Radiative data in the Zr I spectrum obtained by Laser Induced Fluorescence G. Malcheva 1, R. Mayo 2, M. Ortiz 2, J. Ruiz 2, L. Engström 3, H. Lundberg 3, H. Nilsson 4, P. Quinet 5,6, É. Biémont 5,6 and K. Blagoev 1 1 Institute of Solid State Physics, 72 Tzarigradsko Chaussee, BG - 1784 Sofia, Bulgaria 2 Department of Atomic, Molecular and Nuclear Physics, Univ. Complutense de Madrid, E-28040 Madrid, Spain, 3 Department of Physics, Lund Institute of Technology, P.O. Box 118, S-221 00 Lund, Sweden 4 Lund Observatory P.O. Box 43, S-221 00 Lund, Sweden 5 IPNAS (Bât. B15), University of Liège, Sart Tilman, B-4000 Liège, Belgium 6 Astrophysics and Spectroscopy, University of Mons-Hainaut, B-7000 Mons, Belgium E-mail: bobcheva@issp.bas.bg ABSTRACT Radiative lifetimes of 17 excited states in Zr I, in the energy interval 29000 40974 cm -1, have been investigated using the Time-Resolved Laser-Induced Fluorescence (TR-LIF) method. The levels belong to the 4d 2 5s5p, 4d 3 5p and 4d5s 2 5p electronic configurations were excited in a single - step excitation process, from levels belonging to the ground 4p 2 5s 2 a 3 F or to low-lying 4p 2 5s 2 a 3 P, a 5 F terms. For 14 levels, the lifetimes have been measured for the first time. Experimental results are compared with theoretical calculations performed with a multiconfigurational relativistic Hartree-Fock method including core polarization effects. Keywords: Zirconium atom, radiative lifetimes, transition probabilities, time-resolved spectroscopy 1. INTRODUCTION With the extraordinary technological development of laser sources and detectors during the past twenty years, the analytical possibilities of the Laser Induced Fluorescence (LIF) technique and of the laser-induced spark discharges have become more obvious. Particularly, those techniques have demonstrated their possibilities as efficient tools for the determination of atomic and ionic radiative lifetimes and transition probabilities. The most common laser methods for obtaining radiative lifetimes and transition probabilities are the Time-Resolved Laser-Induced Fluorescence (TR-LIF) technique and the Laser-Induced Breakdown Spectroscopy (LIBS) approach, respectively. In the present work, we apply the TR-LIF method for radiative lifetime measurements of high-lying levels of Zr I. Accurate values of radiative lifetimes and oscillator strengths for spectral lines of neutral zirconium are needed in astrophysics for the determination of the chemical composition of solar and, more generally, stellar atmospheres. In a series of previously published papers 1-4, low lying excited levels of Zr I have been studied. The excitation was performed by a modified beam-foil method or by sputtering from a Zr target followed by excitation of the Zr atoms with a fast Ar + beam. Hannaford & Lowe 5 used the TR-LIF method and the sputtering from a hollow cathode for measuring radiative lifetimes of z 3 G 3,4,5 ; y 5 G 2,3,4,5,6 and y 3 G 3,4,5 states of Zr I. In 6 radiative lifetimes of 11 levels from z 3 G, y 5 G and y 3 G terms of Zr I have been investigated by TR-LIF applied to a Zr atomic beam, produced by a sputtering process in a hollow cathode discharge.
A method based on the measurement of the fluorescence decay following a pulsed laser excitation of sputtered metal vapor has been used by Biémont at al 7 to obtain radiative lifetimes for 34 levels of Zr I and the branching fractions and oscillator strengths for the transitions depopulating these levels have been determined by measuring their relative intensities. The delayed-coincidence method with pulsed laser excitation was used in 8 for the measurement of radiative lifetimes of the 15 excited states y 5 G 2,3,4,5 ; y 3 G 3,4,5 ; x 3 F 2,3,4 ; x 3 D 1,2 ; z 1 G 4; w 3 F 2,3, of Zr I, all of them having energies in the interval 25630-29002 cm -1. In 9 the picosecond LIF, combined with a hollow cathode discharge, was applied to measure the radiative lifetimes of four excited levels of Zr I i.e. y 4 G 4, x 3 G 5, z 1 G 4 and x 3 D 2. In the present paper, some high-lying Zr I levels, belonging to different multiplets and having energies included between 29000 and 40974 cm -1, have been investigated. A partial energy level diagram of Zr I is presented on Figure1. 