Lifetime measurements and transition probability calculations in singly ionized tungsten (W II)

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1 Eur. Phys. J. D (2008) DOI: /epjd/e THE EUROPEAN PHYSICAL JOURNAL D Lifetime measurements and transition probability calculations in singly ionized tungsten (W II) H. Nilsson 1,L.Engström 2, H. Lundberg 2,P.Palmeri 3,V.Fivet 3 3,4, P. Quinet,andÉ. Biémont3,4,a 1 Lund Observatory, Lund University, P.O. Box 43, Lund, Sweden 2 Department of Physics, Lund Institute of Technology, P.O. Box 118, Lund, Sweden 3 Astrophysique et Spectroscopie, Université de Mons Hainaut, 20 Place du Parc, 7000 Mons, Belgium 4 IPNAS (Bâtiment B15), Université deliège, Sart-Tilman, 4000 Liège 1, Belgium Received 13 May 2008 / Received in final form 5 June 2008 Published online 2nd July 2008 c EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2008 Abstract. New measurements of radiative lifetimes for 9 levels in singly ionized tungsten (W ii) have been performed with the time-resolved laser-induced-fluorescence technique. Transition probabilities have been obtained from a combination of experimental lifetimes and theoretical branching fractions. The reliability of the present results is assessed through the good agreement observed between the calculated lifetimes and the experimental values from this work and from previous publications. These new results fill in a gap in the available data for this atomic species particularly important for fusion reactors. PACS Cs Oscillator strengths, lifetimes, transition moments Jm Plasma production and heating by laser beams 1 Introduction Radiative data of tungsten ions are important in plasma physics. With its low yield and high threshold for sputtering [1], tungsten is widely used in fusion reactors as a divertor target. Tungsten is also important in astrophysics: neutral tungsten has been identified in Ap stars [2,3] and has been found to be seriously enhanced in some Ba stars [4,5]. More recently, W i lines have been detected and investigated in the spectrum of HD [6,7] but, in the latter case, only an upper limit could be deduced for the abundance of tungsten. The dominant species, except in cool stars, is in fact expected to be W ii. The line of singly ionized tungsten at 203 nm has been observed in the UV spectrum of one Am star [8]. Several lifetime measurements or experimental transition probability determinations have been reported in W ii but radiative data are still lacking for many transitions of this ion. The first determination of experimental transition probabilities in W ii is due to Corliss and Bozman [9] but their arc measurements have been recognized to be affected by large systematic errors. These results were supplemented later on by the relative measurements of Clawsonand Miller [10] and by the absolute measurements a e.biemont@ulg.ac.be of Obbarius and Kock [11]. In the latter case, a stabilized arc, operated in argon, was used for measuring oscillator strengths for 27 W ii lines in the wavelength range nm, the results differing sometimes by large factors from the previous values. The most substantial progress in radiative parameters in W ii has resulted from the combination of lifetime measurements with branching fraction (BF) determinations. Different sets of lifetimes have been reported. The first is due to Kwiatkowski et al. [12] who measured 3 lifetime values using selective laser excitation and time-resolved observation of the reemitted fluorescence (TR-LIF), the ions being produced by the sputtering technique in a lowpressure discharge. Using also a TR-LIF technique, radiative lifetime measurements have been performed by Schnabel et al. [13] for 19 selected levels with energies between and cm 1 and by Schulz-Johanning et al. [14] who used a linear Paul trap for investigating two W ii lifetimes. More recently, Henderson et al. [15] reported three lifetime values using the beam-foil method. These results were combined with theoretical and experimental BFs deduced from Corliss and Bozman arc measurements [9] to deduce the required f values. BFs of 280 W ii lines originating from 19 excited levels in the wavelength range nm were obtained by Kling et al. [16] from emission measurements on a highcurrent hollow cathode and a Penning discharge lamp.

