Rotational band with seven γ-ray transitions between states with spin 2ħ and 16ħ has been observed in the doubly magic, self-conjugate nucleus 4020Ca20. The measured transition quadrupole moment of 1.80+0.39−0.29eb indicates a superdeformed shape with a deformation β2 = 0.59+0.11−0.07. The features of this band are explained by cranked relativistic mean field calculations to arise from an 8-particle 8-hole excitation

Afanasjev, A.V.

Axelsson, A.

Baktash, C.

Carpenter, M.P.

Devlin, M.

Galindo-Uribarri, A.

Ideguchi, E.

Janssens, R.V.F.

LaFosse, D.R.

Lauritsen, T.

Lerma, F.

Lister, C.J.

Reiter, P.

Reviol, W.

Sarantites, D.G.

Seweryniak, D.

Ullrich, J.

Weiszflog, M.

Wilson, J.N.

Carolina Digital Repository

VOLUME 87, NUMBER 22 P H Y S I C A L R E V I E W L E T T E R S 26 NOVEMBER 200122Superdeformation in the Doubly Magic Nucleus 4020Ca20E. Ideguchi,1 D. G. Sarantites,1 W. Reviol,1 A. V. Afanasjev,2,3,4 M. Devlin, 1,* C. Baktash,5 R. V. F. Janssens,2D. Rudolph,6 A. Axelsson,7 M. P. Carpenter,2 A. Galindo-Uribarri,5 D. R. LaFosse,8 T. Lauritsen,2 F. Lerma,1C. J. Lister,2 P. Reiter,2 D. Seweryniak,2 M. Weiszflog,7 and J. N. Wilson,1,†1Chemistry Department, Washington University, St. Louis, Missouri 631302Physics Division, Argonne National Laboratory, Argonne, Illinois 604393Physics Department, University of Notre Dame, Indiana 46556-56704Laboratory of Radiation Physics, University of Latvia, LV2169, Miera str. 31, Latvia5Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee, 37831-63716Department of Physics, Lund University, S-22100 Lund, Sweden7The Svedberg Laboratory and Department of Radiation Science, Uppsala University, S-75121 Uppsala, Sweden8Department of Physics and Astronomy, SUNY-Stony Brook, New York 11794(Received 23 July 2001; published 8 November 2001)A rotational band with seven g-ray transitions between states with spin 2h̄ and 16h̄ has been observedin the doubly magic, self-conjugate nucleus 4020Ca20. The measured transition quadrupole moment of1.8010.3920.29eb indicates a superdeformed shape with a deformation b2  0.5910.1120.07. The features of thisband are explained by cranked relativistic mean field calculations to arise from an 8-particle 8-holeexcitation.DOI: 10.1103/PhysRevLett.87.222501 PACS numbers: 21.10.Tg, 21.10.Re, 23.20.Lv, 27.40.+zStudies of superdeformed (SD) rotational bands in nu-clei have been the focus of major experimental and theo-retical efforts in the past 15 years. The occurrence of thesebands is the manifestation of large shell gaps at a 2:1 axisratio of the deformed shape for specific particle numbers.Lately, the attention in this field has shifted somewhat fromthe “traditional” regions of superdeformation at mass num-bers 80, 150, and 190 to the lighter nuclei, where protonsand neutrons occupy similar orbitals. This trend was ini-tiated by the discovery of superdeformed and highly de-formed bands in nuclei near 56Ni [1].Some fascinating aspects of superdeformation in nucleiwith A , 80 are (i) the appearance of spherical and su-perdeformed magic numbers at similar particle numbers,which results in dramatic examples of shape coexistence,and (ii) the observation of intense discrete-energy linkingtransitions between the structures in the second (highlyor superdeformed) and the first (spherical or normal-deformed) potential well, including particle decays [1].This allows for firm spin and parity assignments for thesuperdeformed bands in most cases. Furthermore, an im-portant consideration for studying these nuclei is that theyare amenable to different theoretical treatments that in-clude shell model calculations within a large configurationspace [2], quantum Monte Carlo shell model descrip-tions [3], and a variety of mean field approaches [4,5].Therefore, these nuclei provide an ideal testing groundto compare and confront these complementary models.An interesting prospect for a new