A highly-deformed rotational band has been identified in the N=Z nucleus 36Ar. At high spin the band is observed to its presumed termination at I=16+, while at low spin it has been firmly linked to previously known states in 36Ar. Spins, parities, and absolute excitation energies have thus been determined throughout the band. Lifetime measurements establish a large low-spin quadrupole deformation (beta_2=0.46+-0.03) and indicate a decreasing collectivity as the band termination is approached. With effectively complete spectroscopic information and a valence space large enough for significant collectivity to develop, yet small enough to be meaningfully approached from the shell model perspective, this rotational band in 36Ar provides many exciting opportunities to test and compare complementary models of collective motion in nuclei

Appelbe, D E

Austin, R A E

Baktash, C B

Ball, G C

Carpenter, M P

Caurier, E

Clark, R M

Cromaz, M

Deleplanque, M A

Diamond, R M

Fallon, P

Furlotti, M

Galindo-Uribarri, A

Janssens, R V F

Juodagalvis, A

Lane, G J

Lee, I Y

Lipoglavsek, M

Macchiavelli, A O

Nowacki, F

Paul, S D

Poves, A

Radford, D C

Ragnarsson, I

Sarantites, D G

Seweryniak, D

Stephens, F S

Svensson, C E

Tomov, V

Vetter, K

Ward, D

Yu, C H

Åberg, S

arXiv

A highly-deformed rotational band has been identified in the N = Z nucleus 36Ar. At high spin the band is observed to its presumed termination at Iπ = 16+, while at low spin it has been firmly linked to previously known states in 36Ar. Spins, parities, and absolute excitation energies have thus been determined throughout the band. Lifetime measurements establish a large low-spin quadrupole deformation (β2 = 0.46 ±0.03) and indicate a decreasing collectivity as the band termination is approached. With effectively complete spectroscopic information and a valence space large enough for significant collectivity to develop, yet small enough to be meaningfully approached from the shell model perspective, this rotational band in 36Ar provides many exciting opportunities to test and compare complementary models of collective motion in nuclei

Svensson, O.E.

Macchiavelli, A.O.

Juodagalvis, A.

Poves, A.

Ragnarsson, I.

Åberg, S.

Appelee, D.E.

Austin, R.A.E.

Baktash, C.

Ball, G.G.

Caurier, E.

Clark, R.M.

Cromaz, M.

Deleplanque, M.A.

Diamond, R.M.

Fallon, P.

Furlotti, M.

Galindo-Uribarri, A.

Janssens, R.V.F.

Lane, G.J.

Lee, I.Y.

Lipoglavsek, M.

Nowacki, F.

Paul, S.D.

Radford, D.C.

Sarantites, D.G.

Seweryniak, D.

Stephens, F.S.

Tomov, V.

Vetter, K.

Ward, D.

Yu, C.H.

