Chopped-beam techniques and γ-ray spectroscopy with Gammasphere have been used to measure the lifetime of the 1112-keV 8- isomeric state in Er174. The value obtained of τ=5.8(4) s corresponds to a reduced hindrance of fν=98 for the 163-keV E1 transition to the 8+ state of the ground-state band, in good agreement with the systematics of the corresponding E1 strengths in the N=106 isotones. The K-mixing in the 8- states is calculated in the context of the particle-rotor model and used to extract the underlying reduced hindrances

Carpenter, M.P.

Chiara, C.J.

Dracoulis, G.D.

Janssens, R.V.F.

Kondev, F.G.

Lane, G.J.

Lauritsen, T.

Lister, C.J.

McCutchan, E.A.

Seweryniak, D.

Stefanescu, I.

Watanabe, H.

Zhu, S.

Carolina Digital Repository

RAPID COMMUNICATIONSPHYSICAL REVIEW C 79, 061303(R) (2009)Lifetime of the Kπ = 8− isomer in the neutron-rich nucleus 174Er, and N = 106 E1 systematicsG. D. Dracoulis,1,* G. J. Lane,1 F. G. Kondev,2 H. Watanabe,3 D. Seweryniak,4 S. Zhu,4 M. P. Carpenter,4 C. J. Chiara,2,†R. V. F. Janssens,4 T. Lauritsen,4 C. J. Lister,4 E. A. McCutchan,4 and I. Stefanescu4,51Department of Nuclear Physics, R. S. Phys. S. E, Australian National University, Canberra ACT 0200, Australia2Nuclear Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439, USA3RIKEN Nishina Center, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan4Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA5Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, USA(Received 1 June 2009; published 29 June 2009)Chopped-beam techniques and γ -ray spectroscopy with Gammasphere have been used to measure the lifetimeof the 1112-keV 8− isomeric state in 174Er. The value obtained of τ = 5.8(4) s corresponds to a reduced hindranceof fν = 98 for the 163-keV E1 transition to the 8+ state of the ground-state band, in good agreement with thesystematics of the corresponding E1 strengths in the N = 106 isotones. The K-mixing in the 8− states iscalculated in the context of the particle-rotor model and used to extract the underlying reduced hindrances.DOI: 10.1103/PhysRevC.79.061303 PACS number(s): 21.10.Tg, 23.20.−g, 23.35.+g, 27.70.+qThere is continuing interest in understanding the propertiesof metastable states in deformed nuclei. Such states arise forvarious reasons [1] including the fact that electromagneticdecays involving large charges in K , the quantum numberthat describes the projection of the total angular momentumon the nuclear symmetry axis, can be very inhibited. Theability to classify the decay strengths plays an important rolein the assignment of intrinsic configurations, as seen in therecent studies of very heavy deformed nuclei (for example,Refs. [2–4]). These studies aim to define the Nilsson orbitalsnear the Fermi surface and hence the nuclear potential. In turn,systematic studies of the properties of states with well-definedconfigurations can contribute to a more quantitative descriptionof “forbidden” transitions.Partly in this context, but also motivated by our interest inprobing the nuclear structure of neutron-rich nuclei, we reporthere new results for 174Er and an analysis of E1 strengthsfor the N = 106 isotones. A long-lived 8− isomer wasrecently identified [5] in 174Er, establishing simultaneouslyits previously unknown yrast sequence and extending thesequence of isomers in the N = 106 isotones arising fromthe ν27/2−[514] ⊗ 9/2+[624] two-quasiparticle configura-tion, from Z = 82 down to Z = 68. However, only a limit ofτ > 8 ms on the lifetime was obtained previously, making thiscase the only one in an extensive chain for which the lifetime,and therefore the inhibited E1 strength, is not known. Thedecay sequence is shown in Fig. 1.To define the lifetime, new measurements were madeunder conditions similar to those in which the isomer wasfirst identified. These involved the use of chopped 840-MeV136Xe beams provided by the ATLAS facility at ArgonneNational Laboratory. The beams were incident on an enriched*Corresponding author: george.dracoulis@anu.edu.au†Present address: Physics Division, Argonne National Laboratory,Argonne, Illinois 60439, USA, and Department of Chemistry andBiochemistry, University of Maryland, College