A number of single step linking transitions were observed in 152Dy. The first superdeformed (SD) band was linked to the normal yrats states and its spin, parity and excitation energy was established. An angular distribution analysis of the 4011 keV transition was performed to determine the spin of the 11893 keV SD level. The excitation energy of the lowest SD band member was 10644 keV and its spin and parity was determined to be 24+

Abu Saleem, K.S.

Ahmad, I.

Carpenter, M.P.

Clark, R.

Cromaz, M.

Fallon, P.

Greene, J.P.

Hannachi, F.

Heinz, A.M.

Herskind, B.

Janssens, R.V.F.

Jenkins, D.G.

Khoo, T.L.

Kondev, F.G.

Korichi, A.

Lane, G.

Lauritsen, T.

Lister, C.J.

Lopez-Martens, A.

Macchiavelli, A.O.

Reiter, P.

Seweryniak, D.

Siem, S.

Vondrasek, R.C.

Ward, D.

Wiedenhãver, I.

Carolina Digital Repository

VOLUME 88, NUMBER 4 P H Y S I C A L R E V I E W L E T T E R S 28 JANUARY 20020Direct Decay from the Superdeformed Band to the Yrast Line in 15266Dy86T. Lauritsen,1 M. P. Carpenter,1 T. Døssing,2 P. Fallon,3 B. Herskind,2 R. V. F. Janssens,1 D. G. Jenkins,1 T. L. Khoo,1F. G. Kondev,1 A. Lopez-Martens,4 A. O. Macchiavelli,3 D. Ward,3 K. S. Abu Saleem,1 I. Ahmad,1 R. Clark,3M. Cromaz,3 J. P. Greene,1 F. Hannachi,4 A. M. Heinz,1 A. Korichi,4 G. Lane,3 C. J. Lister,1 P. Reiter,1,5D. Seweryniak,1 S. Siem,1 R. C. Vondrasek,1 and I. Wiedenhöver1,61Argonne National Laboratory, Argonne, Illinois 604392Niels Bohr Institute, DK-2100 Copenhagen, Denmark3Lawrence Berkeley National Laboratory, Berkeley, California 947204C.S.N.S.M, IN2P3-CNRS, bat 104-108, F-91405 Orsay Campus, France5Ludwig-Maximilians-Universität, Munich, Germany6NSCL, Michigan State University, East Lansing, Michigan 48824(Received 17 August 2001; published 8 January 2002)The excitation energy, spin, and parity of the yrast superdeformed band in 152Dy have been firmlyestablished. The evidence comes mainly from the measured properties of a 4011 keV single-step tran-sition connecting the yrast superdeformed level fed by the 693 keV transition to the 272 yrast state.Four additional, weaker, linking g rays have been placed as well. The excitation energy of the lowestsuperdeformed band member is 10 644 keV and its spin and parity are determined to be 241.DOI: 10.1103/PhysRevLett.88.042501 PACS numbers: 23.20.Lv, 21.10.Re, 23.20.En, 27.70.+qThe first superdeformed (SD) band was observed in1986 in the nucleus 152Dy [1]. A sequence of nineteen al-most equally spaced g rays revealed the presence of a SDnucleus with an axis ratio of nearly 2:1. Since then, 175SD bands have been found in the A  150 and A  190SD mass regions. However, the energy, spin, and parityof only a handful of these SD bands have been establishedfrom discrete transitions which connect SD and normalyrast states in one step. The first such single-step linkingtransitions were found in 194Hg [2], and linking transitionswere reported in 194Pb shortly thereafter [3,4]. Since then,very few links have been found [5,6] and there has beenonly one report of weak two-step decays in the A  150mass region [7]. Several attempts have been made tosearch for the single-step decays out of the yrast SD bandin 152Dy [8]. Obviously, even with modern g-ray detectorarrays such as Gammasphere [9] and Euroball [10], it isvery difficult to find the weak, single-step transitions thatallow for an unambiguous determination of the spin, par-ity, and excitation energy of SD bands. It is necessary todetermine some or all of those quantities for as many SDbands as possible in order to address such issues as (i) themagnitude of shell corrections at large deformation, (ii) theparticle configuration of the bands, (iii) the origin of iden-tical SD bands [11], and (iv) the mechanisms responsiblefor the sudden decay-out of the SD bands. A number ofnew SD nuclei have been found in the A  60, 40, 80, and130 [12–15] mass regions, where it has proven easier toconnect the SD bands to normally deformed states becausethe lower level densities result in predominantly discretedecay-out lines. However, in the A  190 and A  150SD mass regions, the decay is dominated by quasicontin-uum g rays and sharp lines are very weak [16].42501-1 0031-90070288(4)042501(4)$20.00The first experimental evidence for a 4011 keV linkingtransition in 152Dy, as well as hints of others, was foundin a Gammasphere experiment