2 2 The European Physical Journal D The most recent summary of the transition probabilities in W ii can be found in the compilation of Kramida and Shirai [17]. In the present paper, we report on TR-LIF lifetime measurements for 9 levels in W ii. These new experimental lifetimes, and those previously reported by several authors [12,13,15], have been used to assess the reliability of theoretical oscillator strengths calculated within the framework of the relativistic Hartree-Fock (HFR) approach [18] modified by the inclusion of core-polarization effects (HFR+CP). This new set of data for 290 transitions of W ii complements and updates the previous results available in this ion. The procedure followed in the present paper is similar to that adopted in a recent paper devoted to lifetime measurements and transition probability determinations in doubly ionized tungsten (W iii) [19]. 2 Level and term values in W II The ground configuration of W ii is 5d 4 6s, with 6 D 1/2 as the lowest level. The first excited configurations are 5d 5,5d 3 6s 2,5d 4 6s, 5d 3 6s6p and 5d 4 6p. 76 even levels and 187 odd levels are reported in the compilation of Kramida and Shirai [17], the most recent summary of W ii levels. This compilation, as far as the energy levels are concerned, is essentially based on the extensive investigations of the W ii spectrum by Ekberg et al. [20] and by Cabeza et al. [21]. 3 Lifetime measurements The experimental setup used in the present experiment is the same as that described for W iii [19] and has been presented previously (e.g. [22,23]). Consequently, only a brief description will be given here. The W ii ions were generated by focusing a laser pulse onto a tungsten target. A laser system consisting of a Nd:YAG laser, a pulse compressor, a dye laser and nonlinear crystals for frequency doubling and mixing produced tunable pulses with wavelengths around 210 nm and with a duration of about 1.5 ns. The excitation pulses interacted with the tungsten ions about 5 mm above the target which consisted of a rotating foil in a vacuum chamber. The fluorescence, emitted from the excited levels, was focused onto the entrance slit of a 1/8 m monochromator and then detected by a micro-channel-plate photomultiplier tube with a risetime of 0.2 ns and a fall time of 0.6 ns. The signal was finally recorded with a transient digitizer having a time resolution of 0.5 ns. In the measurements the laser pulse and the fluorescence signal were recorded alternatively with the same detection system. A computer code called DECFIT has been developed to analyse the decay curves. DECFIT operates on a Windows platform and provides the user with an efficient graphical environment. Lifetimes are extracted by a weighted least-squares fit of a single exponential decay, convoluted by the measured laser pulse. A polynomial background representation may also be considered. Approximate weights are derived assuming Poisson statistics. The transient digitizer is not strictly a counting measurement but extensive tests have shown that this weighting mode is still a useful representation of the relative errors in the recorded data. However, the statistical uncertainties derived for the fitted lifetimes are typically too low by at least a factor of two compared to the variation of the results with repeated measurements. The experimental lifetimes of the nine levels considered in the present work are reported in Table 1 where they are compared with the previous experimental values and with theory (present work and previous results). Each value represents an average of at least ten recordings. As a test, the lifetime of one previously investigated level ( cm 1 )[13] was remeasured with a consistent result. 4 Calculations of branching fractions Tungsten being a heavy element appearing in the sixth row of the periodic table (Z = 74), both relativistic and correlation effects must be considered simultaneously in the calculations. This is why the HFR approach [18] was applied to calculate the BFs in W ii. Therelativistic corrections were the Blume-Watson spin-orbit, massvelocity and one-body Darwin terms. The Blume-Watson spin-orbit term includes the part of the Breit interaction that can be reduced to a one-body operator [24]. The correlation effects were included in different ways according to the type of interactions, i.e. valence-valence or core-valence correlation. Core-valence interactions were taken into account through a polarization model potential and a correction to the dipole operator following a well-established approach (see e.g. [25]) giving rise to the HFR+CP method. We considered two different core-polarization models. In the first one, referred to as HFR+CP(A), an Er-like ioniccore(4f 14 ) surrounded by 5 valence electrons was chosen. As the dipole polarizability was not tabulated in Fraga et al. [26], a value of 2.80a 3 0 was extrapolated along the isoelectronic sequence using Figure 2 of reference [27]. The HFR value, 1.26a 0, for the mean radius of the outermost core orbital, i.e. 5p, was used for the cut-off radius. The second core-polarization model, HFR+CP(B), considers a 4f 14 5d 2 Yb-like ionic core surrounded by 3 valence electrons. The value tabulated in reference [26] forwv has been chosen for the dipole polarizability, i.e. 4.59a 3 0.The cut-off radius used was the HFR mean radius of the 5d orbital in the 5d 2 6s 2 6p configuration of W ii, i.e. 1.77a 0. Concerning the valence-valence interactions in both core-polarization models, we included in the vectorial basis the following configurations: 5d 5,5d 4 ns, 5d 3 6sns, 5d 4 6d, 5d 3 6s6d, 5d 2 6s 2 6d and 5d 3 6p 2 (n =6 8) in the even parity and 5d 4 np, 5d 3 6snp, 5d 2 6s 2 6p and 5d 2 6p 3 (n =6 8) in the odd parity. To take into account the remaining interactions with far configurations not considered explicitly by the vectorial basis or implicitly by