Park, Maryland20742, USA.target of 176Yb, approximately 6mg/cm2 in thickness, witha 25 mg/cm2 Au foil directly behind. The target was thickenough to integrate over the main yield of inelastic processesfrom ∼20% above the Coulomb barrier, down to the barrier.Gamma rays were detected with Gammasphere [6], with 99 Gedetectors in operation. The nucleus 174Er is populated throughtwo-proton removal from the target, at an intensity level ofabout 5% of the population of the related 8− isomer in 176Yb.Distinguishing 174Er from the much stronger product,176Yb, has the complication that their ground-state-bandtransitions are close in energy (differing by 1–2 keV), andthe corresponding 8− isomer in 176Yb also has a long lifetime,in this case 17 s (see Ref. [7] and references therein). However,the primary E1 decays from the 8− isomer to the 8+ ground-state band are significantly different in energy. Figure 2 isa representative γ -ray spectrum obtained by gating on the163-keV E1 transition in a γ -γ matrix in the out-of-beamtime region, which shows the ground-state-band transitions in174Er without significant contamination.As well as the transition energies in the yrast bands of 174Erand 176Yb being similar, so are the corresponding sequencesin the N = 104 isotonic pair, 172Er and 174Yb, consistentwith saturation of the deformation near midshell as notedpreviously [5]. Furthermore, the experimental E4+/E2+ ratiosare essentially identical for the N = 104 and N = 106 isotoneswith Z = 68, 70, and 72, as seen in Fig. 3. This results in anexperimental issue in identifying other structures in 174Er sinceit is not possible to correlate through the isomers because of thelong lifetimes, and, at least for the simplest two-quasiparticleconfigurations, such as the expected 8− rotational band itself,they may be very similar to, and possibly unresolvable from,corresponding structures in more strongly populated nucleisuch as 176Yb.The lifetime limit reported previously [5] was obtained frommeasurements using a macroscopically chopped beam with(beam on)/(beam off) conditions of 1 ms/3 ms for the 176Ybtarget, and with out-of-beam dual coincidence events recordedin reference to a precision clock. Gamma-gamma matrices as afunction of the time were constructed, allowing long lifetimes0556-2813/2009/79(6)/061303(4) 061303-1 ©2009 The American Physical SocietyRAPID COMMUNICATIONSG. D. DRACOULIS et al. PHYSICAL REVIEW C 79, 061303(R) (2009)   00 +  822 + 2704 + 5616 + 9498 +1112     8       -81.6188.2291.0387.8162.9  = 5.8 sEr 68  106174FIG. 1. Decay scheme of the 8− isomer in 174Er [5] including thenew lifetime result from the present work.to be isolated by gating on specific cascades within the nucleusof interest. Similar conditions and analysis techniques wereused in the present experiment, but with longer time ranges,progressing in steps of factors of 10 from an initial value of10 ms/33 ms up to 1 s/3.3 s, the longest time range that couldbe accessed conveniently.Figure 4 provides the intensity of the 174Er ground-state-band transitions obtained with gates on the 163-keV transitionas outlined earlier, together with a fit, which gives τ = 5.8(5) s.The 163-keV transition is the only branch observed from theisomer: A limit on the possible 551-keV M2 branch fromthe 8− isomer to the 6+ state of <2% of the intensity of the163-keV γ ray corresponds to a limit on the reduced hindrance(defined in the following) of fν > 46, consistent with itsnonobservation. Such branches are therefore not competitivein this case and in others such as 176Yb, 178Hf, 180W, and 182Os(see Ref. [5]).As is well known, the isomerism in these nuclei arisesfrom the forbidden nature of the decays between the Kπ = 8−countsenergy [keV]163 keV gate  100 200 300 400 500 600020040060080082188.2 291.0387.8122   SnFIG. 