Character of an 8− isomer of 130Ba

Physics Letters B 547 (2002) 200–204 www.elsevier.com/locate/npe

Character of an 8− isomer of 130Ba R. Moore a , A.M. Bruce b , P. Dendooven c,1 , J. Billowes a , P. Campbell a , A. Ezwam a , K.T. Flanagan a , D.H. Forest d , J. Huikari c , A. Jokinen c , A. Nieminen c , H.L. Thayer d , G. Tungate d , S. Zemlyanoi a , J. Äystö c a Schuster Laboratory, University of Manchester, Manchester M13 9PL, UK b School of Engineering, University of Brighton, Brighton BN2 4GJ, UK c Department of Physics, University of Jyväskylä, PB 35 (YFL) FIN-40351 Jyväskylä, Finland d School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UK

Received 18 July 2002; accepted 3 October 2002 Editor: V. Metag

Abstract The static moments and isomer shift of the J π = K π = 8− isomeric state in 130 56 Ba have been measured using the technique of collinear laser spectroscopy. The isomer has been found to have a magnetic dipole moment of −0.043(28) µN and a static − + quadrupole moment of +2.77(30) b. These values have been used to assign the state as a two neutron 72 [404] ⊗ 92 [514] configuration corresponding to a prolate shape. The half-life of the isomer has been confirmed as 9.54(14) ms. The change in the mean square charge radius was found to be r 2 130m − r 2 130g–s = −0.0473(30) fm2 .  2002 Published by Elsevier Science B.V. PACS: 21.20.Ft; 21.10.Ky; 21.10.Tg; 42.62.Fi Keywords: Nuclear static moments; Isomer shift

The shape of the J π = K π = 8− isomeric state in has been the focus of much recent attention [1] as the E1 gamma decay from the state does not fit in with the systematics of the isotonic chain. Two possible explanations for this have been proposed, one in terms of the shape of the isomer itself and another in terms of the structure of the J π = 8+ yrast state to which the isomer decays [1]. The analogous 130 Ba 56

E-mail address: [email protected] (R. Moore). 1 Present address: KVI, Zernikelaan 25, 9747 AA Groningen,

The Netherlands.

isomeric states in 138 Gd, 136 Sm, 134 Nd and 128Xe have been shown [2–5] to comprise two neutrons − + in the 72 [404] ⊗ 92 [514] orbitals which are near the Fermi surface at prolate deformation. However, in the case of 130 Ba two possible configurations for the isomeric 8− state have been discussed [6], a two-proton configuration with an oblate shape and a two-neutron configuration with a prolate shape. The authors [6] decided in favour of the neutron configuration in 130 Ba because a similar state had been seen in 132Ce. However, it has been proposed [1] that the observed deviation from the decay systematics of

0370-2693/02/$ – see front matter  2002 Published by Elsevier Science B.V. PII: S 0 3 7 0 - 2 6 9 3 ( 0 2 ) 0 2 7 8 4 - 3

R. Moore et al. / Physics Letters B 547 (2002) 200–204

the 8− state in 130 Ba could be due to a change in configuration of the observed isomeric state across the region, with the oblate state being observed in 130Ba and the prolate state being observed for the higher Z nuclei. This is a realistic possibility since nuclei in this region are known [7] to exhibit gamma-softness and calculations suggest that for 130 Ba the potential well has a lower minimum for an oblate shape [6] whereas the opposite is true for 136 Sm [8]. A small difference in the shape of the potential between the N = 74 nuclei could be the underlying reason for the observed decay systematics of the isomeric states. In order to resolve this debate, the static moments and isomer shift have been measured by collinear laser spectroscopy at the IGISOL (Ion Guide Isotope Separator On-Line) facility in Jyväskylä, Finland [9]. The IGISOL allows the production of fast radioactive beams without the inherent problems associated with most ISOL techniques. Conventional ISOL methods use a hot target catcher which has the disadvantages of being chemically selective with slow release rates. The IGISOL uses fast flowing helium gas to catch the reaction products, thermalise them and charge exchange them into the 1+ ionic state. This method has the important benefit of being very fast. The extraction time for ions from the ion-guide is approximately 1 ms, which makes the study of millisecond isomers possible. The 130m Ba isomers were produced with a 2 µA beam of 45 MeV deuterons on a 130 µg/cm2 target of CsI supported on a 17 µg/cm2 carbon foil, via the 133 Cs(d, 5n) 130m Ba reaction channel. Reaction products recoiled into the gas volume of the ion guide which was operated at a pressure of 250 mbar. The products were extracted, accelerated to 37.2 kV and magnetically mass-separated. The large energy spread of the beam, which is inherent in the IGISOL technique, was reduced by passage through an ioncooler, which takes the form of a gas-filled linear Paul trap [10]. The trap was held at 37.113 kV, slightly lower than the IGISOL voltage, so that the ions were slowed down to ∼100 eV as they entered the trap. In the device the ions were thermalised by viscous collisions in 0.1 mbar helium and squeezed onto the geometric axis by a RF field. As they left the RF trap they were reaccelerated by the cooler voltage (37.113 kV) which was monitored and controlled to an accuracy of 0.1 V throughout the experiment. The