3 H. Nilsson et al.: Lifetimes and transition probabilities in W ii 3 the polarization model, all the radial Coulomb parameters were first scaled down by 0.85 according to a wellestablished procedure [18]. The HFR+CP method was then combined with a least-squares optimization routine minimizing the discrepancies between calculated and experimental energy levels published in the recent compilation of Kramida and Shirai [17]. All the 263 experimentally known energy levels were included in the fitting process. These levels belong to the 5d 5,5d 4 6s, 5d 3 6s 2,5d 4 6p, 5d 3 6s6p and 5d 2 6s 2 6p configurations. The standard deviations of the fits were found to be 99 cm 1 and 138 cm 1 for the even and odd parities, respectively. 5 Results and discussions A comparison between the calculated lifetimes obtained with both core-polarization models and the present measurements, the available experimental values in the literature [12,13,15] and the theoretical values of Ekberg et al. [20] are presented in Table 1. It has to be noticed that the calculated lifetimes published in Table 8 of reference [20] are the ab initio radial dipole moment values and are therefore on average 30% lower than the measurements and 15% and 25% lower than our HFR+CP(A) and HFR+CP(B) models, respectively. In Table 1, the values reported as modified radial dipole moment lifetimes are the calculated values published in Table 8 of reference [20] divided by the 0.69 scaling factor [20]. After this ad hoc correction, the results are, not surprisingly, in good agreement with our measurements and our HFR+CP(B) model. Our HFR+CP(A) values are on average 20% shorter than experiment while our HFR+CP(B) model is in a reasonably good agreement with the measurements although a 5% systematic discrepancy on average remains between both sets of results. The differences between our HFR+CP(A) and HFR+CP(B) models are mainly due to the choice of the ionic core, the CI expansions being the same. In this respect, HFR+CP(B) is expected to include more correlation than HFR+CP(A) because all the virtual single electron excitation 5d nl are taken into account implicitly by building a core-polarization potential that incorporates the 5d shell into the ionic core. The lifetime measured by Kwiatkowski et al. [12] for the /2 level has to be definitely rejected. The beamfoil (BFS) data of Henderson et al. [15] fortheastrophys- levels are longer ically important /2 and /2 than our best calculations [HFR+CP(B)] by about 30%. This can be explained through comparisons between the TR-LIF data (this study and Schnabel et al. [13]) with these BFS measurements [15]. There is a 30% discrepancy between both sets of results indicating that perhaps the cascade effects had not been taken into account adequately in the BFS experiment. The disagreement between our TR-LIF measurement and our theoretical models concerning the lifetime of level /2 remains problem- Fig. 1. Comparison between HFR+CP(B) weighted oscillator strengths and the experimental values from Kling et al. [16]. The straight line of equality has been drawn. The mean scatter is ±0.18 dex. atic. The good agreement between our calculations and thebfsvaluelooksfortuitous. In Figure 1, a comparison between HFR+CP(B) weighted oscillator strengths (in logarithmic scale), which are considered as the best results of the present paper, and the experimental values from Ekberg et al. [20] is shown. The straight line of equality has been drawn. Both data sets are in fair agreement showing a mean scatter of ±0.18 dex. Some HFR+CP(B) and experimental oscillator strengths (log gf), transition probabilities (ga) and branching fractions (BF) for the decay channels of the odd parity levels of W ii, measured in our TR-LIF experiment, are reported in Table 2. In the last column of the table, we report the cancellation factor as defined by Cowan [18]: CF = [ y γ βj βj P (1) β J y γ β J y γ βj βj P (1) β J y γ β J ]2. (1) In (1), S γγ = γj P (1) γ J 2 is the line strength and it has been assumed that the wavefunction γj can be expanded in terms of a suitable set of basis functions βj according to γj = β yγ βj βj. Small values of CF (typically 10 3 ), which are by no means unusual in a complex transition array, indicate that the computed line strengths are expected to show large errors. Due to space limitations, the sample of transitions of Table 2 is restricted to the most intense transitions i.e. those with ga 10 7 s 1. The whole set of results will be listed in the DE- SIRE database that will be available at the address: astro/desire.shtml.

