presented in two variants: (a) the list of observed lines and (b) the corrected (by an empirical calibration factor of 1.00000294) version of the observed data; the correction was made to achieve closer agreement with the line positions specified in the second data list. We consider the ACE data list 1 (uncorrected) to be the most relevant to compare with our results since the above correction (by a calibration factor of 1.00000294) was performed in the ACE atlas (Hase et al. 2010) to aid the assignment of the spectral signatures in the ACE solar spectrum with the line positions given in current spectroscopic line-lists.

thumbnail Fig. 2

Emission spectra from Na i ablation plasma and the ACE (Hase et al. 2010) solar spectra.

Table 2

Improved energy measurements (cm-1) of several Na i levels.

The largest discrepancies occur for the lines corresponding to transitions from high-l levels (5g, 6g, 6h, 7h). These discrepancies could be explained by the Stark shift of solar lines due to high (up to 1000 V cm-1) electric fields in the Sun’s atmosphere. For instance, Mg I solar lines in the range of 7–12 μm (corresponding to transitions from nl levels with n,l ≥ 6) can differ from laboratory measurements by  −0.01 to  +0.03 cm-1 (Chang & Schoenfeld 1991). The quadratic Stark effect is determined by the polarizability. Even in its ground state, the polarizability of Na i is twice as high as that of Mg in its first excited state (Chernov et al. 2005a,b). Therefore, the wavenumbers of the high-l Na solar lines can differ from their laboratory values by more than 0.03 cm-1, explaining the discrepancies in Table 1. Improved atomic spectra measurements of transitions from the high-l levels, below 2000 cm-1 (λ > 5 μm), may yield more precise solar electric field strengths.

New laboratory spectroscopic measurements are important for a proper interpretation of current and future astrophysical spectra in the IR domain. Measured spectra and ACE-FTS solar spectra in the vicinity of the most prominent lines are shown in Fig. 2.

The energies, Ek, of the levels involved in the corresponding transitions can be extracted from the measured νki values.For this refinement we used a least-squares fitting algorithm that is similar to the one proposed by Radziemski et al. (1972). To obtain the best estimates for the level energy values Ek, we performed a minimization of a sum of deviations not only between Ek − Ej and the measured wavenumbers, but also included the deviations between some Ek and the “reference” values for these levels taken from Ralchenko et al. (2010) and Litzen (1970). The weights in the sum of squared deviations were proportional to the inverse uncertainties of the corresponding wavenumbers or “reference” energies. These revised values, together with the new h-level energies, are presented in Table 2.

For most of the observed levels, the extracted Ek agrees with the calculated uncertainties using the level values given by the NIST database and compilation tables (Ralchenko et al. 2010; Sansonetti 2008). The exceptions are the 5d and 7s levels. The slight disagreement with previous works (Martin & Zalubas 1981; Juncar et al. 1981) can be caused by uncertainties in the wavenumbers of the lines involving these levels (as compared to other lines listed in Table 1). Our energies for the nd levels (with n = 3,4,6) and ns levels (with n = 5,6) agree with the higher precision values measured in previous works (Martin & Zalubas 1981; Juncar et al. 1981). For the 4s, 4p, 5p, 6p, 4f, 5f and 5g levels, we report more accurate energies than previous measurements (Risberg 1956; Johansson 1961; Litzen 1970; Arqueros 1988).

The energies of the 7h, 6h, and 6g levels, given in square brackets in Table 2, have not been measured before. However, theoretical predictions based on extrapolation from the higher nh and ng levels with n ≥ 13 (Dyubko et al. 1997) were available. Our spectral resolution does not allow us to resolve the fine structure of the h and g levels. The fine splitting of these levels should be less than the nf-levels, which generally decreases with n and is resolved here only for n = 4. This fine splitting (~0.06 cm-1) is clearly observed in our spectra (see inset in Fig. 1).

To check the adequacy of the QDT calculations, we compared the dipole matrix elements calculated using QDT with other experimental and calculated values. Although all these dipole matrix elements (f- or A-values) can be easily expressed through each other, we kept the original data of the sources being compared (A-values for 3p–ns, nd transitions and f-values for 3s–np transitions).

Table 3

Comparison of probabilities (A-values) for several 3p32\hbox{$3\rm {p}_{\frac{3}{2}}$}–ns12\hbox{$n{\rm s}_{\frac{1}{2}}$}, nd32\hbox{$n{\rm d}_{\frac{3}{2}}$} transitions in Na i with the NIST database values (Ralchenko et al. 2010).