42000 40000 4d5s 2 5p t 3 P 1 o Energy (cm -1 ) 38000 36000 34000 32000 30000 28000 0 4d 3 5p w 3 G o 319.12 nm 4d5s 2 5p u 3 P o 4d 3 5p t 3 D o 4d 3 5p u 3 F o 301.44 nm 507.83 nm 464.48 nm 4d 3 5s 3 F 4d 2 5s 2 3 4d 3 5s 5 2 P F 1.0 1.5 2.0 2.5 0 2 4d 2 5s 2 3 F 2 3.0 305.03 nm 312.92 nm 4d 3 5p v 3 P o 2 1 4d 2 5s5p y 3 o S 1 x 3 o G 5 4d 2 5s5p Figure 1. A partial energy level diagram of Zr I. Some of the excitation and decay channels are shown. Energy levels and designation are according to Moor tables 10. 2. LIFETIME MEASUREMENTS The experimental set-up, at the Lund Laser Center(LLC), Sweden used in the present work, is shown in Figure 2. Free atoms and ions, in different ionization stages, have been produced by laser ablation, using the second harmonic of a Nd:YAG laser (532 nm). The sample, in our case a Zr foil, is placed in a vacuum chamber with a vacuum of about 10-6 - 10-5 mbar. The excitation of the Zr I excited states was performed using a pulsed tunable dye laser working with a DCM dye. The laser is pumped by a second Nd:YAG laser. The pulses of the laser are shortened by a stimulated Brillouin scattering (SBS) compressor to approximately 1 ns. The repetition rate of the lasers is 10 Hz. In the experiment, the second harmonic of the dye laser pulse was used for the excitation of the Zr I levels as well as Raman Stokes and anti- Stokes wavelengths of the second harmonic. The Stokes and anti-stokes components are produced in a tube filled with hydrogen at a pressure of about 10 bar. The excitation and observation wavelengths as well as the excitation schemes are presented in Table 1. The two Nd:YAG lasers are synchronized by a pulse generator, which determines the delay between the ablation and the excitation pulses. The digitized LIF signals were typically averaged over 1000 laser pulses
and stored in a computer. The LIF decay curves are treated by a deconvolution process for short lifetimes and by considering a single exponential decay in the case of long lifetimes. At least 10 decay curves were registered for each excited state of interest. Furthermore, measurements were made on at least 2 different occasions to investigate possible systematic effects Different intensities of the excitation pulses were considered to avoid saturation effects which could affect the decay curves and make the deconvolution process less accurate. A decay curve from the t 3 P 1 level of Zr I is presented in Figure 3. The experimental set-up at the LLC is very flexible allowing measurements of radiative lifetimes between 1 ns and 1000 ns. The device is also suitable for investigation of refractory elements. In addition, lifetimes of ions up to the fourth ionization stage can be investigated. Figure. 2 Experimental set-up
Table 1. Odd levels measured in Zr I and the corresponding excitation schemes. State E,(cm -1 ) Excitation Detection, λ (nm)air Scheme λ (nm)air x 3 G 5 29001.65 626.12 2ω+S 432.54 w 3 G 3 31326.81 637.88 2ω 507.83 w 3 G 4 31694.52 642.04 2ω 506.49 y 3 S 1 31850.77 627.40 2ω 361.51 w 3 G 5 32152.16 646.46 2ω 515.87 u 3 F 2 33163.98 602.55 2ω 464.48 u 3 F 3 33420.47 608.32 2ω 465.76 u 3 F 4 33559.34 618.32 2ω 471.19 t 3 D 1 36125.16 626.06 2ω 408.31 t 3 D 3 36220.45 623.80 2ω 354.97 t 3 D 2 36294.87 626.05 2ω 410.76 v 3 P 1 36489.10 618.81 2ω 451.54 u 3 P 0 36538.27 621.32 2ω 485.16 u 3 P 1 36970.65 627.03 2ω 305.03 v 3 P 2 37008.40 626.29 2ω 448.08 u 3 P 2 37450.23 616.25 2ω 300.54 t 3 P 1 40973.94 630.03 2ω+AS 271.83 2ω means the second harmonic, S and AS are written for the first Stokes and anti-stokes components of the Raman scattering. Figure 3. Decay of the level 40974 cm -1 in Zr I with an evaluated lifetime of 5.5 ± 0.5 ns. Data points, after background subtraction, with error bars together with the fitted single exponential convoluted by the measured laser pulse (solid line). The dashed curve shows the recorded laser pulse.