201

Fig. 1. Singles gamma-ray spectrum and partial decay scheme of the isomer, collected after the cooler.

ion beam was then electrostatically transported for measurement. A station after the cooler was used to collect gamma-ray spectra in order to optimise the IGISOL and cooler conditions. A typical gamma-ray spectrum is shown in Fig. 1 which includes a partial decay scheme showing the decay of the isomeric J π = K π = 8− level. From this it was determined that the isomer flux under optimum conditions was ∼150 s−1 . From the ion rate detected on microchannel plates (9000 s−1 ) it was possible to determine that an isomer to ground-state ratio of at least 0.02 was present in the ion beam. In fact as the beam was not purely barium the true ratio of isomer to g–s was larger (a ratio of 0.12 was determined from the fluorescence spectra shown in Fig. 3). The isomer lifetime was measured by pulsing the ion beam (20 ms on, 30 ms off) using deflector plates. The gamma-ray spectrum was measured versus time in the pulsing cycle by registering multi-parameter (gamma-ray energy, time) events. Fig. 2 shows the time dependence of the gamma-ray peak intensity summed over the main gamma-rays emitted following the isomer decay. The first 25 ms of the beamoff period were used in the half-life analysis. A χ 2 minimization fit with a single exponential gave a halflife of 9.54(14) ms which lies between two previous, mutually inconsistent measurements of 8.8(2) ms [11] and 13.5(10) ms [12]. For the laser spectroscopy measurement the ion beam was electrostatically transported to the collinear

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Fig. 3. Sample of the experimental data collected, showing the two best fits and their corresponding underlying hyperfine structures. Fig. 2. Time dependence of the gamma-ray peak intensity, showing the exponential fit to the data.

beams station, where the ion beam was overlapped with a counter-propogating laser beam. A 1 mm aperture in the beam line was used to focus the ion beam to a tight waist in the light collection region. It was possible to focus ∼35% of the ions through the aperture. A counter-propogating laser beam from a stabilized Spectra Physics 380D dye laser was focused to match the shape of the ion beam in the light collection region and overlapped with it, using the same aperture. The aperture was removed during the measurements. Photons from an 18 mm length of the beam were imaged onto the surface of a Hamamatsu R5900P03-L16 segmented photomultiplier tube mounted perpendicular to the beam. The photon–ion coincidence method was used [13] with the cooler operating in a continuous beam mode. This method allowed a reduction in the background level of the spectra (due to scattered laser light) from 150 to 0.03 s−1 , making the sensitive measurements on barium possible. The laser was locked to an absorption line of 130 Te2 in a vapour cell at 500 ◦ C. The absorption line was at a frequency of 21 935.602 cm−1 [14]. The barium ionic ground-state (g–s) transition at 21 952.422 cm−1 (455.5 nm, 2 S1/2 – 2P 3/2 ) was Doppler-tuned to resonance with this fixed laser frequency. A wide search was made for the isomer components in the frequency region of the 130 Ba g–s resonance. This was achieved by scanning the Doppler-