2. Coincidence spectrum with a single 163-keV gate in theout-of-beam time region.Z68 70 72 74 76 78 8023E(4 )/E(2 )   +     +N = 106N = 104FIG. 3. Ratio of 4+ and 2+ state energies for the N = 104 andN = 106 isotones.two-quasiparticle state and the K = 0 ground-state-bandmembers. The E1 transitions have forbiddenness ν = K −λ = 7, where λ is the multipolarity. The hindrance factor F isgiven by the ratio of the partial mean lives to the Weisskopfestimates τW , so that F = ττW . The corresponding reducedhindrances fν = F 1/ν for the N = 106 isotones, including thenew result for 174Er, are given in Fig. 5.The fν values vary relatively smoothly from a value of98 in 174Er to ∼30 in 188Pb, a nucleus where the presenceof this isomer has been used as an argument for the prolatenature of the secondary well in a situation where three shapescountstime [s]0.0 1.0 2.0 3.0210310  = 5.8 sτFIG. 4. Time dependence of the decay of the 8− isomer in 174Ertogether with a fit to an exponential curve.061303-2RAPID COMMUNICATIONSLIFETIME OF THE Kπ = 8− ISOMER IN THE . . . PHYSICAL REVIEW C 79, 061303(R) (2009)A 174 176 178 180 182 184 186 188110210310f νPbHgPtOsWHfYbEr f 0FIG. 5. Reduced hindrances for the E1 decays from the 8−isomers in the N = 106 isotones. The value for the 178Hf casehas been corrected for the known mixing between the two-neutronconfiguration and a competing two-proton configuration [9–12]. Thesmaller symbols, connected by the dashed line, are the values obtainedafter correction for Coriolis mixing in the initial state (see text).coexist [8]. The only point that might deviate significantlyin the systematic behavior is that obtained for 184Pt. Thereare two issues with this value. The first one is experimentalin that a significant branch occurs through an unobservedlow-energy transition. The second is that this is a case wherethe deformation of the final states may be less well definedthan in nuclei where either the ground state is well deformedor where shape coexistence is sufficiently well establishedthat the potential minima are well separated in deformation.Triaxiality may therefore be a factor in 184Pt, although ingeneral one would expect this to lead to the lowering ofapparent hindrances because of a broader K-distribution inthe final states.Note that the E1 strengths extracted here do not includethe additional factor of 103–104 often arbitrarily used in theevaluation of reduced hindrances, but the hindrances couldbe seen already, as being relatively low for E1 transitions.In actuality, K-forbidden E1 strengths show large variationsbetween specific mass regions, probably indicative of theunderlying configuration, configuration-change, or couplingdependencies (see, for example, Refs. [12–15]). Such nuclearstructure effects could be disguised by using additionalarbitrary reduction factors.Walker et al. [12] pointed out a correlation between thefall in the fν values for the E1 transitions from the 8−isomers (as they were known then) and the ratio of thedynamic to the kinematic moment of inertia in the ground-statebands, which was taken to imply the presence of higherK-components in the (nominally) K = 0 ground-state band.This particular contribution is difficult to treat quantitatively;however, another factor that will affect the absolute rates isK-mixing in the initial state, as was also noted in Ref. [12].Mixing is expected since the two-neutron 8− configurationcontains the 9/2+[624] orbital from the i13/2 neutron configu-ration and, thus, will be Coriolis-mixed, even though the Fermisurface is relatively high in the shell.We have estimated the K-mixing in the initial state in thecontext of a simplified model [16] that treats the non-high-jparticles, in this case a single 7/2−[514] neutron, as spectators,since Coriolis-mixing among its partner orbitals is small.In this model there are (2j + 1) possible projections of thei13/2 set of orbitals,  = −13/2,−11/2, . . . ,+11/2,+13/2.(Note that the sign relative to the nonparticipating orbitalsneeds to be retained in enumerating the set of basis states[17].) There are various parameters in this model, particularlythe pairing strengths, whose choice can be guided by themass differences (see also the discussion in Ref. [5]) and theunperturbed band moments of inertia. The approach takenhas been to approximately constrain these by reproducing theenergies of states in the 8− rotational bands. These are nowknown for 176Yb [18,19], 178Hf [9–11], 180W [20], 182Os [21],184Pt, [22], 186Hg [23,24], and 188Pb [8]. This structure has notbeen identified in 174Er but, as noted earlier, in all likelihood,it