A&A 381, 1090-1093 (2002)
DOI: 10.1051/0004-6361:20011540

Experimental oscillator strengths in U II of cosmological interest

H. Nilsson 1 - S. Ivarsson 1 - S. Johansson 1 - H. Lundberg 2


1 - Lund Observatory, Lund University, PO Box 43, 22100 Lund, Sweden
2 - Department of Physics, Lund Institute of Technology, PO Box 118, 22100 Lund, Sweden

Received 17 October 2001 / Accepted 30 October 2001

Abstract
Oscillator strengths for 57 U II lines in the region 3500-6700 Å  have been derived by combining new branching fraction measurements with recently measured lifetimes. The lines combine six upper levels with numerous low levels having excitation energies of 0-1.5 eV. The data include the U II line at 3859 Å, which is used for cosmochronology.

Key words: atomic data - stars: evolution - Galaxy: evolution


1 Introduction

Determination of stellar ages using radiative dating requires a high accuracy in the determination of chemical abundances, which is based on the analysis of spectral lines. The crucial atomic parameter is the oscillator strength. The method of radioactive dating is based upon the change with time in the abundance ratio of two elements, either a radioactive and a stable isotope, or two radioactive isotopes with different half-lifes. Cayrel et al. (2001) determined the age of the metal poor star CS 31082-001, using a uranium-thorium cosmochronometer. In order to increase the accuracy in this age determination, new f-values for Th II have been reported by Nilsson et al. (2001), and in the present paper we present new f-values for U II. Previous measurements of relative line intensities in U II were made by Meggers et al. (1961), using an arc as a light source. Corliss & Bozman (1962) put the measurements of Meggers et al. on an absolute scale by estimating the plasma parameters in the arc. Voigt (1975) measured oscillator strengths from an arc, which enabled Corliss (1976) to rescale the line intensities from Meggers et al. (1961). In a study by Palmer et al. (1980), relative line intensities and accurate wavenumbers were measured from uranium hollow cathode (HC) spectra recorded with the Fourier transform spectrometer (FTS) at Kitt Peak National Observatory. That work also includes a semi-empirical formula for putting the relative intensities on a absolute scale using the values reported by Corliss (1976). Values of the oscillator strengths of the $\lambda\lambda$ 3859.6 and 4050.0 lines were later reported by Chen & Borzileri (1981), who measured the lifetimes of the 5f36d7p 6M13/2 level at 26191 cm-1, the upper level of the 3859.6 line, and the 5f37s7p 6I level at 24684 cm-1, the upper level of the 4050.0 line, and combined them with unpublished branching fractions (BF). Henrion et al. (1987) measured relative intensities from a HC and scaled them to the values of Corliss (1976).

In the present paper we present relative intensities of 57 U II lines measured in FTS spectra and recalculated to BFs. Combining these BFs with radiative lifetimes (Lundberg et al. 2001) yields oscillator strengths for the 57 lines.


 

 
Table 1: U II branching fractions (BFs) and gf-values. The lines are sorted by the upper level.
Upper Lower $\lambda_{\rm air}$ $\sigma$ BF gf log gf Unc.
level level (Å) (cm-1)     This work Ka Cb C&Bc (% in gf)
23315.090 7166 6190.822 16148.460 0.003 0.002 -2.632       27
$\tau=84$ ns 5401 5580.801 17913.586 0.04 0.022 -1.668 -2.345 -1.94   12
J=4.5 914 4462.965 22400.325 0.17 0.059 -1.229 -1.782 -1.65   11
  289 4341.683 23026.049 0.59 0.199 -0.700 -1.161 -1.24   7
  0 4287.858 23315.090 0.20 0.065 -1.184 -1.709 -1.62   11
                     
24684.132 9690 6667.728 14993.471 0.002 0.003 -2.534       51
$\tau=49$ ns 8379 6131.603 16304.436 0.004 0.004 -2.393       41
J=4.5 7598 5851.199 17085.777 0.01 0.011 -1.949       17
  7547 5833.792 17136.759 0.01 0.008 -2.105       17
  7166 5706.993 17517.502 0.03 0.026 -1.591 -2.148     9
  6445 5481.204 18239.097 0.13 0.116 -0.937 -1.677 -1.51   9
  5790 5291.356 18893.491 0.01 0.009 -2.061       10
  5667 5257.045 19016.801 0.06 0.051 -1.289 -1.924 -1.70   9
  5401 5184.571 19282.628 0.09 0.076 -1.120 -1.855 -1.66   9
  4420 4933.662 20263.262 0.06 0.047 -1.330 -2.212 -1.92   9
  2294 4465.139 22389.436 0.06 0.035 -1.453 -1.944 -1.78   9
  289 4098.029 24395.091 0.15 0.076 -1.117 -1.239 -1.34   9
  0 4050.041 24684.132 0.39 0.197 -0.706 -0.713 -0.99 -0.675 7
                     