tuning voltage applied to the light collection region, while looking for resonant laser fluorescence on the photomultiplier tube. Although there are six components in the hyperfine structure (HFS) of the isomer, only two components could be clearly identified in the fluorescence spectra. However there are indications in all the spectra of peaks lying in the shoulders of the g–s peak. The remaining peaks were either under the g–s peak, or they were outside the frequency range examined. There are several possible arrangements of the HFS which hide several peaks under the g–s resonance. Fig. 3 shows some of the data taken in the region of the single component of the g–s resonance. The figure indicates the difference between the best fit, Fig. 3(a) and the second best fit, Fig. 3(b), where the isomer components are constrained to have the same peak shape as the g–s component. It can be seen that while the overall fit seems reasonable in Fig. 3(b), it reproduces neither the widths and relative intensities of the isomer peaks, nor the features on the shoulders of the g–s peak. The best fit of the HFS, shown in Fig. 3(a), gives a reduced chi-squared of χr2 = 1.22. This is considerably better than any other arrangement of the HFS (determined by a combination of the nuclear moments and the isomer shift). It is also the only fit from which the value for the quadrupole deformation parameter calculated from the isomer shift and that derived from the quadrupole moment, are mutually consistent. This point is discussed in more detail below. The fit clearly follows the trends of the g–s

R. Moore et al. / Physics Letters B 547 (2002) 200–204

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shoulders well. From this fit an isomer shift of, ν 130m − ν 130g–s = +241(14) MHz was determined on the 455.5 nm line in ionic barium, which corresponds to a change in mean square charge radius of r 2 130m − r 2 130g–s = −0.0473(30) fm2 (see Fig. 4). The HFS can be related to the nuclear dipole and quadrupole moments via 

µA =





AA I A A µ AA I A



and QA s =



BA A Q , BA s

(1)

where A is the mass number of the isomer of interest and A is that of an isotope with well-known nuclear moments. A and B are the hyperfine coefficients of the upper or lower ionic levels and are directly related to the position of the hyperfine components in the fluorescence spectra. The ratio of A(2 S1/2 )/A(2 P3/2 ) was fixed at +31.95. This ratio was determined from known hyperfine coefficients for these levels in the stable barium isotopes [15,16]. The best fit gave hyperfine parameters of A(2 S1/2 ) = −34.67(57) MHz and B(2 P3/2 ) = +912(13) MHz. From these the nuclear moments were calculated using Eqs. (2) and (3) to be µ = −0.0431(7) µN (assuming no hyperfine anomaly), and Qs = +2.77(30) b. The value of the magnetic dipole moment is very small, so there is potential in this case for a large hyperfine anomaly to be present. To estimate approximately how large this anomaly could be, a comparison was made to the isotopes of caesium for which a number of anomalies are known [17]. It was considered that an anomaly of up to 65% could be present, in which case µ = −0.043(28) µN . Fig. 4 shows the trend of the mean square charge radii across the barium isotope chain. The isomer measurement is shifted to a smaller mean square radius than the g–s. The box shown in Fig. 4 indicates the range in δr 2  covered by the search for the other hyperfine components. Rotter et al. [6] have shown that all possible J π = 8− states in this region (whether prolate or oblate) that may be responsible for the isomer would have a quadrupole deformation parameter of β2 ∼ 0.2. It is therefore most unlikely that the structure could lie outside the range covered. Fig. 4 also shows the normal odd–even staggering of the charge radii across the isotope chain. Normal staggering is seen throughout the table of isotopes (except in a few cases where the staggering is reversed by specific nuclear structure effects [18]). This effect may be qualitatively understood as a blocking effect of

Fig. 4. The trend of the mean square charge radii across the barium isotope chain, showing the new isomer measurement and the quadrupole-deformed droplet model isodeformation contours.

