Lifetimes of prolate intruder states in 186Pb and oblate intruder states in 194Po have been determined by employing, for the first time, the recoil-decay tagging technique in recoil distance Doppler-shift lifetime measurements. In addition, lifetime measurements of prolate states in 188Pb up to the 8+ state were carried out using the recoil-gating method. The B(E2) values have been deduced from which deformation parameters |β2|=0.29(5) and |β2|=0.17(3) for the prolate and the oblate bands, respectively, have been extracted. The results also shed new light on the mixing between different shapes

Beausang, C

Christen, S

Darby, I G

Dewald, A

Eeckhaudt, S

Gorgen, A

Grahn, T

Greenlees, P

Helariutta, K

Jolie, J

Jones, Peter G

Julin, Rauno Juhani

Juutinen, S

Kettunen, H

Kroll, T

Krucken, R

Le Coz, Y

Leino, M

Leppanen, A.P

Meierbeck, P

Melon, B

Meyer, D A

Moeller, O

Nieminen, Paivi

Nyman, M

Page, R.D

Pakarinen, J

Petkov, P

Rahkila, P

Saha, B

Sandzelius, M

Saren, J

Scholey, C

Uusitalo, J

Physical Review Letters

The Australian National University

Collectivity and Configuration Mixing in 186;188Pb and 194PoT. Grahn,1,* A. Dewald,2 O. Möller,2 R. Julin,1 C. W. Beausang,3,† S. Christen,2 I. G. Darby,1,4 S. Eeckhaudt,1P. T. Greenlees,1 A. Görgen,5 K. Helariutta,6 J. Jolie,2 P. Jones,1 S. Juutinen,1 H. Kettunen,1 T. Kröll,7 R. Krücken,7Y. Le Coz,5 M. Leino,1 A.-P. Leppänen,1,‡ P. Maierbeck,7 D. A. Meyer,3 B. Melon,2 P. Nieminen,1,x M. Nyman,1R. D. Page,4 J. Pakarinen,1,4 P. Petkov,8 P. Rahkila,1 B. Saha,2 M. Sandzelius,1,k J. Sarén,1 C. Scholey,1 and J. Uusitalo11Department of Physics, University of Jyväskylä, P. O. Box 35, FI-40014 Jyväskylä, Finland2Institut für Kernphysik, Universität zu Köln, Zülpicher Straße 77, 50937 Köln, Germany3Wright Nuclear Structure Laboratory, Yale University, New Haven, Connecticut 06520, USA4Department of Physics, Oliver Lodge Laboratory, University of Liverpool, Liverpool L69 7ZE, United Kingdom5CEA-SACLAY, DSM/DAPNIA/SPhN, F-91191 Gif-sur-Yvette Cedex, France6Laboratory of Radiochemistry, University of Helsinki, P. O. Box 55, FI-00014 Helsinki, Finland7Physik-Department E12, TU München, 85748 Garching, Germany8Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria(Received 28 March 2006; published 7 August 2006)Lifetimes of prolate intruder states in 186Pb and oblate intruder states in 194Po have been determined byemploying, for the first time, the recoil-decay tagging technique in recoil distance Doppler-shift lifetimemeasurements. In addition, lifetime measurements of prolate states in 188Pb up to the 8 state were carriedout using the recoil-gating method. The BE2 values have been deduced from which deformationparameters j2j  0:295 and j2j  0:173 for the prolate and the oblate bands, respectively, havebeen extracted. The results also shed new light on the mixing between different shapes.DOI: 10.1103/PhysRevLett.97.062501 PACS numbers: 21.10.Tg, 23.20.Lv, 27.70.+q, 27.80.+wIn mesoscopic systems such as atomic clusters andnuclei, the coexistence of states having almost degenerateenergies but different shapes is a topic of strong currentinterest. The investigation of the origin of the shape coex-istence [1] observed in the vicinity of Z  82 nuclei closeto the proton dripline is one of the central current chal-lenges, experimentally as well as theoretically. In the neu-tron midshell nucleus 186Pb, the first two excited statesabove the spherical ground state are assigned as 0 states.In the shell model approach these states can be associatedwith intruder 2p 2h and 4p 4h excitationsacross the Z  82 gap [2]. This picture is supported byhindrance factors derived from the  decays feeding thesestates [3]. These excitations of small numbers of particlesover the shell gap lead to