25714.049 10740 6676.804 14973.092 0.01 0.023 -1.638       26
$\tau=35$ ns 8510 5811.266 17203.183 0.02 0.036 -1.438   -1.72   17
J=6.5 8276 5733.237 17437.316 0.01 0.026 -1.590 -1.976 -1.71   17
  6283 5145.083 19430.618 0.02 0.024 -1.615 -2.117 -2.85   17
  5259 4887.559 20454.397 0.003 0.004 -2.371       43
  4585 4731.594 21128.615 0.09 0.125 -0.902 -1.509 -1.48   18
  4420 4695.026 21293.179 0.01 0.010 -2.022       26
  1749 4171.589 23964.926 0.32 0.336 -0.474 -0.606 -0.92   14
  289 3932.022 25425.008 0.52 0.482 -0.317 -0.528 -0.89   12
                     
26191.309 10740 6470.556 15450.352 0.01 0.032 -1.494       34
$\tau=18.6$ ns 8510 5654.397 17680.443 0.01 0.030 -1.516       18
J=6.5 8276 5580.497 17914.576 0.003 0.010 -2.021       52
  6283 5021.736 19907.878 0.01 0.022 -1.650       22
  5790 4900.432 20400.668 0.01 0.023 -1.647       19
  5526 4837.851 20664.561 0.002 0.004 -2.349       52
  4585 4627.075 21605.875 0.11 0.255 -0.593 -1.178 -1.27   14
  4420 4592.098 21770.439 0.002 0.006 -2.241       43
  1749 4090.132 24442.187 0.35 0.655 -0.184 -0.377 -0.78   13
  289 3859.571 25902.269 0.51 0.856 -0.067 -0.105 -0.62 -0.204 12



 

 
Table 1: continued.
Upper Lower $\lambda_{\rm air}$ $\sigma$ BF gf log gf Unc.
level level (Å) (cm-1)     This work Ka Cb C&Bc (% in gf)
28154.450 8755 5153.520 19398.810 0.002 0.009 -2.053       41
$\tau=12.4$ ns 8510 5089.302 19643.584 0.003 0.012 -1.917       46
J=5.5 8379 5055.543 19774.754 0.01 0.029 -1.533       17
  7166 4763.336 20987.820 0.004 0.012 -1.937       41
  6283 4570.979 21871.019 0.03 0.082 -1.084   -1.68   9
  4585 4241.664 23569.016 0.30 0.789 -0.103 -0.431 -0.83   8
  4420 4212.253 23733.580 0.06 0.154 -0.811 -1.294 -1.42   9
  2294 3865.917 25859.754 0.18 0.380 -0.421 -0.273 -0.77   9
  914 3670.069 27239.685 0.33 0.642 -0.192 -0.173 -0.72   7
  0 3550.822 28154.450 0.09 0.164 -0.785 -0.584 -1.01   9
                     
30341.675 12629 5644.217 17712.325 0.01 0.040 -1.400       26
$\tau=24.0$ ns 9626 4825.914 20715.562 0.02 0.041 -1.391       9
J=7.5 8521 4581.717 21819.753 0.05 0.098 -1.010       9
  8394 4555.087 21947.313 0.11 0.224 -0.650 -1.167 -1.34   9
  8276 4530.802 22064.942 0.01 0.014 -1.854       41
  6283 4155.404 24058.244 0.14 0.248 -0.606 -0.759 -1.10   9
  5526 4028.691 24814.927 0.004 0.006 -2.241       51
  5259 3985.789 25082.023 0.33 0.528 -0.278 -0.165 -0.71   8
  4585 3881.451 25756.241 0.21 0.310 -0.509 -0.279 -0.80   9
  1749 3496.411 28592.552 0.12 0.151 -0.821 -0.691 -1.12   9

a Value from the Kurucz (1993).
b Value measured by Corliss (1976).
c Value measured by Chen & Borzileri (1981).

2 Branching fractions

The BFs are derived from line intensities, which have been measured in spectra recorded with a Chelsea Instrument FT500 FTS in the wavelength interval 3300-7000 Å. As a light source we ran a HC at different currents between 0.1 and 0.5 A and with argon as a carrier gas. The cathode is a 3 cm long iron tube with an inner diameter of 0.5 cm, in which a piece of uranium was inserted. The U II transitions with $\lambda$ > 5000 Å are predicted to be weak, and they were not observed in the spectra as the FTS response is low above 5000 Å. However, a spectrum recorded at Kitt Peak National Observatory and extracted from the Kitt Peak FTS archive could be used to measure the intensities of these lines. The Kitt Peak spectrum was recorded from a HC with a discharge current of 0.3 A and argon as a carrier gas in the wavelength interval 2400-12800 Å. In order to get relative intensities the FTS spectra were corrected for the instrument response by using known branching ratios in argon (Whaling et al. 1993).