is expected be very similar to that of 176Yb. The energiesof the intrinsic states were taken from the Nilsson model byassuming predicted deformations [25,26]. A 14 × 14 matrixcan be constructed for the highest spins in each case, withoff-diagonal matrix elements within the i13/2 set of orbitalsconnecting states of the same spin and with K = ±1 (asshown schematically in Fig. 17 of Ref. [17]). The Coriolismatrix can then be diagonalized to give the perturbed energiesand the wave function admixtures in terms of the normalizedamplitudes, AK .The results of these calculations give very similar ad-mixtures for all cases. Those for 182Os, for example,are A(K = 8) = 0.9625; A(K = 7) = 0.2644; A(K = 6) =0.0590; A(K = 5) = 0.0120; A(K = 4) = 0.0025; lowerK-components are negligible.By including such components explicitly, it is possible toextract the underlying reduced hindrance f0 with the implicitassumption that the reduced hindrance is independent ofthe rank of the forbiddenness, ν. This was the approachtaken recently in analyzing hindrances in another case whereadmixtures can be calculated [27]. The formulation followsfrom the fact that the inverse of the total hindrance F is relatedto the total decay width and, therefore, can be constructed fromthe sum of partial widths for each K-component. In the generalsituation there are K-admixtures AKi and BKf in the initialand final states, with νKiKf = Ki − Kf − 1 and therefore (forνKiKf > 1)1F=∑Ki,Kf(AKi BKf)2(f0)νKiKf.In the present case, we assume that the final state (8+ in theground-state band) is pure Kf = 0 (i.e., B0 = 1.0), and thushave, for the 8− states,1F (8−)= (A8)2(f0)7+ (A7)2(f0)6+ (A6)2(f0)5+ (A5)2(f0)4+ (A4)2(f0)3+ · · · .061303-3RAPID COMMUNICATIONSG. D. DRACOULIS et al. PHYSICAL REVIEW C 79, 061303(R) (2009)The value of f0 was then varied to reproduce the totalE1 hindrance for each isotone. The values recovered in thisway are given in Fig. 5. For 182Os, for example, the observedtotal hindrance of 6.34 × 1011 (corresponding to fν = 48.5)can be reproduced with the calculated mixed-K amplitudesand f0 = 165. A similar rescaling is seen in all cases, withthe extracted value for 174Er rising by an order of magnitudefrom 98 to 970. It should be noted, however, that the dominantterm is that from the lowest K value of K = 4, despite itsvery low amplitude. The presence of very small amplitudes ofeven lower K that might fall below the numerical accuracy ofthe present calculations would result in an underestimate off0. For example, components of K = 0, 1 become significantat amplitude levels of ∼10−5. This (obvious) sensitivitymeans that the extracted values will only be approximate,given the uncertainties in the model calculation. Nevertheless,the high values for the underlying hindrances exposed when theadmixtures are taken into account are more in line with thoseexpected for K-forbidden E1 transitions. This quantitativeapproach avoids the need to resort to the inclusion of arbitraryreduction factors in evaluating (and comparing) E1 transitionstrengths.From another perspective, the high sensitivity to theadmixture of low-K components in highly forbidden tran-sitions implies that random fluctuations could be expected,yet a relatively smooth behavior is observed. This apparentcontradiction can be attributed to two factors, one being thenear-yrast nature of the 8− isomers in most cases and theother being the very small mixing matrix elements betweenstates with large K , as revealed through specific instances ofrandom mixing [5] that introduce collective components intothe wave functions. These are distinct from situations wheresequential K-mixing occurs from known Coriolis effects astreated here.The authors thank R. B. Turkentine for producing thetarget and the staff of the ATLAS accelerator facility for theirassistance in various phases of the experiment. 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Lifetime of the Kπ=8- isomer in the neutron-rich nucleus Er174, and N=106 E1 systematics

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Lifetime of the Kπ=8- isomer in the neutron-rich nucleus Er174, and N=106 E1 systematics

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