EDP Sciences
Free Access
Issue
A&A
Volume 600, April 2017
Article Number A108
Number of page(s) 13
Section Atomic, molecular, and nuclear data
DOI https://doi.org/10.1051/0004-6361/201629615
Published online 10 April 2017

© ESO, 2017

1. Introduction

The final stage of exothermal element production in massive stars is the iron-group elements, with nickel itself having the maximum binding energy per nucleon closely followed by iron. Higher Z elements are produced by subsequent neutron capture. Nickel is therefore one of the most abundant iron-peak elements in cosmic objects. In addition, Nickel shows a line-rich spectrum due to its complex atomic structure and the lines appear in a variety of objects, from the interstellar medium and stars to the solar corona and supernova explosions. Nuclear statistical equilibrium models predict that iron and nickel are produced in high-temperature environments, i.e. explosive nucleosynthesis (Nadyozhin 2003), such as supernovae type Ia, where a white dwarf ignites, or supernovae type II, where the core of a massive star collapses into a neutron star (Stritzinger et al. 2006). The dominating product of these events is 56Ni, which is distributed to the surrounding gas during the outburst. Abundance determinations of nickel in stars serve as important constraints of stellar evolution and supernova explosion models. The current challenges for accurate elemental abundances are the development of 3D-model atmospheres and non-LTE modeling (Wongwathanarat et al. 2011; Lind et al. 2012). Atomic data for levels of different excitation energies are important for this development. For example, in metal-rich stellar photospheres, transitions from low excitation states with a high population can be saturated whereas those from the less populated highly excited states are more likely to be optically thin. The present investigation of Ni II is part of an ongoing effort to provide such data for the second spectra of selected iron-group elements: Ti II (Lundberg et al. 2016), Cr II (Engström et al. 2014), Fe II (Hartman et al. 2015) and Co II (Quinet et al. 2016).

There are two papers in the literature on experimental determination of radiative lifetimes in Ni II. Lawler & Salih (1987) used the time-resolved laser-induced fluorescence (TR-LIF) method on a slow Ni+ beam from a hollow-cathode source. Radiative lifetimes of 12 odd-parity levels of Ni II in the energy range from 51 550 to 57 080 cm-1 are reported in that paper. Later, Fedchak & Lawler (1999) improved the experimental set-up, confirmed and extended the previous results to a total of 18 experimental lifetimes and reported transition probabilities for 59 lines in the VUV and UV spectrum of Ni+, Ni II.

Table 1

Levels measured in the 3d8(3F)4d configuration of Ni II and the corresponding excitation schemes.

thumbnail Fig. 1

HST/GHRS spectrum of Chi Lupi in the region around 2205 Å, showing the prominent Ni II lines at 2205.548 and 2205.862 Å studied in the present work. The solid line is the observed spectrum and the dashed line is the synthetic spectrum. Courtesy of Brandt et al. (1999) and reproduced by permission of the AAS.

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In the present work, we have measured lifetimes for seven even-parity levels in the energy range 98 400 to 100 600 cm-1. The lifetimes are measured using the TR-LIF method, and the high-lying states are populated using two-step photon excitation of ions produced by laser ablation. Furthermore, we report theoretical lifetimes obtained with a pseudo-relativistic Hartree-Fock method in good agreement with the experimental results, and calculated transition probabilities for 477 lines depopulating highly excited levels belonging to the even-parity 3d84d configuration in singly ionized nickel.

The lines studied in the present work appear strong in spectra of hot stars, such as the B9.5V type HgMn star Chi Lupi A (Brandt et al. 1999), where the lines form prominent absorption features despite their higher excitation. As an example, a spectral segment of Chi Lupi from the HST/GHRS atlas is presented in Fig. 1. In addition, the Ni II lines are identified in several cooler template stars, e.g. the solar type star α Cen A (spectral type G2 V) and Arcturus (K1.5 III) as reported by Hinkle et al. (2005). In the linelists of these stars, several Ni II lines are presented without multiplet number, indicating that they are of too high excitation to be listed in the multiplet table by Moore (1959). All the Ni II lines in the 20003000 Å region without multiplet number are included in our study.