performed at ArgonneNational Laboratory. The SD band in 152Dy was populatedwith the nearly symmetric reaction 76Ge80Se, 4n152Dy.Beams were delivered by the ATLAS accelerator atan energy of 311 MeV (at midtarget). Data were col-lected for 4.5 days. Because of the low intensities ofthe observed linking transitions, another much longerexperiment (12 days) was performed with Gammasphereat Lawrence Berkeley National Laboratory. This timethe 152Dy SD band was populated with the reaction108Pd48Ca, 4n152Dy. Beams were delivered by the88 inch cyclotron at an energy of 191 MeV (at midtar-get). The target consisted of a stack of two 0.4 mgcm2self-supporting 108Pd foils. Gammasphere contained100 Compton suppressed germanium detectors.The 152Dy yrast SD band is known to decay almostentirely through an 86 ns isomer [8]. This feature was ex-ploited for clean channel selection by tagging on isomers,which were emitted from residues caught on a 28 mgcm2Pb stopper foil, 35 cm downstream from the target,among the forward bismuth germanate (BGO) Comptonshield detectors. The efficiency for isomer detection in152Dy was measured to be 80%. The energy and timesignals of the forward ring of BGO detectors were writtenon tape only if the event satisfied a high-multiplicity(M $ 5) condition. A total of 4.6 3 109 (after prompttime requirements) triple-or higher-fold coincidenceevents were collected. With the requirement of delayedg rays in the forward BGO detectors (between 12.5 and185 ns after the reaction), 1.6 3 109 events remainedwhich were almost exclusively from 152Dy.© 2002 The American Physical Society 042501-1VOLUME 88, NUMBER 4 P H Y S I C A L R E V I E W L E T T E R S 28 JANUARY 2002Figure 1a shows the spectrum obtained by placing pair-wise coincidence gates on transitions in the yrast SD bandin 152Dy. At higher g-ray energies, shown in Fig. 2a, sev-eral candidates for decay-out transitions are clearly seen.In particular, g rays at 2713 and 4011 keV are prominentwhile a number of other, weaker, candidates are visible aswell. No transitions above 4011 keV are observed.The coincidence spectrum obtained by placing pairwisegates on SD lines and on the 4011 keV transition is pre-sented in Fig. 1b. It is clearly seen that the 647 and 602 SDlines (see Fig. 3) are not in coincidence with the 4011 keVg ray, whereas the 693 keV and higher SD lines are. Thisunambiguously establishes that the 4011 keV transitionoriginates from the SD level fed by the 693 keV line. Ofthe normal yrast transitions in the spectrum [17], the 221and 541 keV g rays have the full intensity of the SD band[0.8(3) and 0.9(2), respectively], whereas there is no in-dication of the normal 967 keV transition [the intensity is0.3(3)], which should be detectable despite the proximityof the 970 keV SD g ray. A comparison with the spec-trum in Fig. 1a shows no new peaks with an area largerthan three standard deviations. This strongly suggests thatthe 4011 keV g ray feeds directly into the 272 yrast statein a single step. This establishes the excitation energy ofthe SD level fed by the 693 SD line as 11 893 keV— asshown in the partial level scheme of Fig. 3.To determine the spin of the 11 893 keV SD level, anangular distribution analysis of the 4011 keV transitionwas performed. The intensity of this g ray, as a functionof polar angle, is presented in Fig. 2b. Using the func-tional form W u  A01 1 A2P2cosu 1 A4P4cosu[18], the angular distribution coefficients were determined200 400 600 800 1000 1200Energy [keV]060120180Counts/1.33 keV0100000200000784829221254262 541525602647693738876923 97010171065 [a][b]FIG. 1. (a) Spectrum from pairwise coincidence gates in theyrast SD band of 152Dy. The 94 cleanest combinations of thefollowing SD transitions were used: 647, 693, 738, 784, 829,876, 923, 1017, 1065, 1161, 1209, 1257, 1305, 1353, 1402, and1449 keV. (b) Spectrum obtained from setting pairwise gateson a SD line and the 4011 keV transition. All SD transitionslisted above (except that of 647 keV) were used as gates.042501-2to be A2  20.3512 and A4  20.0216—consistentonly with a stretched or antistretched dipole character [18].Thus, based on the 4011 keV transition, the feeding SDlevel must have a spin of either 26h̄ or 28h̄.Based on Weisskopf estimates [19], transitions of E1character are expected to be nearly 2 orders of magnitudefaster than those with M1 