the unpaired neutron in odd-N isotopes (a one quasiparticle effect). In the same manner the negative shift between the isomer and its ground-state could be due to blocking by the two unpaired neutrons producing a reduction in pairing correlations in the isomer. The shift observed for 130m Ba is approximately twice the size of the odd–even staggering in this region and consistent with being a two quasiparticle state. It has been suggested that the negative isomer shifts observed in 177 Lu and 178 Hf have a similar origin [19]. The quadrupole deformation parameter, β2 may be estimated, assuming axially-symmetric quadrupole distortions, from the change in mean square charge radius, using  
2
2 5
2 β , r = r sph 1 + (2) 4π 2 where r 2 sph is the mean square charge radius of the spherical nucleus of the same volume. Using the known value for the g–s deformation parameter (β2rms = 0.217(1)) [20], δr 2  between the g–s and the isomer and spherical droplet model calculations for r 2 sph , yields a value of β2rms = 0.205(1). The value of β2 calculated from the spectroscopic quadrupole

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moment, Qs , using the standard relations for the intrinsic quadrupole moment, Qo : (I + 1)(2I + 3) Qo = Qs I (2I − 1)

and

5Zr 2 sph βs (1 + 0.36βs), Qo ∼ = √ 5π

(3)

is +0.223(12). These β2 values are consistent (within two standard deviations), as is expected for a staticallydeformed nucleus. None of the other possible arrangements of the HFS produced this consistency (or produced a satisfactory fit to the experimental data). The value of β2 is in agreement with values of 0.19 and 0.20 calculated by Xu for the two-neutron and twoproton configurations, respectively [21]. However, the small dipole moment confirms the two-neutron configuration if a small (∼4%) admixture of the two-proton state (calculated using the g-factors in Ref. [5]), is included. To conclude, the measurement of the properties of the isomeric state in 130 Ba has resolved the debate [1] about the systematics of the E1 decay in 8− isomeric states in N = 74 nuclei. The positive quadrupole moment reported here indicates that the isomer is prolate in shape. The calculations performed [6] indicate that in the case of a prolate deformation the isomer must have a two-neutron configuration, which is consistent with the small dipole moment observed. This suggests that it is the structure and shape of the yrast states to which the isomers decay which determine the systematics of decays from analogous states in the N = 74 isotones, rather than the structure of the isomeric states themselves.

Acknowledgements This work has been supported by the UK Engineering and Physical Sciences Research Council, the Academy of Finland under the Finnish Centre of Excellence Programme 2000–2005 (Project No. 44875), and by the European Union Fifth Framework Programme “Improving Human Potential—Access to Research Infrastructure”. Contract No. HPRI-CT-199900044. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21]

A.M. Bruce, et al., Phys. Rev. C 55 (1997) 620. D.M. Cullen, et al., Phys. Rev. C 58 (1998) 846. P.H. Regan, et al., Phys. Rev. C 51 (1995) 1745. D.G. Parkinson, I.A. Fraser, J.C. Lisle, J.C. Willmott, Nucl. Phys. A 194 (1972) 443. T. Lönnroth, S. Vajda, O.C. Kistner, M.H. Rafailovich, Z. Phys. A 317 (1984) 215. H. Rotter, et al., Nucl. Phys. A 133 (1969) 648. R. Wyss, et al., Nucl. Phys. A 505 (1989) 337. E.S. Paul, et al., J. Phys. G 19 (1993) 861. J. Äystö, Nucl. Phys. A 693 (2001) 477. A. Nieminen, et al., Phys. Rev. Lett. 88 (2002) 9. H.F. Brinkman, et al., Nucl. Phys. 81 (1966) 233. D. Ward, UCRL-18667 (1969) 54. J.M.G. Levins, et al., Phys. Rev. Lett. 82 (1999) 2476. J. Cariou, P. Luc, Atlas du Spectre d’Absorbtion de la Molecule de Tellure, Aime-Cotton, Orsay, France, 1980. W. Becker, R. Blatt, G. Werth, J. Phys. 42 (1981) C8-339. K. Wendt, et al., Z. Phys. A 318 (1984) 125. S. Büttgenbach, Hyperfine Interact. 20 (1984) 1. J. Billowes, P. Campbell, J. Phys. G 21 (1995) 707. J. Billowes, Nucl. Phys. A 682 (2001) 206c. A.C. Mueller, et al., Nucl. Phys. A 403 (1983) 234. F. Xu, private communication.