changes in the nuclear shape. Incalculations based on the deformed mean field they appearas oblate and prolate minima intruding down close to theground state when approaching the neutron midshell [4,5].Configuration mixing calculations of angular-momentumprojected mean-field states using the Gogny [6] andSkyrme [7] interactions find prolate yrast rotational bandsand excited oblate bands for 182–186Pb and a complex shapecoexistence with mixed states for 188Pb. Experimentallythe yrast bands in 182–188Pb have been interpreted as beingbased on prolate shapes [8–11]. Recently, candidates forcollective nonyrast bands built on the coexisting oblateminimum have been observed in 186Pb and 188Pb [12,13].The extension of spectroscopic studies to Z  84 hasrevealed even further behavior of similar intruder struc-tures in the neutron-deficient Po isotopes. When approach-ing the neutron midshell aroundN  104, states associatedwith oblate deformed 4p 2h configurations cross theyrast line of nearly spherical states and reach the groundstate in 192Po [14,15]. Furthermore, a sudden change to anyrast band similar to the prolate bands in 182–188Pb isobserved in 190Po [16]. This picture is supported by earlierNilsson-Strutinsky calculations [4].Calculations based on the mean field predict that thedeformation associated with the prolate shape of midshellPb and Po nuclei is larger than that for the oblate shape.Experimentally, the degree of deformation is in many casesdeduced from moments of inertia, which are in generallarger for prolate than oblate bands. However, when thelevel lifetimes are known, the absolute transition probabil-ities provide a more direct measure of collectivity andallow fundamental questions such as the degree of mixingof shapes as a function of spin to be addressed. In addi-tion to predictions of various theoretical calculations[6,7,17,18], simple mixing calculations based on experi-mental data have been carried out for Pb and Po nuclei nearthe neutron midshell [13,19,20]. To verify these resultsmeasurements of level lifetimes are needed.Nuclei around 186Pb can be produced in heavy-ion in-duced fusion-evaporation reactions, thus rendering it pos-sible to use the recoil distance Doppler-shift (RDDS)method in lifetime measurements. However, due to thevery low production cross section of these nuclei, in-beam detection of the  rays of interest requires highselectivity. In the present work such selectivity has beenachieved by employing the recoil-decay tagging (RDT)technique [21] for the first time in RDDS lifetime mea-surements. In this Letter, the results from lifetime mea-PRL 97, 062501 (2006) P H Y S I C A L R E V I E W L E T T E R Sweek ending11 AUGUST 20060031-9007=06=97(6)=062501(4) 062501-1 © 2006 The American Physical Societysurements of prolate yrast states up to I  8 in 186Pband oblate yrast states up to I  4 in 194Po are pre-sented. Additionally, lifetime information in 188Pb wasobtained up to the 8 yrast state by using the recoil-gatingmethod. This measurement significantly improves on theresults of an earlier RDDS measurement at ArgonneNational Laboratory [19], where lifetimes of the first 2and 4 states in 188Pb were determined.In the present RDDS experiments the Köln plungerdevice has been combined with the JUROGAM Ge detec-tor array and the RITU gas-filled separator [22] of theAccelerator Laboratory at the University of Jyväskylä. Inthe plunger device the usual stopper foil was replaced by adegrader foil allowing fusion-evaporation residues to recoilinto RITU and thus to be separated from other reactionproducts. Experimental details are listed in Table I. FifteenJUROGAM Ge detectors were used for -ray detection.Separation between the fully shifted and degraded compo-nents of the peaks in the final -ray spectra ranged from1.6 keV (320 keV 2 ! 