Intensities of strong lines to low energy levels can be affected by self absorption. In order to check for this effect spectra were recorded at different currents through the HC, and the intensity ratio between two lines coming from the same upper level was plotted as a function of the current. A linear fit was applied, and the extrapolated intensity ratio at zero current was adopted. The study of self absorption effects was performed in two ways. Firstly, we ran the HC with high currents and high density of uranium ions to force the strong lines to be self absorbed, and the intensities were corrected as described above. Secondly we removed the uranium piece from the cathode leaving only the layers of sputtered uranium deposited on the cathode walls. This gives a plasma having a low density of uranium ions. By plotting intensity ratios as a function of discharge current we get a constant value and hence no indication of self absorption. A comparison of the results of the two different sets of runs gave a difference of <10% for the strong lines, which is within the experimental uncertainties.

In the recorded spectrum it was possible to measure all lines from a given level having a BF > 0.004, but some lines may occur outside the observed wavelength interval. This residual intensity can in some cases be estimated from calculations, but in the case of U II there are no calculations available probably due to the complex atomic structure. In the wavelength interval 2020 to 24600 Å it was possible to check for "missing'' lines in the atlas by Steinhaus et al. (1971). The spectra in this atlas were recorded on photographic plates which are more sensitive and therefore include weaker lines. The atlas contains no lines outside the wavelength interval and from the energy levels studied in the present investigation. However, we found some extra lines in the interval covered in our recordings. Since these lines do not appear in our spectra, they should have a BF < 0.004. These facts imply that the residual is small and has no significant impact on the BF value of the strongest lines.

The wavenumbers and line identifications are taken from the analysis of Palmer et al. (1980) and Steinhaus et al. (1971).

3 Oscillator strengths

The oscillator strength (f) of a line can be derived from the relation,

\begin{displaymath}% f = 1.4992 \times 10^{-16} \frac{g_{i}}{g_{k}}\lambda^{2} A_{ik}, \end{displaymath} (1)

where gi and gk are the statistical weights for the upper and lower level, respectively, $\lambda$ is the wavelength of the transition in Å  and Aik the transition probability in s-1. The transition probability of the line can be derived from the observed BF and lifetime ($\tau$),

\begin{displaymath}% A_{ik} = \frac{(BF)_{ik}}{\tau_{i}}\cdot \end{displaymath} (2)

The experimental lifetimes used to derive the f-values were measured by Lundberg et al. (2001) with the laser induced fluorescence technique. In Table 1 the measured BFs, gf and log gf-values are reported. For comparison, Table 1 also include values from the Kurucz database (Kurucz 1993) (K) based on estimates from line intensities measured by Meggers et al. (1961), the values reported by Corliss (1976) (C), and the values reported by Chen & Borzileri (1981) (C&B). The uncertainties given in Table 1 are calculated using the method suggested by Sikström et al. (2001), which includes the uncertainty in the intensity measurements and intensity calibration, the uncertainty introduced by the combination of different spectral regions, the uncertainty in the self absorption correction and the uncertainty in the lifetimes.

4 Conclusion

The method of Cayrel et al. (2001) to use uranium for radioactive dating of a star provides a spectacular illustration of atomic astrophysics. An accurate value of the oscillator strength for a specific line $\lambda$ 3859.6 of ionized uranium, U II, is needed to derive the present uranium abundance in the star CS 31082-001. The decay rate of uranium and the change in abundance define together a time scale for the evolution of the star.

We present in this paper the results of branching fraction measurements of 57 U II lines, including the line $\lambda$ 3859.6. By combining these BFs with previously measured lifetimes by Lundberg et al (2001) we can derive oscillator strengths for the lines. The atomic structure of U II is very complex with five valence electrons in three open shells, which makes theoretical calculations of the atomic structure and the line strengths very difficult. It is, therefore, natural that most of the experimental energy levels have not been assigned and no calculated gf-values have been published.

The uncertainties in the f-values have contributions from various sources and vary substantially in size. In general, strong lines have the smallest uncertainty. (However, they are in general the lines, which are most sensitive to self absorption.) The experimental method used has for other complex spectra, e.g. Fe II (Sikström et al. 1999; Nilsson et al. 2000), given consistent results. The agreement with theoretical data are typically within the error bars. The difference between measurements in Fe II and U II is that all energy levels and all transitions of relevance are known in Fe II. In the case of Fe II, it has been posssible to estimate the contributions from unobserved lines in the BF measurements, "the residual'', to a high degree of accuracy. This is not the case for U II, but there is no indication, experimental or theoretical, of a residual that would add an extra uncertainty in the gf-value of the cosmochronometer line, $\lambda$ 3859.6. It is one of the strongest lines in the spectrum, but we find no signs of self absorption that would affect the BF outside the error bar.

The oscillator strength obtained for $\lambda$ 3859.6 is $gf=0.86\pm0.10$ (log $gf=-0.067\pm 0.05$), which is 36% higher than the value of 0.62 (log gf= -0.204) given by Chen & Borzileri (1981).

Acknowledgements
This work was supported by the Crafoord Foundation (HL), the Swedish National Space Board (SJ) and the Swedish Natural Science Research Council (SJ). We thank Prof. U. Litzén for his support and advice.

References

 
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