superdeformed is-land with similar features as those described above is theregion around 4020Ca20. In this nucleus several relativelylow-lying 01 states have been observed, which suggeststhe presence of coexisting shapes, as is the case near othershell closures. Indeed, large transition quadrupole mo-2501-1 0031-90070187(22)222501(4)$15.00ments for some of the low-spin states in 40Ca have beenreported [6], and discussed [7] as multiparticle-multiholedeformed excitations.Early calculations by Gerace and Green [8] explainedthe low-lying levels of 40Ca as a mixture of sphericalshell model and deformed states formed by raising par-ticles from the sd to the fp shell. The configurations ofthe first and second excited 01 states (012 and 013 ) weresuggested to be 4-particle 4-hole (4p-4h) and 8-particle8-hole (8p-8h) excitations, respectively. Recently, Zhenget al. [4] using a fixed configuration deformed Hartree-Fock calculation predicted for 40Ca an 8p-8h SD band withb2  0.599 starting at 7.08 MeV. If deformed shapes in-deed exist in 40Ca, one should observe rotational bandsbuilt on the excited 01 states [4,7].Although a superdeformed band was recently observedin 36Ar [9,10], experimental difficulties had so far ham-pered observation of the highest spin states in 40Ca. Inthis Letter, we report the first observation of a superde-formed band extending up to spin 161 in the doubly magicself-conjugate nucleus 4020Ca20.High-spin states in 40Ca were populated via the28Si20Ne, 2a40Ca reaction. A 20Ne beam of 84 MeVwas provided by the ATLAS accelerator at the ArgonneNational Laboratory. A thin 0.45 mgcm2 28Si targetevaporated on a 1.0 mgcm2 Ta foil was used. Afterpassing through the Ta foil, the effective beam energy was80 MeV. The GAMMASPHERE array [11], comprising 101Compton-suppressed Ge detectors, and the MICROBALL[12], a 4p array of 95 CsI(Tl) scintillation counters, wereused to detect g rays and charged particles, respectively.In this reaction the efficiencies of the MICROBALL forprotons and a particles were 68% and 51%, respectively.The charged particles were identified using pulse shape© 2001 The American Physical Society 222501-1VOLUME 87, NUMBER 22 P H Y S I C A L R E V I E W L E T T E R S 26 NOVEMBER 2001discrimination on the signals from the CsI(Tl) scintilla-tors. With a trigger condition of three or more Compton-suppressed Ge detectors firing in coincidence, a total of1.2 3 109 events were collected. From the number ofhits in the charged particle detectors, events were sortedinto an Eg 2 Eg coincidence matrix for each evaporationchannel. However, the channel selection is limited bythe efficiency of the MICROBALL and by the occasionalmisidentification of charged particle signals. The 2a gatedg 2 g matrix, therefore, contains contaminations from the2a1p 39K and 2a2p 38Ar channels. Their contribu-tions were subtracted to obtain a clean data set for 40Ca.Some of the high-spin structures in 40Ca have previouslybeen studied [13,14]up to spin 81 at 8.1 MeV. An inter-esting feature of the previous level schemes is the presenceof second 012 and third 013 states, which are indications ofshape coexistence [7]. In our work, the level scheme wasextended up to spin 161 at 22.1 MeV. Figure 1 shows apartial level scheme for 40Ca, where only positive paritystates are reported. An article reporting the complete levelscheme is forthcoming [15]. The cascades ending at thelevels of 5213 (013 ) , 3352 (012 ) , 8103 (81), and 6030(31) keV are labeled as bands 1, 2, 3, and 4, respectively.Attention is focused on band 1 with g-ray transitions be-Excitation Energy (MeV)02468101214161820220 0239054528066933101168812 1311713 151548 81035 73997 89379 1171011 1353710 110051214234141653116205816797667678898561012338121527114 1872513 1658115 19197141850116220644654425630033521418056893070521314 17700(10 ) 12594(12 ) 157502 52493 60304 6509137516531429203711701538358521201827277329021617254622974050341418802482293330444043 3454 32303563143291455332292004 29232178239826962639390523812374303138225630162921123466328731564491524978113431260 129513691698123440CaFIG. 