Table 3 compares the probabilities (A-values) for the 3p32\hbox{$3{\rm p}_{\frac{3}{2}}$}–ns12\hbox{$n{\rm s}_{\frac{1}{2}}$}, nd32\hbox{$n{\rm d}_{\frac{3}{2}}$} transitions with model potential calculations (modified Coulomb approximation) (Miculis & Meyer 2005) and NIST data (obtained from Dirac-Hartree-Fock, Froese Fischer 2002; or the R-matrix, Taylor 1995, theory). The Dirac-Hartree-Fock calculations differ from our QDT results by not more than 6%. The NIST A-values for n < 8 are closer to our values. For higher n, the QDT approximation should give more adequate results than the Dirac-Hartree-Fock calculations.

For some 3s–np transitions only the multiplet f-values (i.e., summed over the fine structure components) were measured using laser-based Faraday rotation spectroscopy (Nawaz et al. 1992). We compare the multiplet f-values with the NIST database and our calculations in Table 4. For n < 17 our calculations agree well (1–5%) with the laser-based Faraday rotation spectroscopy measurements (Nawaz et al. 1992) while for n = 18 the difference is about 19%. The NIST values are taken from quite old measurement by Filippov & Prokofjew (1929). Their results disagree more strongly with our calculations and the measurements by Nawaz et al. (1992).

Table 4

Multiplet f-values of Na i.

While the theoretical publications report f-values, most experimental studies measured the radiative lifetimes. However, f-values can be extracted from the reported lifetimes in a way similar to that used in our previous work (Civiš et al. 2010). In our comparison, we used QDT to calculate the ratios between f-values. These ratios are used to determine the absolute f-values from previously published experimental or theoretical lifetimes of the 3p12,32\hbox{$\rm 3{p}_{\frac12,\frac32}$}, 4p12,32\hbox{$\rm 4{p}_{\frac12,\frac32}$} and 4d32\hbox{$\rm 4{d}_{\frac{3}{2}}$} levels. Table 5 compares several QDT calculated f-values with f-values extracted from experimental and theoretical lifetimes. The overall agreement of our QDT calculation with the experimental values is not worse than that of other theoretical values given in the last column of Table 5.

Table 5

Comparison of Na i oscillator strengths (f × 100) with strengths obtained from previously published experimental or calculated lifetimes.

Tables 3–5 show that the QDT calculations agree well with other methods. Table 6 presents the oscillator strength and the transition probability for each transition between the observed Na i states. Except where noted, the Ritz wavenumbers ν and air wavelengths λ given in Table 6 were calculated using the energy levels given in Table 2. In some instances, the energy was taken from more accurate sources (Martin & Zalubas 1981; Juncar et al. 1981). Therefore, some wavenumbers presented in Tables 6 and 1 may be slightly different. To our knowledge, no dipole matrix elements have been reported for most of the Na i transitions listed in Table 6.

4. Conclusion

We report the results of an FTIR spectroscopy study of Na i transitions in the range of 700–7000 cm-1 (1.4–14 μm). Few spectra of Na i have been measured in this spectral range (Johansson 1961; Litzen 1970) and no laboratory measurements of metal spectra are known below 1800 cm-1 (λ > 5.5   μm). Although the recorded wavenumbers agree with previous laboratory measurements within the corresponding uncertainties, they only partially agree with the data from the ACE solar spectrum (Hase et al. 2010) and infrared spectral atlases of the Sun from NOAO (Wallace et al. 1996). Therefore, new laboratory spectroscopic measurements are needed for the proper interpretation of current and future astrophysical spectra in the infrared domain.

Table 6

QDT-calculated transition dipole moments for the observed transitions between Na i levels.

The recorded spectra allowed us to extract the excitation energies of the 7h, 6h, and 6g states of Na i for which only theoretical predictions were available. These predictions were calculated by extrapolation from the higher nh and ng levels with n ≥ 13 (Dyubko et al. 1997). The present study yielded more accurate energies for the 4s, 4p, 5p, 6p, 4f, 5f, and 5g levels of Na i (Risberg 1956; Johansson 1961; Litzen 1970; Arqueros 1988). For instance, the NIST energies of 4f52,72\hbox{$\rm 4{f}_{\frac{5}{2},\frac{7}{2}}$} levels were reported a half century ago (Johansson 1961) without fine-structure resolution.

The f-values calculated using the quantum-defect theory approximation were presented for all transitions involving the observed Na i levels. The approximation technique compares well with transition probabilities and oscillator strengths measured in other works (Miculis & Meyer 2005; Nawaz et al. 1992).

