Lifetime measurements in Tl

Lifetimes are reported for the 6s6p P1, 6s6d D2 and 6s7s S0 levels in Hg-like Tl II, measured using beam-foil excitation. The values obtained were τ(P1) = 0.59 ± 0.02 ns, τ(P1) = 39 ± 2 ns, τ(D2) = 6.5 ± 0.5 ns, and τ(S0) = 3.0 ± 0.4 ns. Isoelectronic trends for line strengths of the resonance and intercombination transitions are studied through comparisons with earlier measurements for Hg I–Bi IV. We report here lifetime measurements of the 6s6p P1, 6s6p P1, 6s6d D2, and 6s7s S0 levels in singly ionized thallium in the mercury isoelectronic sequence. This sequence is the heaviest homologue in the group II-B alkaline-earth Zn-, Cdand Hg-like systems, which have (n − 1)d10ns2 ground configurations. Oscillator strength data for Tl II are needed for many specific applications. Spectral lines from Tl II have been identified in astrophysical observations of Hg–Mn-type stars made using the Goddard high resolution spectrograph on board the Hubble space telescope [1, 2]. Because it can be confined in an ion trap and possesses a very long-lived metastable 6s6p P0 level, Tl II can be utilized as a high accuracy atomic clock [3]. In terms of fundamental theory, the 80-electron Hg isoelectronic sequence provides a severe challenge to existing calculational methods [4, 5], which can only be tested by acquiring a base of reliable measurements. Moreover, semi-empirical regularities have been observed [6] which may permit the interpolation of line strengths of the resonance and intercombination lines to be made based on a few precise measurements at low stages of ionization and an asymptotic high-Z limit [7, 8]. Earlier curve fitting studies have been made [9–11] for the P1, D2 and S0 levels, but this is the first lifetime measurement of the P1 level, and the first cascaded–correlated [12, 13] lifetime measurement of the P1 level. The measurements utilized the 300 kV University of Toledo heavy ion accelerator. Detailed descriptions of this facility can be found in reports of earlier studies in this series (e.g. [14, 15]) as well as in instrumentation reviews [16, 17]. Ions of Tl2+ were produced in the ion source, accelerated through 20 kV, and magnetically analysed. After momentum and mass-to-charge selection, the ions were post-accelerated to final energies of 500 keV for study of the resonance line, and 520 keV for study of the intercombination line. The ions then entered an electrostatic switchyard and were steered into the experimental station and collimated before passage through a thin carbon foil (ranging from 2.1–2.5μg cm−1). At beam energies of 500–520 keV, the observed spectroscopic excitations were primarily in Tl II, Tl III, and Tl IV. The Tl II emission lines were analysed with an Acton 1-m normal incidence VUV monochromator, with three sets of concave gratings and detectors: a 1200 lines/mm grating coupled with a solar blind detector for the region λ1321.7 Å transition; a 1200 lines/mm 0953-4075/96/170629+06$19.50 c © 1996 IOP Publishing Ltd L629 L630 Letter to the Editor grating coupled with a bialkali detector for the λ1908.7 Å transition; and a 600 lines/mm grating coupled with a bialkali detector for the λ2531 and 3092 Å transitions. The postfoil velocity was determined to within 2.5% by taking into account uncertainties in energy calibration, foil thickness, and possible beam divergence. Using the Danfysik model 911A ion source, ions were obtained from pure thallium metal. To minimize foil breakage, the current was limited to less than 200 nA (100 particle nA for Tl2+). It was relatively easy to produce Tl2+ currents greater than 200 nA, and it was possible to obtain currents approaching 1 μA. The methods used to obtain doubly charged thallium in the ion source are similar to those used earlier for obtaining Cd2+, and are discussed in [15]. Due to the nonselective nature of beam-foil excitation, the level populations (and hence the decay curves) are affected by cascade repopulation. Thus, while they produce a negligible contribution in the case of long-lived decays such as the 6s2 S0–6s6p P1 intercombination transition, cascades can distort the decay curves of shorter-lived levels such as the 6s2 S0–6s6p P1 resonance transition, which is repopulated by the yrast chain through the 6s6p P1–6s6d D2 transitions, as well as by Rydberg transitions such as 6s6p P1– 6s7s S0. Situations in which cascading is dominated by a few strong channels are ideally suited to analysis by the ANDC method [12, 13], which performs a joint analysis of the decay curves of the level of interest together with those of levels that directly repopulate it. The decay curves were all analysed by the multiexponential fitting program DISCRETE [18]. In the case of the 6s6p P1 resonance transition this was supplemented by ANDC analyses made jointly with the 6s6d D2 and 6s7s S0 decay curves. Two ANDC codes were used: one makes use of the numerical differentiation of the raw data; the other utilized the program CANDY [19], which uses data that have been smoothed through the application of a multiexponential filter. The uncertainties in our multiexponential fits were computed by combining statistical uncertainties in the individual fits, scatter among the independent measurements and estimates of possible errors introduced by cascade corrections. For the DISCRETE fits of each if the three singlet decay curves the primary exponential was much stronger than, and well separated in effective lifetime from, the cascade contributions. Thus, while ANDC analysis reduced the uncertainties in the determination of the lifetime of the resonance transition, it did not significantly alter the extracted value. The intercombination transition was well represented by a single exponential, and estimates [20] of possible beam divergence caused by multiple scattering in the foil indicated that more than 95% of the beam particles were within the volume viewed by the optical system over the full range of the decay curves. The results of our lifetime measurements are given in table 1, and compared with earlier measurements and theoretical calculations. Comparisons of the degree of core–valence and core–core correlation included in these calculations are given in [4]. Our lifetime measurements for the resonance and intercombination transitions correspond to absorption oscillator strength values f (Res) = 1.33(9) and f (Int) = 0.042(2). We have also examined the isoelectronic trends of the lifetimes of the resonance and intercombination levels using an energy-level-based reduction of the line strengths. For ns2 S0–nsnp P1 transitions LS notation is valid for the lower level but is only nominal for the upper level, since it is spin-hybridized by intermediate coupling. In the absence of configuration interaction, the spin hybridization of the nsnp configuration can be characterized by a singlet–triplet mixing angle θ . The mixing angle can be independently determined from either the energies of the four nsnp levels, the decay rates of the two J = 1 levels (to within factors of the radial transition element), or the magnetic g-factors of the levels with J > 0. This mixing angle formulation has provided the basis for a semiempirical Letter to the Editor L631 Table 1. Measured lifetimes, compared with other experiments and theoretical values.