A&A 381, 1090-1093 (2002)
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
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
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 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.
|level||level||(Å)||(cm-1)||This work||Ka||Cb||C&Bc||(% in gf)|
|level||level||(Å)||(cm-1)||This work||Ka||Cb||C&Bc||(% in gf)|
a Value from the Kurucz (1993).
b Value measured by Corliss (1976).
c Value measured by Chen & Borzileri (1981).
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).
The oscillator strength (f) of a line can be derived from the relation,
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 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 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, 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 3859.6 is (log ), which is 36% higher than the value of 0.62 (log gf= -0.204) given by Chen & Borzileri (1981).
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.