0 transition in 194Po, measuredat 134) to 6.8 keV (724 keV 2 ! 0 transition in 188Pb,measured at 158). The beam intensity was limited to 1–3 pnA by the Ge detector counting rates.The separated recoils were detected at the RITU focalplane by the GREAT spectrometer [23]. Temporal andspatial correlations of a recoil and its subsequent radioac-tive decay in the double-sided silicon strip detectors ofGREAT were performed and singles in-beam RDT andrecoil-gated -ray spectra were constructed.In the RDDS measurement of 186Pb, RDT -ray spectratagged with the 186Pb  decay (t1=2  4:8 s, E 6:38 MeV) were collected at 11 different target-to-degrader distances ranging from 10 m to 1600 m. Inthe corresponding measurement for the  emitter 194Po(t1=2  390 ms, E  6:99 MeV), 13 distances rangingfrom 5 m to 3000 m were used. For 188Pb, recoil-gatedsingles -ray spectra were collected at 10 target-to-degrader distances from 10 m to 600 m. Sample-ray spectra are shown in Fig. 1. It is essential to notethat in spite of the low number of events in the 186Pb and194Po spectra compared to those for 188Pb, the much lowerbackground still enables resolution of the peaks of interest.The spectra of the two JUROGAM Ge detector ringswere both separately analyzed by means of the differentialdecay curve method (DDCM) [24]. Intensities of the fullyshifted components of the transitions under investigation,recorded at different target-to-degrader distances, werenormalized to the sum of the areas of the fully shiftedand degraded components. The resulting lifetime of eachlevel is an average of the lifetimes extracted from the decaycurves measured by the detector rings at 158 and 134.Sample decay curves are illustrated in Fig. 2.Lifetimes of the four lowest yrast states in 186Pb and188Pb, and the two lowest yrast states in 194Po were ex-tracted (Table II). The time behavior of the unobservedfeeding was assumed to be similar to that of the observedfeeding, which has been experimentally tested and found tobe realistic in several cases [see, e.g., [25,26] ]. The ex-ception is in 188Pb where ambiguities arise due to therelatively slow feeding of the 2 state from the yrast 4TABLE I. Experimental details. In order to maximize the transmission of RITU, several types of degrader foils were used in the186Pb measurement.Reaction Ebeam [MeV]  v=c Target thickness [mg=cm2] Degrader(s) [mg=cm2] Tagging mode106Pd83Kr; 3n186Pb 357  280 b 3.8% 1.0 Au: 2.6, 2.2 RDTAl: 1.0, Mg: 1.0106Pd83Kr; 3n188Pb 340  1:1 mb 3.8% 0.95 Au: 2.5 Recoil gating114Cd83Kr; 3n194Po 375  120 b 3.6% 1:0 1:0 Ta support Mg: 1.0 RDT01020194Po 13 µm300 310 320 330 340 350 360 370 380 390Energy [keV]01020Counts [arbitrary units]700 µm2+→ 0+4+→ 2+0204025 µm240 260 280 300 320 340 360 380 400 420 44002040660 680 700 7201600 µm050100150Counts [arbitrary units]50 µm240 260 280 300 320 340 360 380 400 420 440050100150660 680 700 720186Pb188Pb200 µm2+→ 0+8+→ 6+6+→ 4+4+→ 2+4+→ 2+6+→ 4+8+→ 6+2+→ 0+FIG. 1. Singles RDT -ray spectra of 186Pb (two upper panels)and 194Po (two lower panels) as well as recoil-gated singles-ray spectra of 188Pb (two panels in the middle) measured attwo target-to-degrader distances with five JUROGAM detectorsat 158. Lines indicate the positions of the fully Doppler-shifted(dashed line) and degraded (dotted line) components of the yrasttransitions presented in Table II. The relevant peaks are shadedto guide the eye.PRL 97, 062501 (2006) P H Y S I C A L R E V I E W L E T T E R Sweek ending11 AUGUST 2006062501-2state. The resulting value for the lifetime of the 2 statevaries between 5 ps and 12 ps corresponding to lifetimes ofunobserved feeding of 16 ps and 0.1 ps, respectively. Themeasured lifetime of 15.9(10) ps for the 4 state in 188Pb isin agreement with the value of 16(8) ps