Acknowledgments

This work was financially supported by the Grant Agency of the Academy of Sciences of the Czech Republic (grant No. IAA400400705), by the Ministry of Finance of the Czech Republic (Project ECPF:049/4V) and the Ministry of Education, Youth, and Sports of the Czech Republic (grant No. LM2010014).

References

  1. Anderson, E. M., & Zilitis, V. A. 1964, Opt. Spectrosk., 16, 177 [Google Scholar]
  2. Andrievsky, S. M., Egorova, I. A., Korotin, S. A., & Burnage, R. 2002, A&A, 389, 519 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  3. Aragon, C., & Aguilera, J. A. 2008, Spectrochim. Acta, 63, 893 [Google Scholar]
  4. Arqueros, F. 1988, Opt. Commun., 67, 341 [NASA ADS] [CrossRef] [Google Scholar]
  5. Babánková, D., Civiš, S., & Juha, L. 2006, Prog. Quant. Electron., 30, 75 [Google Scholar]
  6. Barthélemy, O., Margot, J., Chaker, M., et al. 2005, Spectrochim. Acta, 60, 905 [Google Scholar]
  7. Biémont, E. 1994, in Infrared Solar Physics, ed. D. M. Rabin, J. T. Jefferies, & C. Lindsey, IAU Symp., 154 [Google Scholar]
  8. Carlsson, J., Jönsson, P., Sturesson, L., & Fischer, C. F. 1992, Phys. Scr., 46, 394 [NASA ADS] [CrossRef] [Google Scholar]
  9. Chang, E. S., & Schoenfeld, W. G. 1991, ApJ, 383, 450 [NASA ADS] [CrossRef] [Google Scholar]
  10. Charbonneau, D., Brown, T. M., Noyes, R. W., & Gilliland, R. L. 2002, ApJ, 568, 377 [NASA ADS] [CrossRef] [Google Scholar]
  11. Chernov, V., Manakov, N., & Starace, A. 2000, Eur. Phys. J. D, 8, 347 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  12. Chernov, V. E., Dorofeev, D. L., Kretinin, I. Y., & Zon, B. A. 2005a, Phys. Rev. A, 71, 022505 [NASA ADS] [CrossRef] [Google Scholar]
  13. Chernov, V. E., Dorofeev, D. L., Kretinin, I. Y., & Zon, B. A. 2005b, J. Phys. B, 38, 2289 [NASA ADS] [CrossRef] [Google Scholar]
  14. Civiš, S., Matulková, I., Cihelka, J., et al. 2010a, Phys. Rev. A, 81, 012510 [NASA ADS] [CrossRef] [Google Scholar]
  15. Civiš, S., Matulková, I., Cihelka, J., et al. 2010b, Phys. Rev. A, 82, 022502 [NASA ADS] [CrossRef] [Google Scholar]
  16. Civiš, S., Matulková, I., Cihelka, J., et al. 2011a, J. Phys. B, 44, 105002 [NASA ADS] [CrossRef] [Google Scholar]
  17. Civiš, S., Matulková, I., Cihelka, J., et al. 2011b, J. Phys. B, 44, 025002 [Google Scholar]
  18. Dyubko, S., Efremov, V., Podnos, S., Sun, X., & MacAdam, K. B. 1997, J. Phys. B, 30, 2345 [NASA ADS] [CrossRef] [Google Scholar]
  19. Filippov, A., & Prokofjew, W. 1929, Z. Phys., 56, 458 [Google Scholar]
  20. Froese Fischer, C. 2002, The MCHF/MCDHF Collection, non-orthogonal B-spline CI caclulations, http://atoms.vuse.vanderbilt.edu [Google Scholar]
  21. Gaupp, A., Kuske, P., & Andrä, H. J. 1982, Phys. Rev. A, 26, 3351 [NASA ADS] [CrossRef] [Google Scholar]
  22. Giacomo, A. D., Shakhatov, V., & Pascale, O. D. 2001, Spectrochim. Acta Part B: Atomic Spectrosc., 56, 753 [Google Scholar]
  23. Gomes, A., Aubreton, A., Gonzalez, J. J., & Vacquié, S. 2004, J. Phys. D, 37, 689 [NASA ADS] [CrossRef] [Google Scholar]
  24. Grava, C., Schneider, N. M., & Barbieri, C. 2010, in Galileo’s Medicean Moons: Their Impact on 400 Years of Discovery, ed. C. Barbieri, S. Chakrabarti, M. Coradini, & M. Lazzarin, IAU Symp. Proc. Ser., 269, 224 [Google Scholar]
  25. Grevesse, N., & Noels, A. 1994, Phys. Scr. T, 51, 47 [Google Scholar]