2. Experiment

The ground term in Ni II is [Ar] 3d92D, but as a starting point in the excitation schemes we used the J = 9/2 and 7/2 levels in the second lowest term of even parity, 3d8(3F)4s 4F, at 8394 and 9330 cm-1, respectively (Shenstone 1970). These levels were populated directly in the plasma produced by the ablation laser. The first tuneable laser excited the intermediate, odd parity, levels in the 3d84p configuration around 55 000 cm-1, from where the final, even parity, levels in 3d84d around 100 000 cm-1 were reached with the second tuneable laser. The excitation and detection channels used in this work are given in Table 1.

The experimental set-up for two-step excitations at the Lund High Power Laser Facility has recently been described by Lundberg et al. (2016), and for an overview we refer to Fig. 1 in that paper. Here we only give the most important details. Ni+ ions in the 3d8(3F)4s 4F term were created by focusing 532 nm, 10 ns long, laser pulses onto a rotating nickel target placed in a vacuum chamber with a pressure of about 10-4 mbar. The two short wavelength excitation laser beams entered the vacuum chamber at a small relative angle and were focused on the expanding plasma plume about 5 mm above the target. All lasers operated at 10 Hz and were synchronized by a delay generator. The time resolved fluorescence from the excited states (both intermediate and final) was detected at right angles to the lasers by a 1/8 m grating monochromator, with its 0.28 mm wide entrance slit oriented parallel to the excitation laser beams and perpendicular to the ablation laser. The dispersed light was registered by a fast micro-channel-plate photomultiplier tube (Hamamatsu R3809U) and digitized by a Tektronix DPO 7254 oscilloscope. A second channel on the oscilloscope simultaneously registered the excitation pulse shape, as detected by a fast photo diode. The PM tube has a rise time of 200 ps and the oscilloscope sampled the decay and pulse shape at every 50 ps. All spectral measurements were performed in the second spectral order, which is closer to the optimum efficiency of the blazed grating, resulting in a linewidth of about 0.5 nm.

Table 2

Radiative lifetimes (in ns) for selected energy levels belonging to the 3d8(3F)4d configuration of Ni II.

For both the first and the second excitations we used the frequency tripled output from Nd:YAG pumped dye lasers (Continuum Nd-60), primarily operating with DCM dye. The first step had a pulse length of 10 ns whereas, by injection seeding and compressing, for the second Nd:YAG laser a pulse length of about 1 ns could be obtained. Before every measurement the delay between the two lasers was checked and, if necessary, adjusted so that the short pulse from second laser coincided with the maximum population of the intermediate level. The short pulse length in the second step and the high time resolution of the detection system is necessary to accurately measure the short lifetimes involved (1.21.3 ns). To reach a sufficient statistical accuracy each decay curve was averaged over 1000 laser pulses. The final lifetime analysis used the code DECFIT (Palmeri et al. 2008) to fit a single exponential decay, convoluted by the measured pulse shape, and a background function to the observed decay curve. Typically 10 to 20 measurements, performed during different days, were averaged to obtain the final lifetimes, given in Table 2. The quoted uncertainties in the results are mainly due to the scatter between the individual measurements.

As discussed by Lundberg et al. (2016), two step measurements may lead to complicated blending situations that must be taken into account in the planning and execution of the experiment. In the Ni case, we note from Table 1 that the two excitation lasers as well as the fluorescence channels all occur in the narrow wavelength interval 210226 nm. Thus, most of the recorded decay curves are influenced by the very intense decay from the intermediate levels. This contribution extends over more than 10ns, due to the length of the first step laser pulses, and is noticeable even at rather large wavelength differences. Fortunately, this effect may be accurately compensated for by subtracting a separate decay measurement, with the second step laser blocked, before the final lifetime analysis. A worse case is encountered in the measurement of the 4d 4H13/2 level where also scattered light from the second laser influences the decay. This is illustrated in Fig. 2, and corrected for by a “background” measurement where the second laser is not blocked but detuned slightly from resonance. Finally, transitions from levels in the 3d84p configuration populated through the decay of the 4d level under investigation, so called cascades, may cause blending problems. Since this cannot be compensated for, one has to carefully choose the fluorescence channels to use, and if no sufficiently intense channels remain this particular level has to be omitted from the investigation. An example of this is the failure to measure the 4d 4G7/2 level at 100 475.8 cm-1 since all strong decay channels are blended by cascades.