1. Partial level scheme of 40Ca; the energy labels aregiven in keV, and the widths of the arrows are proportional tothe relative intensities of the g rays. Only the levels below thedashed line were known prior to this work.222501-2tween 914 and 3563 keV. These are highlighted in Fig. 2.Transitions above the 9856 keV level of the band are in co-incidence with the previously known transitions of 3905,1375, and 1653 keV and appear as strong peaks in thespectrum.Since band 1 is connected to the previously reported fastE2 41 ! 21 transition of 914 keV [BE2  100 W.u.,Qt  1.69eb] [7], and linked to the ground state by the5630 keV transition, it is assigned to be built on the 013level. In addition, the newly observed one- and two-steplinks () to members of band 2 ensure the placement ofthe individual transitions  in band 1.Spins of the observed excited levels are assigned on thebasis of angular distributions. The multipolarities of thein-band transitions of band 1 and band 2 are found to beconsistent with a stretched quadrupole character. The re-maining transitions also have a quadrupole character, ex-cept for the 2120, 2004, and 2037 keV transitions from the7399, 8937 (band 4), and 15 154 keV (band 3) levels, re-spectively, which are dipole in nature. Assuming that thequadrupole transitions correspond to an E2 multipolarity,the parity of the excited states is assigned as positive. Allstates for each spin in band 1 lie at higher excitation thanthose in band 2 (i.e., band 1 is not “yrast”).In order to determine the deformation of the bands 1and 2 in 40Ca, the residual Doppler shifts [16] of the g-rayenergies were measured. The procedure is described inRef. [17]. The average recoil velocity b is expressed asa fraction of the initial recoil velocity to obtain Ft bb0. In Fig. 3, the fractional Doppler shifts Ft areplotted as a function of the g-ray energies. The experi-mental Ft values are compared with the calculated val-ues based on the known stopping powers from SRIM-2000[18]. In this calculation the side feeding into each state isFIG. 2. A g-ray spectrum obtained by summing coincidencegates set on all members of band 1  starting from the 21up to the 161 state, except for the 1432 keV transition. The symbols indicate the transitions decaying from the band. Thepeaks marked by } are background peaks due to accidentaldoublets or identified single-escape peaks.222501-2VOLUME 87, NUMBER 22 P H Y S I C A L R E V I E W L E T T E R S 26 NOVEMBER 2001Q =1.80t+0.39-0.29 [eb]1.0 1.5 2.0 2.5 3.0 3.5 4.01.000.980.960.94Ca SD band40E [MeV] F()τ FIG. 3. Fractional Doppler shift Ft as a function of g-rayenergy. Data points for the SD band (filled circles) and othersingle-particle transitions with similar spins (open squares) areextracted from the residual Doppler shift of the g-ray energies(see text). The solid line represents Qt  1.80eb, and the dashedlines correspond to the quoted uncertainties.assumed to consist of a cascade of two transitions with thesame lifetime as the in-band transitions. The intensitiesof the side-feeding transitions were modeled to reproducethe observed intensity profile. The data are best fitted witha transition quadrupole moment Qt  1.8010.3920.29eb. Thededuced Qt value corresponds to a quadrupole deforma-tion of b2  0.5910.1120.07, assuming a rigid axially symmet-ric rotor. Thus band 1 is associated with a superdeformedshape. Using a similar procedure, the deformation of band2 was determined from the Qt  0.74 6 0.14eb to beb2  0.27.In the single-particle diagram shown in Fig. 4, inaddition to the spherical gap, two prolate and one oblatedeformed shell gaps are present at particle numberN  Z  20 with values of b2  0.6, 0.3, and 20.4,0.0 0.2 0.4 0.6-0.6 -0.4 -0.204321-1-2-3-4-5-6-7-8-9-10Protonsingle-particlelevels(MeV) [303]7/2[404]1/2[202]3/2[321]1/2[312]5/2[200]1/2[202]5/2[321]3/2[211]1/2[330]1/220 20221828202820FIG. 4. Woods-Saxon orbitals as a function of the deforma-tion, b2, for particle numbers near N  Z  20. The solidand dashed lines are for positive and negative parity orbitals,respectively. Here b4  0 was assumed. The dark shaded areasindicate the gaps responsible for the larger deformation of band1 and the smaller deformation of band 2 in 40Ca.222501-3respectively (shaded areas). The gap at b2  0.6 is mostlikely associated with the SD band 1. The lower de-formation gaps at b2  0.3 and b220.4 could be re-sponsible for band 2 and could lead to g softness of theshapes. Directly below the prolate Z  20 gap, anothergap is seen with “intermediate” deformation at N , Z  18(lighter shading). The deformed configuration associatedwith this gap has been assigned to the b2  0.46 6 0.03band in 36Ar [9,10].The pronounced large deformation observed in the ro-tational band built on the 013 state is consistent with themultiparticle-multihole nature of this state in the calcula-tions of Refs. [4,8](8p-8h excitation). In order to under-stand the configuration of the observed SD band, we haveperformed cranked relativistic mean field (CRMF) calcu-lations [19] without pairing employing the NL3 force [20]for the RMF Lagrangian. The results of these calculationsare shown in Fig. 5. The SD configuration assigned toband 1 is of the p34n34 type, where the superscripts givethe number of protons and neutrons occupying the N  3(f72) intruder orbital. That is, the proposed configura-tion is indeed an 8p-8h excitation. For this configurationthe g deformation is 210± and the Qt  2.0eb, in closeagreement with experiment.The calculations reproduce reasonably well the trendof the excitation energies as a function of spin and theJ 1 moment as a function of rotational frequency, v. For0 4 8 12 16 20Angular  momentum01234567E−0.06909 I(I+1) [MeV]π34ν34  (γ ∼ −10ο)  Qt ~ 2e b0.0 0.5 1.0 1.5 2.0 2.5Rotational  frequency  ω  [MeV]5791113Moments  of  inertia J(1, 2)  [MeV − 1 ]J(1)(exp.)J(2)(exp.)J(1)(th.)J(2)(th.)FIG. 5. Excitation energies (E) relative to a rigid rotor energy,ERLD  0.06909II 1 1, as a function of spin. The experi-mental data for band 1 in 40Ca are shown as unlinked large filledcircles, and the results of the CRMF calculations are shown bythe solid line. Since pairing is not included, the calculated ener-gies are normalized to the data at high spin. The inset shows theexperimental J 1 (filled circles) and J 2 (open circles) valuesas a function of the rotational frequency for band 1 in 40Ca con-nected by solid and dashed lines, respectively. The theoreticalJ 1 and J 2 values from the CRMF calculation are shown forcomparison as the solid and dashed smooth lines, respectively.222501-3VOLUME 87, NUMBER 22 P H Y S I C A L R E V I E W L E T T E R S 26 NOVEMBER 20010.0000.0050.0100.0150.0200.0250.030(1) /A5/3  [MeV-1]0.0 0.5 1.0 1.5 2.0ω [MeV]40Ca (SD)36ArFIG. 6. J 1 moments of inertia scaled by A53 as a functionof rotational frequency for 40Ca and 36Ar.v $ 1.5 MeV, where the alignments of the second pair off72 protons and neutrons take place (reflected in a largejump in the dynamic moment of inertia, J 2), the calcu-lated J 1 values are very close to experiment. This sug-gests that pairing is of minor importance in this frequencyrange. At lower frequencies (spins), the discrepancy be-tween experiment and calculation consistently points to theneed for some pairing. If the pairing would be taken intoaccount, it would lead to the decrease of J 1 at low v andto the lowering of the calculated E 2 ERLD curve at lowspin, bringing both calculated quantities in closer agree-ment with experiment.The CRMF calculations also give insight into the struc-ture of band 2. This was suggested to correspond to a4p-4h triaxial band [21]. According to the present calcula-tions it is a p32n32 structure (4p-4h configuration), whichwill be discussed in detail elsewhere [15]. The presenceof many interband transitions between the SD band 1 andband 2 may indicate an overlap in the wave functions forthe low and medium spins. Configuration mixing betweenbands 1 and 2 (or some other band) may also be an expla-nation for the staggering seen in the J 2 moment of band1 at low v (see Fig. 5).As indicated above, further progress in the descriptionof the new bands requires the introduction of pairing.Unfortunately, unconstrained cranked relativistic Hartree-Bogoliubov (CRHB) calculations [22] converge to thespherical minimum instead of the deformed one, mostlikely because of a small barrier between the two minima.The implementation of constraints on the Q20 and Q262moments into the CRHB code [22], which is needed tostudy the deformed structures, is in progress and theresults will be reported later [15].222501-4Finally, Fig. 6 compares the kinematic moments of iner-tia J 1, for the SD band in 40Ca with that of the rotationalband in 36Ar. Below the backbending in 36Ar, the J 1values of the SD band in 40Ca and in the 36Ar band aresimilar. The fact that the backbending is observed in 36Ar,but not in 40Ca, is due to both the larger deformation ofthe latter and the fact that the alignment is connected withthe first proton and neutron f72 pairs in 36Ar and with thesecond pairs in the SD band of 40Ca.In summary, a discrete-line superdeformed band hasbeen identified in 4020Ca20. This is the first observation ofan SD rotational structure in a doubly magic spherical nu-cleus. Its SD character is inferred from a large transitionquadrupole moment (Qt  1.8010.3920.29eb). The propertiesof the SD band are reasonably well explained by the CRMFcalculations without pairing. According to these calcula-tions the SD band is based on an 8p-8h excitation in thesd  fp shell. Therefore, this band may be identified asthe multiparticle-multihole SD structure that was predictedby shell model calculations more than thirty years ago.This work was supported in part by the U.S. Departmentof Energy, Grants No. DE-FG05-88ER40406, No. DE-AC05-00OR22725, No. W-31-109-ENG38, and theSwedish Natural Sciences Research Councils.*Present address: LANSCE-3, Los Alamos NationalLaboratory, Los Alamos, New Mexico 87545.†Present address: NBI, Copenhagen, Denmark.[1] D. Rudolph et al., Phys. Rev. Lett. 82, 3763 (1999).[2] E. Caurier et al., Phys. Rev. C 50, 225 (1994).[3] T. Mizusaki et al., Phys. Rev. C 59, R1846 (1999).[4] D. C. Zheng et al., Phys. Rev. C 42, 1004 (1990).[5] A. V. Afanasjev et al., Phys. Rev. C 59, 3166 (1999).[6] P. M. Endt, Nucl. Phys. A521, 1 (1990).[7] J. L. Wood et al., Phys. Rep. 215, 101 (1992).[8] W. J. Gerace and A. M. Green, Nucl Phys. A93, 110 (1967);A123, 241 (1969)..[9] C. E. Svensson et al., Phys. Rev. Lett. 85, 2693 (2000).[10] C. E. Svensson et al., Phys. Rev. C 63, 061301(R) (2001).[11] I. Y. Lee, Nucl. Phys. A520, 641c (1990).[12] D. G. Sarantites et al., Nucl. Instrum. Methods Phys. Res.,Sect. A 381, 418 (1996).[13] H. P. Leenhouts, Physica (Utrecht) 35, 290 (1967).[14] J. J. Simpson et al., Phys. Rev. Lett. 35, 23 (1975).[15] E. Ideguchi et al. (to be published).[16] B. Cederwall et al., Nucl. Instrum. Methods Phys. Res.,Sect. A 354, 591 (1995).[17] F. Lerma et al., Phys. Rev. Lett. 83, 5447 (1999).[18] J. F. Ziegler, http://www.research.ibm.com/ionbeams[19] A. V. Afanasjev et al., Nucl. Phys. A608, 107 (1996).[20] G. A. Lalazissis et al., Phys. Rev. C 55, 540 (1997).[21] W. J. Gerace et al., Nucl. Phys. A285, 253 (1977).[22] A. V. Afanasjev et al., Nucl. Phys. A676, 196 (2000).222501-4

Superdeformation in the Doubly Magic Nucleus 4020Ca20

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Superdeformation in the Doubly Magic Nucleus 4020Ca20

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