  26. Hase, F., Wallace, L., McLeod, S. D., Harrison, J. J., & Bernath, P. F. 2010, J. Quant. Spectrosc. Radiat. Trans., 111, 521 [Google Scholar]
  27. Jensen, A. G., Redfield, S., Endl, M., et al. 2011, ApJ, 743, 203 [NASA ADS] [CrossRef] [Google Scholar]
  28. Johansson, I. 1961, Ark. Fys., 20, 135 [Google Scholar]
  29. Johansson, S. 2005, in High Resolution Infrared Spectroscopy In Astronomy, Proceedings, ed. H. U. Kaufl, R. Siebenmorgen, & A. Moorwood, ESO Astrophysics Symposia, ESO (Germany: Springer-Verlag Berlin), 62 [Google Scholar]
  30. Jones, K. M., Julienne, P. S., Lett, P. D., et al. 1996, Europhys. Lett., 35, 85 [NASA ADS] [CrossRef] [Google Scholar]
  31. Jönsson, P., Ynnerman, A., Froese Fischer, C., Godefroid, M. R., & Olsen, J. 1996, Phys. Rev. A, 53, 4021 [NASA ADS] [CrossRef] [PubMed] [Google Scholar]
  32. Jorissen, A. 2004, Phys. Scr. T, 112, 73 [NASA ADS] [CrossRef] [Google Scholar]
  33. Juncar, P., Pinard, J., Hamon, J., & Chartier, A. 1981, Metrologia, 17, 77 [NASA ADS] [CrossRef] [Google Scholar]
  34. Kaiser, D. 1975, Phys. Lett. A, 51, 375 [NASA ADS] [CrossRef] [Google Scholar]
  35. Kandela, S. A. 1984, Appl. Opt., 23, 2152 [NASA ADS] [CrossRef] [Google Scholar]
  36. Karstensen, F., & Schramm, J. 1966, Z. Phys., 195, 370 [Google Scholar]
  37. Kawaguchi, K., Sanechika, N., Nishimura, Y., et al. 2008, Chem. Phys. Lett., 463, 38 [NASA ADS] [CrossRef] [Google Scholar]
  38. Kelleher, D. E., & Podobedova, L. I. 2008, J. Phys. Chem. Ref. Data, 37, 267 [NASA ADS] [CrossRef] [Google Scholar]
  39. Kerber, F., Nave, G., Sansonetti, C. J., & Bristow, P. 2009, Phys. Scr. T, 134, 014007 [NASA ADS] [CrossRef] [Google Scholar]
  40. Khalil, A., & Sreenivasan, N. 2005, Laser Phys. Lett., 2, 445 [NASA ADS] [CrossRef] [Google Scholar]
  41. Lednev, V. N., & Pershin, S. M. 2008, Laser Phys., 18, 850 [NASA ADS] [CrossRef] [Google Scholar]
  42. Lee, W.-B., Wu, J.-Y., Lee, Y.-I., & Sneddon, J. 2004, Appl. Spectrosc. Rev., 39, 27 [NASA ADS] [CrossRef] [Google Scholar]
  43. Lee, D.-W., Kim, S. J., Lee, D.-H., Jin, H., & Kim, K.-S. 2011, J. Geophys. Res., 116, 7213 [CrossRef] [Google Scholar]
  44. Lindgård, A., & Nielsen, S. E. 1977, At. Data Nucl. Data Tables, 19, 533 [NASA ADS] [CrossRef] [Google Scholar]
  45. Litzen, U. 1970, Phys. Scr., 1, 253 [NASA ADS] [CrossRef] [Google Scholar]
  46. Lobel, A. 2011, Can. J. Phys., 89, 395 [Google Scholar]
  47. Marek, J. 1977, J. Phys. B, 10, L325 [NASA ADS] [CrossRef] [Google Scholar]
  48. Martin, W. C., & Zalubas, R. 1981, J. Phys. Chem. Ref. Data, 10, 153 [NASA ADS] [CrossRef] [Google Scholar]
  49. Matta, M., Smith, S., Baumgardner, J., et al. 2009, Icarus, 204, 409 [NASA ADS] [CrossRef] [Google Scholar]
  50. Meléndez, J., & Barbuy, B. 1999, ApJS, 124, 527 [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  51. Miculis, K., & Meyer, W. 2005, J. Phys. B, 38, 2097 [Google Scholar]
  52. Mouawad, N., Burger, M. H., Killen, R. M., et al. 2011, Icarus, 211, 21 [NASA ADS] [CrossRef] [Google Scholar]
  53. Nawaz, M., Farooq, W. A., & Connerade, J.-P. 1992, J. Phys. B, 25, 5327 [NASA ADS] [CrossRef] [Google Scholar]
  54. Nilsson, H. 2009, Phys. Scr. T, 134, 014009 [Google Scholar]
  55. Oates, C. W., Vogel, K. R., & Hall, J. L. 1996, Phys. Rev. Lett., 76, 2866 [Google Scholar]