thumbnail Fig. 2

First 30 ns of the decay of 4d 4H13/2 in Ni II (solid line). Combined background contribution from both the first- and second-step lasers, where the latter is detuned 0.04 nm from resonance (dashed line). This background is substracted before the final lifetime analysis.

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3. Theoretical calculations

Calculations of energy levels and radiative transition rates in Ni II have been carried out using the relativistic Hartree-Fock (HFR) approach (Cowan 1981) modified to take core-polarization effects into account (Quinet et al. 1999, 2002). This method (HFR+CPOL) has been combined with a least-squares optimization process of the radial parameters to reduce the discrepancies between the Hamiltonian eigenvalues and the available experimental energy levels from Shenstone (1970). The following 23 configurations were explicitly introduced in the calculations: 3d9, 3d84d, 3d85d, 3d74s4d, 3d74s5d, 3d64s24d, 3d84s, 3d85s, 3d74s2, 3d74s5s, 3d64s25s for the even parity and 3d84p, 3d85p, 3d74s4p, 3d74s5p, 3d64s24p, 3d64s25p, 3d84f, 3d85f, 3d74s4f, 3d74s5f, 3d64s24f, 3d64s25f for the odd parity.

The ionic core considered for the core-polarization model potential and the correction to the transition dipole operator was a 3d6 Ni V core. The dipole polarizability, αd, for such a core is 0.94 a according to Fraga et al. (1976). We used the HFR mean radius of the outermost 3d core orbital, 1.004 a0, for the cut-off radius.

For the 3d9, 3d84d, 3d85d, 3d84s, 3d85s, 3d74s2 even configurations and the 3d84p, 3d85p, 3d74s4p, 3d84f, 3d85f odd configurations, the average energies (Eav), the electrostatic direct (Fk) and exchange (Gk) integrals, the spin-orbit (ζnl) and the effective interaction (α) parameters were allowed to vary during the fitting process. All other Slater integrals were scaled down by a factor 0.80 following a well-established procedure (Cowan 1981). The standard deviations of the fits were 212 cm-1 for the even parity and 77 cm-1 for the odd parity.

thumbnail Fig. 3

Comparison between the oscillator strengths (log gf) calculated in the present work and those reported by Kurucz (2011) for transitions from highly excited even-parity 3d84d levels in Ni II.

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4. Results and discussion

The radiative lifetimes measured and computed in the present work are presented in Table 2. The theoretical lifetimes obtained in this work agree with the experimental values within about 5%. Table 2 includes the theoretical lifetimes obtained by Kurucz (2011). The latter work also used a semi-empirical approach based on a superposition of configurations calculation with a modified version of the Cowan codes (Cowan 1981) and experimental level energies (Shenstone 1970) to improve the results. In this case the calculated values are about 11% higher than the experiments.

Table A.1 presents the computed oscillator strengths and transition probabilities for the strongest transitions (log gf > −4) depopulating the even 3d84d levels located in the range 98 467–103 664 cm-1. This table also presents the cancellation factors (CF) as defined by Cowan (1981). Transitions with a CF lower than 0.05 should be considered with great care as they are affected by cancellation effects.

Most of the previous experimental and theoretical studies of radiative parameters in Ni II were focused on the spectral lines from the odd parity 3d84p configuration ((Zsargó & Federman 1998; Fedchak & Lawler 1999; Fritzsche et al. 2000; Fedchak et al. 2000; Jenkins & Tripp 2006; Manrique et al. 2011) and the 3d84s3d84p or 3d93d84p transitions. Recently, an extensive calculation of atomic structure data for Ni II was published by Cassidy et al. (2016). This work resulted in transition rates and oscillator strengths for 5023 electric dipole lines involving the 3d9, 3d84s, 3d74s2, 3d84p and 3d74s4p configurations.