obtained inRef. [19]. In the same reference the value of 13(7) ps forthe 2 state in 188Pb obtained from the coincidence mea-surement would slightly favor the upper limit of 12 psdetermined in the present work. Table II gives values forthe transition quadrupole moment jQtj extracted from theexperimental BE2 values under the assumption of arotating quadrupole-deformed nucleus [27]. The jQtj val-ues of Table II are plotted in Fig. 3.In the framework of coexistence of spherical, oblate, andprolate shapes, interesting conclusions from the presentresults can be drawn. The weak transition strength reflectsthe low collectivity of the 2 ! 0 transition supportingthe concept of the unmixed spherical ground state of 186Pband 188Pb. If the picture of the prolate yrast band in 186Pband 188Pb is accepted, the observed high collectivity of the4 ! 2 yrast transition indicates a large prolate compo-nent in the 2 states. In 186Pb this transition has a BE2value approximately 3 times larger than that in 188Pb,resulting in a jQtj value as high as those for the transitionsbetween the yrast 4, 6, and 8 states, assumed to be pureprolate states in both of these nuclei. This shows that the2 state in 186Pb is a pure member of the prolate band,while for the yrast 2 state in 188Pb, a prolate contributionof 40% can be derived from the present results in a simpletwo-band mixing calculation as formulated in Ref. [13].This result supports the calculations in Refs. [6,7,17]where a strong admixture of the prolate and oblate struc-tures for the 2 state in 188Pb is deduced.The jQtj values extracted for the 8 ! 6 transitions in186Pb and 188Pb seem to indicate a drop of collectivity.However, taking into account the error bars the collectivitymay well stay at the level of that for the 6 ! 4 tran-sitions as expected on the basis of the smooth behavior ofthe moments of inertia. By using the average jQtj value ofthe transitions between the pure prolate 2, 4, 6, and 8states in 186Pb and 4, 6, and 8 states in 188Pb, aquadrupole deformation parameter j2j  0:295 forboth of these nuclei can be extracted [see Ref. [19] forformulation]. This value is in agreement with the theoreti-cal values obtained from different approaches [5,7,28,29].For 194Po the present results reveal that the collectivityof the 2 ! 0 and 4 ! 2 transitions is much lowerthan that of the transitions between the prolate states in186Pb and 188Pb. In earlier mixing calculations based on themeasured level energies [20] and -decay hindrance fac-tors [14], the yrast 2 and 4 states in 194Po are interpretedas pure 4p 2h oblate states, while the oblate compo-nent in the ground state is predicted to be around 50%. Thesimilar jQtj values for the 2 ! 0 and 4 ! 2 transi-tions from the present results indicate that the oblatecomponent in the ground state could be much larger,2 4 6 8Ii024681012|Qt|[eb]186Pb104188Pb106194Po110FIG. 3. Transition quadrupole moments jQtj extracted fromthe present work for yrast levels in 186Pb, 188Pb, and 194Po.ddsµ2      0+ +6      4+ + 4      2+ +8      6+ +++++++++I  /(I   + I  )target−to−degrader distance [   m] 0 0.2 0.4 0.6 0.8 1 1.2 0  100  200  300  400  500  600  700  8008      6 6      4 4      2 2      0 FIG. 2. Decay curves of yrast transitions in 186Pb measuredwith ten JUROGAM detectors at 134. The smooth lines aredrawn to guide the eye.TABLE II. Electromagnetic properties of the low-lying yraststates in 186;188Pb and 194Po.E [keV]a Ii  [ps] BE2 [W.u.] jQtj [eb]186Pb 662 2 18(5) 6(2) 1.3(2)261 4 18(4) 510(120) 10.3(10)337 6 6(2) 460(160) 10(2)415 8 5(2) 200(140) 6(2)188Pb 724 2 5–12 12–5 2.0–1.3340 4 15.9(10) 160(10) 6.0(2)370 6 4.0(6) 440(70) 9.4(7)434 8 2.4(4) 350(60) 8.2(7)194Po 320 2 37(7) 90(20) 5.5(6)367 4 14(4) 120(40) 5.4(8)aTaken from Refs. [12,13,20].PRL 97, 062501 (2006) P H Y S I C A L R E V I E W L E T T E R Sweek ending11 AUGUST 2006062501-3although the near-spherical shape mixed with the oblateone in the even-mass Po isotopes is not expected to repre-sent such a well-defined energy minimum as the groundstates of the even-mass Pb isotopes. From the average ofthe jQtj values for the 2 ! 