A&A 516, A70 (2010)

Hyperfine structure measurements of neutral niobium with Fourier transform spectroscopy

S. Kröger¹ - A. Er² - I. K. Öztürk² - G. Basar² - A. Jarmola³ - R. Ferber³ - M. Tamanis³ - L. Zacs³

1 - Hochschule für Technik und Wirtschaft Berlin, Fachbereich 1, Wilhelminenhofstr. 75A, 12459 Berlin, Germany
2 - Istanbul University, Faculty of Science, Physics Department, 34134 Vezneciler, Istanbul, Turkey
3 - Laser Centre, The University of Latvia, Rainis Boulevard 19, 1586 Riga, Latvia

Received 21 December 2009 / Accepted 10 March 2010

Abstract
Aims. We report on experimental studies of hyperfine structure splitting of neutral niobium.
Methods. We used high-resolution Fourier transform spectroscopy to record a spectrum of niobium produced with a hollow cathode discharge lamp in the range of wavenumbers from 10 000 cm^-1 to 30 000 cm^-1.
Results. The magnetic dipole hyperfine structure constants A were determined for the 109 levels of odd parity by analyzing the profiles of 224 spectral lines. The A values of 57 of these level are reported for the first time.

Key words: atomic data - methods: laboratory - techniques: spectroscopic - line: profiles

1 Introduction

The abundance patterns of neutron-capture elements in stellar atmospheres play an important role in constraining theoretical models of nucleosynthesis for elements heavier than iron. The recent commissioning of high-resolution spectrographs installed on large-aperture telescopes greatly increased the capacity of abundance analysis. In order to extract more information from high resolution stellar spectra, it is necessary to take into account nuclear effects, such as hyperfine structure and isotopic shifts. Therefore, new laboratory studies of hyperfine structure constants are needed to calculate accurate abundances.

Niobium (Nb), with atomic number 41, is the third member of the 4d-transition group elements and plays an important role in the investigation of the nucleosynthesis of heavy elements. Nb belongs to the few elements with only one stable isotope. The atomic spectrum of this stable isotope ⁹³Nb with nuclear spin I = 9/2 is characterized by a broad hyperfine structure caused by the large nuclear magnetic dipole moment.

The fine and hyperfine structure of atomic niobium has been the subject of several experimental and theoretical investigations (Kröger et al. 2007; Bouzed et al. 2003; Kröger et al. 2004; Singh et al. 1992; Basar et al. 2008; Fraenkel et al. 1988; Kröger & Bouzed 2003; Singh & Rao 1989; Kröger 2007). All recent experimental work has been performed using laser spectroscopic methods, which are restricted in the wavelength range accessible to the cw-lasers currently in use. By means of a Fourier transform (FT) spectrometer the wavelength range could be extended significantly.

In the present work the spectrum of Nb was recorded in the wavelength range from 330 nm to 1000 nm with a high resolution (up to 0.02 cm^-1) Fourier transform spectrometer. These data enabled us to determine the magnetic dipole hyperfine structure constants A of 109 levels of odd parity, more than half of which had been unknown up to now.

It should be noted that laboratory studies for singly ionized niobium Nb  II have been performed recently by FT spectroscopy by Nilsson & Ivarsson (2008), which resulted in new and improved transition probabilities and hyperfine structure data.

2 Experiment

A niobium spectrum was produced with a hollow cathode discharge lamp cooled with liquid nitrogen (for details see Messnarz & Guthöhrlein 2000). Briefly, the hollow cathode, made from copper, was 20 mm long and had a 5 mm bore, the surface of which was covered by a 0.125 mm pure (99.9%) niobium foil. The cathode was placed symmetrically between two hollow aluminium anodes; the distance between the cathode and the anodes was around 1.5 mm. The hollow cathode discharge was produced in an argon atmosphere at a pressure of around 1.7 mbar. The optimal discharge current, which corresponds to the maximum discharge intensity that can be achieved without a high risk of causing a short circuit, was found to be about 110 mA. The current from a high power DC power supply was stabilized with a series resistor.

The spectrum of niobium was recorded in the wavelength range from 10 000 cm^-1 to 30 000 cm^-1 (see Fig. 1) with a high resolution Bruker IFS 125HR Fourier transform spectrometer in the Laser Centre of the University of Latvia. The entrance aperture of the spectrometer was 0.8 mm, and the resolution was fixed to 0.02 cm^-1. Each spectrum was obtained from typically 40 scans. A quartz beam splitter and a Hamamatsu R928 photomultiplier were used to detect the spectra. The calibration of each spectrum was confirmed by using Ar lines presented in a hollow cathode discharge. The position of the lines could be determined with an accuracy better than 0.003 cm^-1 for the entire wavelength range covered by the experiment.