multipolarity. In neutron captureexperiments, indeed, the E1 transitions have been shownto dominate [20]. Therefore, it is most likely that the4011 keV transition is of E1 character and, thus, a positiveparity is assigned to the SD band. This assignment is alsosupported by theoretical expectations [21].With the energy of the SD band determined by the4011 keV line, four additional g rays in the 3 MeV re-gion of Fig. 2 can be placed in the level scheme as directlinks between the SD band and the normal states. Theyare included in Fig. 3. All four of these additional linksare very weak and, thus, it is difficult to place coincidencegates on them. However, in a spectrum of pairwise gatesplaced on the 693 keV line and on clean SD transitionsabove it, the 2895, 3044, 3364, and 3585 keV g rays areclearly present, whereas a similar spectrum with a gateon the 647 keV line shows only the two transitions withthe highest energies, i.e., the 2895 and 3044 keV g raysare absent. Thus, the latter two transitions emanate fromthe 11 893 keV SD level, and the two others are associ-ated with the deexcitation of the SD state directly belowit at 11 246 keV. These weaker one-step linking transi-tions also resolve any remaining ambiguity concerning thespins of the SD band members. Only when 281 is as-signed to the 11 893 SD level are the multipolarities of the2895 and 3364 keV lines reasonable: M1 and E1, respec-tively. A 261 assignment would result in respective M3and E3 multipolarities which are improbable, if only be-cause of the competition with the in-band, highly collective602 keV g ray. Finally, for the strong 2713 keV transitionmentioned above, it was possible to determine that it also2600 2900 3200 3500 3800 4100Energy [keV]0500100015002000Counts/4keV0 50 100 1500202964304729462895271331654011Counts[a]3364Angle[b]358530653185FIG. 2. (a) High-energy portion of the spectrum in coinci-dence with 152Dy SD transitions. (b) Angular distribution ofthe 4011 keV transition.042501-2VOLUME 88, NUMBER 4 P H Y S I C A L R E V I E W L E T T E R S 28 JANUARY 2002FIG. 3. Partial level scheme of 152Dy showing the lowest partof the yrast SD band and normal states to which the SD bandmainly decays. The transition intensities, given in %, reflect therequirement of the isomer tag.originates from the 11 893 keV SD level. However, in thiscase the decay could not be traced all the way into the yrastor near yrast states, as the deexcitation fragments after thefirst transition into several paths involving g rays with in-tensities below the detection threshold.It is worth pointing out that the SD band spin val-ues firmly assigned here are two units higher than thoseproposed by Twin et al. [1] following the discovery ofthe band. Several systematic theoretical investigations ofall SD bands in the A  140 150 region are also avail-able. For 152Dy, cranked Nilsson-Strutinsky calculationsby Ragnarsson [22], and relativistic mean field calculationsby Afanasjev et al. [23] suggested spins of either 28h̄ or30h̄ for the 11 893-keV level, while the cranking calcula-tions with a Woods-Saxon potential of Dudek et al. [24]propose a spin of 26h̄.A solid understanding of superdeformed rotational mo-tion requires data on both the kinematic and dynamic mo-ments of inertia (1, 2), which reflect the first and thesecond derivatives of the energy as a function of spin. Inthe mass 150 region, 1 values have not been availablesince spins have not been firmly established. With thespins now assigned in 152Dy, 1 can be determined: Itvaries from 84.8h̄ to 85.7h̄2 MeV21 between spin 24h̄ and042501-338h̄ before decreasing smoothly back to 84.8h̄2 MeV21 atthe highest spin of 68h̄. Results of calculations withoutpairing [25] are higher by 7%–5%, suggesting some per-sistence of pairing at the lower spins. The inclusion ofpairing improves the agreement (see, e.g., [24,26,27]), buta simultaneous reproduction of 1 and 2 still has notbeen achieved.Extrapolated to zero spin, the excitation energy of theSD band is ESD01  7.5 MeV. The extrapolation wasperformed with a functional form of the excitation energywritten as ESDI  ESD01 1 aII 1 1 1 bII 112, where ESDI is the energy of the SD level at spinI. This procedure is less accurate here than in the A 190 mass region because the spin of the lowest observedSD level is 24h̄ rather than 10h̄. The extrapolated zerospin energy