0 and 4 ! 2 transitions, adeformation parameter j2j  0:173 for 194Po is ob-tained. This is consistent with the value of j2j  0:2 inthe theoretical predictions [4,18].Prolate yrast bands with moments of inertia very similarto the prolate bands of 186Pb and 188Pb have been observedin even-mass Hg and Pt nuclei near the N  104 midshell.Lifetime measurements of yrast levels have been carriedout for 184Hg [30], 186Hg [31], and 184Pt [32]. The resultingj2j values extracted for the assumed prolate states in184;186Hg (j2j  0:27) and in 184Pt (j2j  0:23) mayindicate decreasing collectivity with decreasing protonnumber. The ground state and the lowest 2 state in184;186Hg are assumed to represent a weakly deformedoblate shape. The extracted j2j  0:14 for those statesmight reflect the weaker collectivity of the 0p 2hconfiguration compared to the4p 2h configuration in194Po.In summary, the lifetimes of low-lying yrast states in186;188Pb and 194Pb have been measured in order to estab-lish the collectivity of the bands and to extract the value ofj2j for both prolate and oblate shapes in the neutron-deficient Pb region. As these pioneering RDDS experi-ments have demonstrated, the RDT technique providesessentially background-free -ray spectra for lifetime stud-ies and enables the extension of the RDDS measurementsto exotic nuclei near the proton dripline with relatively lowproduction cross section. For the 2 state in 188Pb the jQtjvalue indicates that mixing of two shapes plays a crucialrole while in 186Pb the present measurements reveal thatthe 2 state is a pure member of the prolate band. In 194Po,the oblate component could dominate the ground state. Inthe heavier Po isotopes, the deformed intruder states liehigher in energy and in order to elucidate the degree ofcollectivity in their low-lying yrast states, further lifetimemeasurements would be required.This work has been supported by the Academy ofFinland (the Finnish Centre of Excellence Programme,Project No. 44875), the EU-FP5 projects EXOTAG(No. HPRI-1999-CT-50017) and Access to ResearchInfrastructure (No. HPRI-CT-1999-00044), the BMBF(Germany) under Contract No. 06K167, EuropeanCommunity Marie Curie Fellowship and the U.S. DOEunder Grant No. DE-FG02-91ER-40609. The UK/France(EPSRC/IN2P3) Loan Pool and GAMMAPOOL networkare acknowledged for the EUROGAM detectors ofJUROGAM.*Corresponding author.Email address: tuomas.grahn@phys.jyu.fi†Present address: University of Richmond, VA, USA.‡Present address: STUK, Rovaniemi, Finland.xPresent address: Department of Nuclear Physics, ANU,Canberra, ACT 0200, Australia.kPresent address: Department of Physics, KTH, S-10691Stockholm, Sweden.[1] J. L. Wood et al., Phys. Rep. 215, 101 (1992).[2] C. De Coster, B. Decroix, and K. Heyde, Phys. Rev. C 61,067306 (2000).[3] A. N. Andreyev et al., Nature (London) 405, 430(2000).[4] F. R. May, V. V. Paskevich, and S. Frauendorf, Phys. Lett.68B, 113 (1977).[5] W. Nazarewicz, Phys. Lett. B 305, 195 (1993).[6] R. R. Rodrı́guez-Guzmán, J. L. Egido, and L. M. Robledo,Phys. Rev. C 69, 054319 (2004).[7] M. Bender, P. Bonche, T. Duguet, and P.-H. Heenen, Phys.Rev. C 69, 064303 (2004).[8] D. G. Jenkins et al., Phys. Rev. C 62, 021302(R)(2000).[9] J. F. C. Cocks et al., Eur. 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Collectivity and configuration mixing in 186,188Pb and 194Po

Collectivity and configuration mixing in 186,188Pb and 194Po

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