Figure 1a presents an overview of the full spectrum from 10 000 cm^-1 up to 30 000 cm^-1. Figure 1b shows a part of the spectrum as an example. Figure 1c zooms in further to show a single line.

The comprehensive list of experimental wavelengths of Nb from Humphreys & Meggers (1945) helped us to identify the spectral lines of atomic Nb. All the lines, which are discussed in the next section, are listed in Table 1.

In the spectra a lot of Argon lines are visible as well, which are not the subject of interest of the present paper.

Table 1:   Nb I transitions investigated by means of Fourier transform spectroscopy.

3 Hyperfine structure analysis

As mentioned above, the atomic spectrum of the stable isotope ⁹³Nb with nuclear spin I = 9/2 is characterized by a broad hyperfine structure caused by the large nuclear magnetic dipole moment (Lederer & Shirley 1978). Therefore, for most transitions it is reasonable to apply Doppler-limited, high-resolution experimental techniques like FT spectroscopy to accurately determine the hyperfine structure constants A. In contrast to the strong magnetic dipole interaction, the additional shift caused by the weak electric quadrupole interaction is very small for Nb, because the nuclear electric quadrupole moment Q= -0.36 (7) b (Lederer & Shirley 1978) is small. Thus, it was not possible to determine the electric quadrupole constants B for Nb from the FT spectra.

To investigate the hyperfine structure of a particular spectral line, the appropriate portion of the FT spectrum was cut out from the entire spectrum. Usually, the width of the structures ranged from 20 to 50 GHz.

The energy splitting of a fine structure level by the magnetic dipole hyperfine interactions is given by the well-known formula (see, for example, Cowan 1981)

where W_F is the energy of the hyperfine level with respect to the centre of gravity of the fine structure energy, while F, J, and I are the quantum numbers associated with the total angular momentum of the atom, the total angular momentum of the electrons, and the nuclear spin, respectively.

For the fitting procedure the program F ITTER (Guthöhrlein 2004) was utilized, which takes into account expression (1) for both levels involved in the transition. The program does an iterative least-squares fit to optimize the fit parameters, which in our case were the hyperfine structure constants A of the upper level and A_l and B_l of the lower level, the centre of gravity of the line, the peak intensity for each hyperfine component, and an appropriate line profile parameters. The fit program F ITTER offers various line profile functions for the user to choose.

For the decision concerning the profile function and the fit parameter settings, fitting tests were done for lines with a completely resolved hyperfine structure. As a result of those tests, the Voigt profile function was chosen, which is a convolution of a Lorentzian profile and a Gaussian profile. The Voigt profile yields two profile parameters for the fit: the total full width at half maximum (FWHM), i.e., the Voigt FWHM, and the parameter , which lies between 0 and 1 and gives the ratio of the Gaussian to the Lorentzian part. From these two parameters, the Gaussian and the Lorentzian FWHM were calculated. The same profile parameters were used for all hyperfine components of a line.

Additionally, the fitting tests demonstrated that the experimental intensities of the hyperfine components in the FT spectrum corresponded very well to the theoretical intensity ratios. Because most of lines were not completely resolved - some of them even were not resolved at all - the intensities of all hyperfine components were held at a constant ratio, which corresponded to the theoretical intensity ratio, during the fit.

As an example of a fit of a completely resolved hyperfine structure, the transition at  nm is shown in Fig. 2. In the lower part of the figure the residuals between the experiment and the fit are given. Only statistical noise can be seen, which suggests that the Voigt profile reproduces the experimental profile very well. Examples of a partially resolved line and of an unresolved line are presented in Figs. 3 and 4, respectively.

Table 2:   Hyperfine structure constants A_l and B_l from the literature for low-lying levels of even parity.

For all investigated transitions the lower level is the level of even parity, the A_l and B_l values of which are mostly very well known from high-resolution laser spectroscopic methods. The A_l and B_l values given in the literature are compiled in Table 2 for all levels of even parity that are involved in the transition under investigation. We decided to fix these values during the fit to increase the accuracy of the constants A of the odd parity upper levels, which were mostly unknown. The constants B of the upper levels were not taken into account for the reason mentioned above.

The whole spectrum was recorded eight times. For each line the mean value of the constant A that resulted from the fits of the eight measurements was determined. The measurement uncertainty for each value A was defined to be the corresponding standard deviation. In a few cases the measurement uncertainty of the hyperfine constant of the lower level, which was fixed during the fit, was higher than the standard deviation of the different fits. In these cases the measurement uncertainty of the hyperfine constant of the lower level was used instead of the standard deviation.

4 Results and discussion

In total, 224 spectral lines were investigated (see Table 1). For all lines except one (marked with the symbol  in Table 1) the classification given in Humphreys & Meggers (1945) was confirmed. The spectral profiles of all lines were fitted in order to obtain the magnetic dipole hyperfine constants A of the upper levels, which were the levels of odd parity in all cases. The resulting 109 hyperfine structure constants A are listed in Table 3, sorted by level energies.