is slightly higher than the values found in192,194Hg: 5.3(5) and 6.0 MeV [2,16]. For 152Dy, a rela-tivistic mean field prediction of the excitation energy is8.32 MeV [28], while the cranked Strutinsky calculation of[21] obtains a value of 8.8 MeV. A recent Hartree-Fock-Bogoliubov calculation estimates the excitation energy tobe 7 MeV [29].The 4011 keV one-step decay line carries only 0.9(2)%of the intensity of the SD band. The quadrupole moment ofthe SD band in 152Dy, 17.52 e b [30], gives a partial life-time of the 647 keV in-band transition of 66 fs and a partiallifetime of the 4011 keV transition of 2.9 ps, equivalent toa strength in Weisskopf units (W.u.) of 2 3 1026. Justas in the A  190 mass region [2], the decay-out transitionis very retarded. This retardation can be understood [2] interms of the decay mechanism out of the SD state firstproposed by Vigezzi et al. [31]. In their interpretation, theSD level mixes with one (or a few) of the adjacent closelyspaced levels in the normal well, on the other side of theSD barrier, and the decay occurs through the admixed com-ponent of the normal state in the wave function.The model of Vigezzi et al. [31,32] was used to fit theSD transition intensities (i.e., decay-out profiles) in 152Dyand 194Hg, where the SD excitation energies are known.In this model, the probability for decay of a SD stateto the normal well depends on the gamma decay widthsGs and Gn, the average separation Dn between excitednormal-deformed states, and the width G for tunnelingacross the barrier. Gs, the decay width within a SD band,is obtained from the measured transition quadrupole mo-ments; Gn, the E1 width for statistical decay from anexcited ND state, and Dn are estimated by scaling [33]values obtained from neutron spectroscopy [34]. Val-ues of the one free parameter G, which reproduce themeasured SD transition intensities, are given in Table I.In both 152Dy and 194Hg, the SD transition intensitiesdrop suddenly at the point of decay. This feature is re-produced by having G increase rapidly as the spin be-comes smaller. The barrier heights Eb , which are deducedfrom G using expressions given in Refs. [31,32], show acorresponding decrease with spin (Table I). Alternative042501-3VOLUME 88, NUMBER 4 P H Y S I C A L R E V I E W L E T T E R S 28 JANUARY 2002TABLE I. Tunneling widths G and barrier heights Eb , ex-tracted using the model of Vigezzi et al. [31,32], for two SDlevels in 152Dy and 194Hg. The decay-out probabilities Pout, aswell as the g widths (Gs, Gn) and normal-deformed level spac-ing Dn , are given.I Gs Gn Dn G Ebh̄ Pout (meV) (meV) (eV) (eV) (MeV)152Dy 28 0.40 10.0 17 220 41 0.7426 0.81 7.0 17 194 220 0.58194Hg 12 0.40 0.108 21 344 0.56 1.1510 0.97 0.046 20 493 37 0.75formalisms for calculating the decay out of SD bands haverecently been published [35,36]. For cases encountered inexperiments, their results agree with those obtained withthe model of Vigezzi et al. [31,32,37]. Indeed, G valuessimilar to those in Table I are obtained with the empiricalexpression given in Ref. [35]. A good approximation ofthe decay-out probability from the SD band is given byPout pp2GnGs GDn [31,35]. At the point of de-cay, Table I shows that, compared to 194Hg, 152Dy has asmaller value of GnGs (due to the larger SD transition en-ergies). Consequently, GDn, which is a measure of thecoupling between SD and ND states, is significantly larger(0.3 vs 0.002 when Pout  0.5), indicating a stronger cou-pling in 152Dy, although the coupling is still weak.In summary, a number of single-step linking transitionshave been observed in 152Dy. Fifteen years after its dis-covery, the first superdeformed band is finally linked to thenormal yrast states, and its spin, parity, and excitation en-ergy have been firmly established.Valuable suggestions by and discussions withK. Hauschild and A. V. Afanasjev are appreciated.This work was supported in part by the U.S. Departmentof Energy, under Contracts No. W-31-109-ENG-38 andNo. DE-AC03-76SF00098, and the Danish Natural Sci-ence Foundation.[1] P. J. 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Direct decay from the superdeformed band to the yrast line in 66152Dy86

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Direct decay from the superdeformed band to the yrast line in 66152Dy86

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