4 4 The European Physical Journal D Table 1. Comparison between measured and calculated lifetimes (in ns) in W ii. The results obtained in the present work are shown in columns 3 and 5. Level E (cm 1 ) i τ exp (this w.) τ exp (prev.) τ calc (this w.) τ calc (prev.) / ± 0.14 b, e, f 9.45 g, h 14.0 ± 0.7 c / ± 0.07 b, 9.11 e,9.82 f 7.71 g,11.17 h 11.3 ± 0.6 c / ± 0.09 b e, f 8.64 g, h / ± 0.19 b 8.34 e,9.04 f 6.52 g,9.45 h / ± 0.13 b 8.30 e,9.00 f 6.96 g, h / ± 0.9 b, e, f g, h 3.0 ± 0.3 c / ± 0.12 b 7.74 e,8.61 f 6.80 g,9.86 h / ± 0.07 b 2.46 e,2.87 f 2.12 g,3.07 h / ± 0.22 b e, f g, h / ± 0.15 b 5.22 e,5.72 f 4.23 g,6.13 h / ± 0.06 b 3.25 e,3.75 f 2.82 g,4.09 h / ± 0.24 b 6.15 e,6.79 f 4.95 g,7.17 h / ± 0.10 b e, f 8.60 g, h / ± 0.3 a 5.71 ± 0.08 b 5.91 e,6.82 f 5.29 g,7.67 h / ± 0.11 b 2.88 e,3.23 f 2.53 g,3.67 h / ± 0.3 a 6.61 e,7.63 f / ± 0.08 b 4.54 e,5.37 f 4.02 g,5.83 h / ± 1.0 a e, f / ± 0.11 b 2.52 e,2.87 f 2.13 g,3.09 h / ± 0.06 b 5.08 e,6.03 f 4.56 g,6.61 h / ± 0.4 a 4.69 e,5.31 f / ± 0.4 a 3.71 e,4.28 f / ± 0.2 a 1.87 e,2.16 f / ± 0.4 a 4.30 e,4.75 f / ± 0.8 d 5.37 e,5.83 f / ± 0.08 b, 2.05 e,2.35 f 1.72 g,2.49 h 3.5 ± 0.3 d / ± 0.2 a 2.7 ± 0.3 d 2.59 e,2.94 f / ± 0.2 a 2.12 e,2.45 f a TR LIF measurements (this work). b TR LIF measurements by Schnabel et al. [13]. c TR LIF measurements by Kwiatkowski et al. [12]. d BFS measurements by Henderson et al. [15]. e HFR+CP(A) calculations (this work). f HFR+CP(B) calculations (this work). g HFR calculations using the ab initio radial dipole moments by Ekberg et al. [20]. h HFR calculations using modified radial dipole moments by Ekberg et al. [20]. i From Kramida and Shirai [17]. 6 Conclusions New transition probabilities have been deduced for a set of 290 W ii transitions depopulating 9 levels for which the lifetimes have been measured by time-resolved laser-induced fluorescence spectroscopy. The theoretical branching fractions have been obtained by the HFR approach. Core-valence interactions have been taken into account through a polarization model potential and a correction to the dipole operator. The derived transition probabilities are expected to be accurate within a few percent at least for the most intense transitions. Uncertainty could be larger for the weaker lines particularly those susceptible to cancellation effects in the calculation of the line strengths.

5 H. Nilsson et al.: Lifetimes and transition probabilities in W ii 5 Table 2. HFR+CP(B) and experimental oscillator strengths (log gf), transition probabilities (ga) and branching fractions (BF) for the decay channels of the odd parity levels of Wii measured in our TR-LIF experiment. Only the transitions with ga 10 7 s 1 are listed. Upper level a Lower level a λ b (Å) HFR+CP(B) log gf ga (s 1 ) BF CF c (o) (e) E (e) E (e) E (e) E (e) E (e) E (e) E (o) (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E (o) (e) E (e) E (e) E (e) E (e) E (o) (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E (o) (e) E (e) E (e) E (e) E (e) E (e) E (o) (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E

6 6 The European Physical Journal D Table 2. Continued. Upper level a Lower level a λ b (Å) HFR+CP(B) log gf ga (s 1 ) BF CF c (o) (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E (o) (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E (o) (e) E (e) E (e) E (e) E (o) (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E (e) E a Each level is designated by its value in cm 1, its parity ((e) and (o) stand for even and odd respectively) and its total quantum number, J. b Calculated from the experimental energy levels of Ekberg et al. [20]. λ>2000 Åaregiveninair. c Cancellation factor as defined by Cowan [18] (seethetextformoredetails).

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