The hyperfine structure constants given in the fifth column of Table 3 are the statistical mean value of the eight measurements, the measurement uncertainty  in the sixth column being the corresponding standard deviation. These errors refer only to the statistical variation of the fit and do not include systematic errors, which may occur, for example, because of neglecting the electric quadrupole hyperfine structure constant B or as a result of other restrictions in the fit. This implies that the measurement uncertainty  may be sometimes too small. This was the case when the hyperfine structure constants  for one level, determined from different lines, did not agree with each other within the limits of measurement uncertainty (see, for example, the level 25 199.81 cm^-1). Nevertheless, the value of  conveys an idea about the accuracy of the  value. If the measurement uncertainty of the hyperfine constant A_l of the lower level, which was fixed during the fit (see Sect. 3), was higher than the standard deviation, it is given as measurement uncertainty  in column six (and is marked by the symbol ).

In the fourth column of Table 3 the transitions are listed that were used to determine the  value. If the hyperfine structure constant A of a level of odd parity was measured in different transitions, the weighted mean value  is taken, weighted by the measurement uncertainty of column six. These values are listed in column seven. The measurement uncertainties given for the mean values  are the standard deviations corresponding to this average. They are much more significant than the  values, particularly if more than two lines were used. For hyperfine constants measured from only one transition, no measurement uncertainty is indicated in column seven.

The FWHM values of the Voigt profile determined from the hyperfine structure fits are shown in Fig. 5 as function of the transition wavenumber, together with the FWHM values corresponding to the Lorentzian and Gaussian parts of the Voigt profile function. For each of the three data sets a linear fit is added to the graph. The results of these linear fits are listed in Table 4. The FWHM of the Gaussian part has nearly the same slope as the FWHM of the Voigt profile whereas the FWHM of the Lorentzian part is nearly independent of the transition wave number.

For some unresolved lines the Voigt FWHM deviated strongly from the trend line FWHM( ) in Fig. 5. If this deviation was more than 200 MHz, the FWHM and the profile parameter were fixed during the fit to the value of the trend line at the corresponding wave number. These transitions are marked by asterisks in Tables 1 and 3. The FWHM values of these lines are excluded from the plot in Fig. 5.

Table 3:   Magnetic dipole hyperfine structure constants A in MHz for the levels of odd parity of Nb  I.

The Gaussian portion of the linewidth results from the Doppler broadening in the hollow cathode lamp and varies between 950 MHz for small wavenumber values and 2000 MHz for large wavenumber values. The respective straight line from the linear fit goes through the origin of the graph (intercept the wavenumber axis at zero), which is in good agreement with the formula for the FWHM of a Doppler broadened line

where T is the temperature, is the Boltzmann constant and m is the mass of the emitting particle (92.906 au for ⁹³Nb). From the values of the Gaussian FWHM, the corresponding temperature in the hollow cathode discharge can be determined. The temperature values calculated for all lines were independent of the wave number (as they should be) and showed statistical variations only. Averaging over all lines leads to a temperature of 1050 (100) K.

The Lorentzian part mainly reflects the apparatus function of the FT spectrometer which was approximately 600 MHz for our resolution. The natural linewidth for the lines under investigation is significantly less than 600 MHz, and its contribution is small.

A further parameter resulting from the fit is the centre of gravity of the hyperfine structure  , i.e., the centre of gravity of a line. The mean values of the eight fits for  are listed in the penultimate column of Table 1. The standard deviation of  was on average 0.002 cm^-1 and always smaller than 0.01 cm^-1. To check the consistency of the fine structure levels, the differences were calculated and listed in the last column of Table 1. All values of  were smaller than 0.07 cm^-1, and the average of the absolute value of  was 0.02 cm^-1. This confirms the fine structure level energies given in Humphreys & Meggers (1945).

The existing experimental values of the hyperfine constants from the literature, together with the specification of the experimental methods used, are given in the last two columns of Table 3. If more than one reference value has been published for a given level, only the most precise one is given.

The A values of 57 levels were measured for the first time. For the other 52 levels our values agree mostly with the previous values within the measurement uncertainty. For a few A values the difference between the  and the  values were slightly outside of the measurement uncertainty, exceeding it by ca. 50%. Only for two levels our new A values lie noticeably outside of the measurement uncertainty of the previous values which were determined by Singh et al. (1992). For these levels, 31 174.65 cm^-1 and 35 156.94 cm^-1, our A values were measured from only one line in each case. For the level 31 174.65 cm^-1 the disagreement between our A value and the reference one was 64 MHz. Singh et al. (1992) used the line at 589.34 nm to determine the A value. However, the constant A_l of the lower level of this line was already the subject of discussion in Bouzed et al. (2003), and it was considered to be wrong because it differed by more than 700 MHz from a more recent A_l value. For this reason we assume the reference value A of the level 31 174.65 cm^-1 to be incorrect and trust our value as much as all other unconfirmed A values measured with only one line. The disagreement for the second level 35 156.94 cm^-1 was 122.5 MHz. Neither our value nor the value from Singh et al. (1992) are confirmed by another measurement.