  56. O’Donovan, F. T., Charbonneau, D., Harrington, J., et al. 2010, ApJ, 710, 1551 [NASA ADS] [CrossRef] [Google Scholar]
  57. OPUS 2010, Opus Spectroscopy Software, http://www.brukeroptics.com/opus.html [Google Scholar]
  58. Pickering, J. C. 1999, Phys. Scr. T, 83, 27 [Google Scholar]
  59. Pickering, J., Blackwell-Whitehead, R., Thorne, A., Ruffoni, M., & Holmes, C. 2011, Can. J. Phys., 89, 387 [NASA ADS] [CrossRef] [Google Scholar]
  60. Qi, H., Sun, Y., Liu, X., Hou, X., & Li, Y. 2007, Laser Phys. Lett., 4, 212 [NASA ADS] [CrossRef] [Google Scholar]
  61. Radziemski, L. J., Fisher, K. J., Steinhaus, D. W., & Goldman, A. S. 1972, Comput. Phys. Commun., 3, 9 [Google Scholar]
  62. Ralchenko, Y., Kramida, A., Reader, J., & NIST ASD Team 2010, NIST Atomic Spectra Database, version 4.0 [Google Scholar]
  63. Redfield, S., Endl, M., Cochran, W. D., & Koesterke, L. 2008, ApJ, 673, L87 [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  64. Risberg, P. 1956, Ark. Fys., 10, 583 [Google Scholar]
  65. Ryde, N. 2010, Astron. Nachr., 331, 433 [NASA ADS] [CrossRef] [Google Scholar]
  66. Sansonetti, J. E. 2008, J. Phys. Chem. Ref. Data, 37, 1659 [NASA ADS] [CrossRef] [Google Scholar]
  67. Spitoni, E., Recchi, S., & Matteucci, F. 2008, A&A, 484, 743 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  68. Sternberg, A., Gal-Yam, A., Simon, J. D., et al. 2011, Science, 333, 856 [NASA ADS] [CrossRef] [Google Scholar]
  69. Taylor, K. T. 1995, TOPBASE (Opacity Project), http://cdsweb.u-strasbg.fr/topbase/topbase.html [Google Scholar]
  70. Theodosiou, C. E. 1984, Phys. Rev. A, 30, 2881 [NASA ADS] [CrossRef] [Google Scholar]
  71. Tiemann, E., Knöckel, H., & Richling, H. 1996, Z. Phys. D, 37, 323 [NASA ADS] [CrossRef] [Google Scholar]
  72. Volz, U., Majerus, M., Liebel, H., Schmitt, A., & Schmoranzer, H. 1996, Phys. Rev. Lett., 76, 2862 [NASA ADS] [CrossRef] [PubMed] [Google Scholar]
  73. Wahlgren, G. M. 2011, Can. J. Phys., 89, 345 [NASA ADS] [CrossRef] [Google Scholar]
  74. Wallace, L., Livingston, W., Hinkle, K., & Bernath, P. 1996, ApJS, 106, 165 [NASA ADS] [CrossRef] [Google Scholar]
  75. Wallace, L., Meyer, M. R., Hinkle, K., & Edwards, S. 2000, ApJ, 535, 325 [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]

All Tables

Table 1

Observed Na lines and their identification.

In the text
Table 2

Improved energy measurements (cm-1) of several Na i levels.

In the text
Table 3

Comparison of probabilities (A-values) for several 3p32\hbox{$3\rm {p}_{\frac{3}{2}}$}–ns12\hbox{$n{\rm s}_{\frac{1}{2}}$}, nd32\hbox{$n{\rm d}_{\frac{3}{2}}$} transitions in Na i with the NIST database values (Ralchenko et al. 2010).

In the text
Table 4

Multiplet f-values of Na i.

In the text
Table 5

Comparison of Na i oscillator strengths (f × 100) with strengths obtained from previously published experimental or calculated lifetimes.

In the text
Table 6

QDT-calculated transition dipole moments for the observed transitions between Na i levels.

In the text

All Figures

thumbnail Fig. 1

Resolved fine structure of the 3d–4f transition.
In the text
thumbnail Fig. 2

Emission spectra from Na i ablation plasma and the ACE (Hase et al. 2010) solar spectra.
In the text

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