3. THEORETICAL CALCULATIONS The theoretical lifetimes of the investigated levels have been obtained by a Relativistic Hartree-Fock method (HFR), taking configuration interaction and core-polarization effects into account. The relativistic corrections were the Blume- Watson spin-orbit, the mass-velocity and the one-body Darwin term. The correlation effects were introduced in different ways according to the type of interactions, i.e. valence-valence or core-valence. Valence-valence correlation was taken into account by explicitly including the most strongly interacting configurations in the expansions. Core-valence interactions were considered through a polarization model potential and a correction to the dipole operator, according to a well established procedure 11 which will not be further described here. The calculated lifetimes are presented in the last column of Table 2. Table 2. Experimental and calculated lifetimes for odd parity levels of Z r I Level E exp (cm -1 ) g exp E calc (cm -1 ) g calc τ exp (ns) τ exp (ns) τ calc (ns) This work Others This work x 3 G 5 29001.65 1.21 28880 1.20 6.9 ± 0.3 6.6 ± 0.2 [7] 6.8 ± 0.2 [9] 7.8 ± 0.5 [8] w 3 G 3 31326.81 0.75 31388 0.76 8.2 ± 0.5 8.2 w 3 G 4 31694.52 1.04 31756 1.05 7.8 ± 0.6 7.7 y 3 S 1 31850.77 31936 1.93 18.2 ± 0.9 4.1 w 3 G 5 32152.16 1.20 32193 1.20 7.7 ± 0.4 7.8 ± 0.3 [7] 7.5 u 3 F 2 33163.98 0.70 33253 0.85 10.1 ± 0.5 10.9 u 3 F 3 33420.47 1.06 33225 1.08 10.2 ± 0.5 9.8 u 3 F 4 33559.34 1.24 33356 1.25 11.4 ± 0.6 11.4 ± 0.4 [7] 10.7 t 3 D 1 36125.16 0.45 36277 0.52 4.0 ± 0.3 3.3 t 3 D 3 36220.45 1.28 36328 1.25 4.2 ± 0.3 3.3 t 3 D 2 36294.87 1.16 36375 1.18 4.0 ± 0.3 3.4 v 3 P 1 36489.10 36849 1.40 6.7 ± 0.7 6.1 u 3 P 0 36538.27 36787 8.8 ± 0.4 7.1 u 3 P 1 36970.65 * 5.2 ± 0.4 * v 3 P 2 37008.40 1.55 37360 1.48 8.1 ± 0.7 6.4 u 3 P 2 37450.23 * 6.0 ± 0.5 * t 3 P 1 40973.94 * 5.5 ± 0.5 * 6.3 * - Level untraceable in the HFR calculations
4. DISCUSSION The Zr atom belongs to the IVA group of the periodic table. Its ground term is [Kr]4d 2 5s 2 a 3 F. Other low-lying even terms, from which excitation of high-lying odd levels is possible, are [Kr]4d 2 5s 2 a 3 P, [Kr]4d 3 5s a 5 F and [Kr]4d 2 5s 2 a 1 D. They are represented in Figure 1. In the same figure, some of the excitation and decay channels of the investigated odd levels are also shown. In Table 2, experimental and theoretical radiative lifetimes are compared. The uncertainties in the experimental lifetimes given in the table include both statistical uncertainties and systematic effects. The experimental and theoretical data are in reasonable agreement for most of the levels. However, for some of them discrepancies exist. The largest difference is observed for the y 3 S 1 (31850.77 cm -1 ) level. Actually, the laser wavelength used to excite this level i.e. 313.873 nm (4d 2 5s 2 3 F 2 4d 2 5s5p y 3 S 1 ) is close to the excitation wavelength of the Zr II excited level 4d 2 5p 4 D 5/2, which has been previously measured 7,9 and has a radiative lifetime of ~ 7 ns. Using a different excitation channel i.e. 361.369 nm (4d 2 5s 2 3 P 2-4d 2 5s5p y 3 S 1 ) and different decay channels for the Zr I y 3 S 1 state, the radiative lifetime of Table 2 (i.e. 18.2 ns) was confirmed. Using the excitation channel at 313.873 nm and a decay channel at 438 nm, the Zr II lifetime of 7.0 ns was obtained. The discrepancy theory-experiment observed for the level at 31850.77 cm -1 has thus a theoretical origin. 5.CONCLUSION In the present work, radiative lifetimes for 17 levels belonging to the odd 4d 2 5s5p, 4d5s 2 5p and 4d 3 5p electronic configurations of Zr I are reported. For 14 of the investigated levels, radiative lifetimes are obtained for the first time. The new measurements have been compared with HFR calculations. For most of the levels, there is good agreement between experimental and theoretical values. The error bars of the measurements are in the interval 4-10%. Measurements of branching fractions are in progress by means of the LIBS technique. ACKNOWLEDGMENTS This work was financially supported by the Swedish Research Council; by the EU-TMR access to Large-Scale Facility Programme (contract RII3-CT-2003-506350) and by the Spanish Ministry of Education and Research (project FIS2006-10117). É. Biémont and P. Quinet are Research Director and Senior Research Associate, respectively, of the Belgian FRS-FNRS. Financial support from this organization is acknowledged. National Science Fund of Bulgaria is acknowledged for financial support (grant 1516/05). G. Malcheva and K. Blagoev are grateful to the colleagues of the Lund Laser Center for their kind hospitality and support. REFERENCES [1]. Ramanujam P. S., " Direct measurement of radiative lifetimes of excited states in refractory-metal atoms using a sputtering technique", Phys. Rev. Lett. 39, 1192(1977). [2]. Anderson T., Ramanujam P. S., Bahr K., " Lifetimes of excited states in Y I, Y II, and Zr I by beam-foil and beamsputtering excitation", The Astrophys. Journal 223, 344(1978). [3]. Poulsen O., Anderson T., Bentzen S. M., Nielsen U., " Spectroscopy of the uranium ion using collinear fast-beamcw-dye-laser modulation spectroscopy. Transition energies and excited-state lifetimes", Phys. Rev. A, 24, 2523(1981).
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