5 Astrophysical interest

A reliable abundance of niobium in the solar photosphere was determined by Hannaford et al. (1985) using original radiative lifetimes of Nb  II lines. Equivalent widths of 11 Nb  II lines were measured in the solar spectrum to calculate the niobium abundance,  = log( /) + 12.00 = 1.42  0.06. The hyperfine structure splitting was neglected in those estimates. The latest review of the standard solar composition (SAD) recommends the value  = 1.39  0.03 (Grevesse et al. 2007), which is in good agreement with the meteoritic abundance. Kwiatkowski et al. (1982) obtained a much higher solar niobium abundance  = 2.10  0.10, using Nb  I lines. The most plausible explanation of such a discrepancy seems to be the uncertainty in measurements of equivalent widths for weak and broad Nb  I absorption lines disturbed by hyperfine splitting. Thus, the hyperfine structure can have a significant effect on stellar absorption line profiles and the corresponding abundances can be substantially overestimated if such effects are not taken into account in the calculations (Booth & Blackwell 1983). Therefore, a detailed consideration of hyperfine structure is important for stellar abundance determinations.

The chemical elements heavier than iron are created by a combination of slow (s) and rapid (r) neutron-capture nucleosynthesis processes (Burbidge et al. 1957). The theory of nucleosynthesis identifies different astrophysical sites for s- and r-processes. The r-process nuclei are the products formed primarily during the evolution of massive stars and supernova explosions. The s-process nuclei are generally thought to have been synthesized during the late stages of the stellar evolution of low mass stars. Recent studies argue about two separate r-processes responsible for the production of the heavier and lighter neutron capture elements (Sneden et al. 2008, and references therein). The detection of lighter neutron capture elements (38  Z  48) in the spectra of metal-poor stars is crucial for determining if there indeed exist two different r-processes. Unfortunately, to date the niobium abundance was calculated only in the atmospheres of a few stars using a couple of identified lines in high resolution absorption spectra (Yushchenko et al. 2004; Honda et al. 2006; Ivans et al. 2005). Future studies of abundance patterns of neutron capture elements including niobium are encouraged to create a statistically significant sample of metal poor stars. The recent measurements of transition probabilities and hyperfine splittings reported for some elements should be incorporated.

6 Conclusion

We used high-resolution FT spectroscopy to obtain new and improved hyperfine structure data for neutral atomic Nb. Up to now, for atomic Nb the hyperfine structure constants A of 68 levels of odd parity have been published, determined by different experimental methods. With our investigations we extended the data for the odd parity levels by an additional 57 levels. That nearly doubles the data that can be used for a detailed and accurate interpretation of high-resolution stellar spectra including nuclear hyperfine structure effects.

Table 4:   Results of the linear fits of the measured full width at half maximum (FWHM).

Acknowledgements

I. K. Öztürk thanks the research fund of the Istanbul University project number 3307 and UDP-700/08032007. A. Er thanks the research fund of the Istanbul University project number 3164. We would like to thank Florian Gahbauer for useful discussions and to acknowledge support from the Latvian Science Council Grant No. LZP 09.1196.

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Appendix A: Nb I lines of special interest for stellar spectroscopy

Figures A.1-A.29 show the Fourier transform spectra for lines of special interest for stellar spectroscopy. The hyperfine components are assigned by the difference  of the total angular momentum of the upper and lower hyperfine levels. As summary, these lines are listed in Table A.1 (which is an extract from Table 1).

Table A.1:   Nb I lines of special interest for stellar spectroscopy.

Footnotes

...Humphreys & Meggers (1945)

At the time, when the cited paper appeared, the element niobium was named columbium.

...(Guthöhrlein 2004)

The program F ITTER (Guthöhrlein 2004) is also able to consider the electric quadrupole interaction in order to fit the B constants and to consider several different isotopes.

Copyright ESO 2010

All Tables

Table 1:   Nb I transitions investigated by means of Fourier transform spectroscopy.

Table 2:   Hyperfine structure constants A_l and B_l from the literature for low-lying levels of even parity.

Table 3:   Magnetic dipole hyperfine structure constants A in MHz for the levels of odd parity of Nb  I.

Table 4:   Results of the linear fits of the measured full width at half maximum (FWHM).

Table A.1:   Nb I lines of special interest for stellar spectroscopy.

All Figures

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Copyright ESO 2010