To our knowledge, the only work listing also oscillator strengths from the 3d84d even levels is the database of Kurucz (2011). Figure 3 shows a good general agreement between the two data sets. However, a closer inspection reveals that our new oscillator strengths are systematically higher than the values by Kurucz (2011). The mean ratio gf(This work)/gf(Kurucz) is 1.22 for lines with log gf > −4. The new log gf values are thus on average 20% larger than the previous calculation by Kurucz (2011). The difference between the two sets of results is possibly due to different values of the radial dipole integrals in calculations of the line strengths. In the case of 3d84p3d84d transition array for example, the reduced matrix element ⟨ 4p | | r1 | | 4d ⟩ computed in our work was 4.55664 a.u. and 4.66532 a.u. with and without core-polarization, respectively, while, as far as we understand, Kurucz used a value scaled down to 4.47840 a.u. which tends to weaken the corresponding oscillator strengths.

5. Conclusion

We report seven new experimental radiative lifetimes for 3d84d levels in Ni II, measured by two-step excitation using time-resolved laser-induced fluorescence on a laser ablation plasma. In addition, we report an extensive theoretical study using a relativistic Hartree-Fock technique optimized on experimental level energies. The theoretical and experimental lifetimes agree within 5%, which serves as benchmark for the accuracy of the 477 calculated oscillator strengths for the strong transitions around 200220 nm belonging to the 3d84p3d84d transition array. Furthermore, on a two-standard deviation level the new theoretical gf values as well as the results from Kurucz (2011) agree with the experimental lifetimes.

Acknowledgments

This work has received funding from LASERLAB-EUROPE (grant agreement No. 284464, EC’s Seventh Framework Programme), the Swedish Research Council through the Linnaeus grant to the Lund Laser Centre and a VR project grant 621-2011-4206 (H.H.), and the Knut and Alice Wallenberg Foundation. P.P. and P.Q. are respectively Research Associate and Research Director of the Belgian National Fund for Scientific Research F.R.S.-FNRS from which financial support is gratefully acknowledged. V.F. acknowledges the Belgian Scientific Policy (BELSPO) for her Return Grant. P.Q., V.F., P.P., G.M. and K.B. are grateful to the colleagues from Lund Laser Center for their kind hospitality and support.

References

Appendix A: Additional table

Table A.1

Transition probabilities and oscillator strengths for spectral lines depopulating highly excited levels belonging to the even-parity 3d84d configuration of Ni II.

All Tables

Table 1

Levels measured in the 3d8(3F)4d configuration of Ni II and the corresponding excitation schemes.

Table 2

Radiative lifetimes (in ns) for selected energy levels belonging to the 3d8(3F)4d configuration of Ni II.

Table A.1

Transition probabilities and oscillator strengths for spectral lines depopulating highly excited levels belonging to the even-parity 3d84d configuration of Ni II.

All Figures

thumbnail Fig. 1

HST/GHRS spectrum of Chi Lupi in the region around 2205 Å, showing the prominent Ni II lines at 2205.548 and 2205.862 Å studied in the present work. The solid line is the observed spectrum and the dashed line is the synthetic spectrum. Courtesy of Brandt et al. (1999) and reproduced by permission of the AAS.

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In the text
thumbnail Fig. 2

First 30 ns of the decay of 4d 4H13/2 in Ni II (solid line). Combined background contribution from both the first- and second-step lasers, where the latter is detuned 0.04 nm from resonance (dashed line). This background is substracted before the final lifetime analysis.

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In the text
thumbnail Fig. 3

Comparison between the oscillator strengths (log gf) calculated in the present work and those reported by Kurucz (2011) for transitions from highly excited even-parity 3d84d levels in Ni II.

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In the text

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