Carolina Digital Repository

arXiv:nucl-th/0104012v1  3 Apr 2001 Fast Rotation of the N = Z Nucleus 36ArC.E. Svensson,1 A.O. Macchiavelli,2 A. Juodagalvis,3 A. Poves,4I. Ragnarsson,3 S. Åberg,3 D.E. Appelbe,5 R.A.E. Austin,5C. Baktash,6 G.C. Ball,7 M.P. Carpenter,8 E. Caurier,9R.M. Clark,2 M. Cromaz,2 M.A. Deleplanque,2 R.M. Diamond,2P. Fallon,2 M. Furlotti,10 A. Galindo-Uribarri,6R.V.F. Janssens,8 G.J. Lane,2 I.Y. Lee,2 M. Lipoglavsek,6F. Nowacki,11 S.D. Paul,6 D.C. Radford,6 D.G. Sarantites,10D. Seweryniak,8 F.S. Stephens,2 V. Tomov,10 K. Vetter,2D. Ward,2 and C.H. Yu61Department of Physics, University of Guelph, Guelph, Canada2Nuclear Science Division, Lawrence Berkeley Laboratory, Berkeley, U.S.A.3Department of Mathematical Physics, Lund University, Lund, Sweden4Departamento de F́ısica Teórica, Universidad de Madrid, Madrid, Spain5Department of Physics & Astronomy, McMaster University, Hamilton, Canada6Physics Division, Oak Ridge National Laboratory, Oak Ridge, U.S.A.7TRIUMF, 4004 Wesbrook Mall, Vancouver, Canada8Argonne National Laboratory, Argonne, U.S.A.9Institut de Recherches Subatomiques, Université Louis Pasteur,Strasbourg, France10Chemistry Department, Washington University, St. Louis, U.S.A.11Laboratoire de Physique Theorique, Université Louis Pasteur,Strasbourg, FranceA highly-deformed rotational band has been identified in the N = Znucleus 36Ar. At high spin the band is observed to its presumed terminationat Iπ = 16+, while at low spin it has been firmly linked to previouslyknown states in 36Ar. Spins, parities, and absolute excitation energieshave thus been determined throughout the band. Lifetime measurementsestablish a large low-spin quadrupole deformation (β2 = 0.46 ± 0.03) andindicate a decreasing collectivity as the band termination is approached.With effectively complete spectroscopic information and a valence spacelarge enough for significant collectivity to develop, yet small enough to bemeaningfully approached from the shell model perspective, this rotationalband in 36Ar provides many exciting opportunities to test and comparecomplementary models of collective motion in nuclei.PACS numbers: 21.10.Re, 21.10.Tg, 21.60.Cs, 23.20.Lv, 27.30.+t(1)2 Svensson printed on November 15, 20181. IntroductionThe microscopic description of collective phenomena is a fundamentalgoal of quantum many-body physics. In the field of nuclear structure, aclassic example is the desire to connect the deformed intrinsic states andcollective rotational motion of nuclei with microscopic many-particle wave-functions in the laboratory system. For nuclei in the lower sd shell, thisconnection is well understood in terms of Elliot’s SU(3) model [1]. Forheavier nuclei, however, the spin-orbit interaction removes the degeneraciesof the harmonic oscillator, destroying the SU(3) symmetry. Furthermore,rotational motion in these nuclei generally involves valence spaces comprisedof two major shells for both protons and neutrons [2]. Exact shell modeldiagonalizations in such spaces are well beyond current computational ca-pabilities, and much effort has therefore been devoted to determining theapproximate symmetries that permit a description of the collective motionin these nuclei within an appropriately truncated model space (cf. [3, 4, 5].)It is clearly desirable to test the validity of such approximate symmetriesin cases where the valence space is large enough for collective motion to de-velop, but small enough to permit exact diagonalizations. Here we discussthe identification [6] of a superdeformed (SD) band in the N = Z nucleus36Ar which, like rotational bands in heavier nuclei, involves two major shellsfor both protons and neutrons, yet satisfies the above criteria.2. ExperimentsHigh-spin states in the N = Z nucleus 36Ar were populated via the24Mg(20Ne,2α)36Ar fusion-evaporation reaction in two experiments with an80-MeV, ∼2 pnA 20Ne beam provided by the ATLAS facility at ArgonneNational Laboratory. In the first experiment, a self-supporting 440 µg/cm224Mg foil was used, while in the second experiment a 420 µg/cm2 24Mg layerwas deposited onto a 11.75 mg/cm2 Au backing in order to measure lifetimesby Doppler-shift attenuation methods. In both experiments, γ rays weredetected with 101 HPGe detectors of the Gammasphere array [7], in coin-cidence with charged particles detected and identified in the Microball [9],a 4π array of 95 CsI(Tl) scintillators. The Hevimet collimators were re-moved from the BGO Compton-suppression shields of the HPGe detectorsin order to provide γ-ray sum-energy and multiplicity information for eachevent [8]. The 2α evaporation channel leading to 36Ar was cleanly selectedin the offline analysis by requiring the detection of 2 alpha particles in theMicroball in combination with a total detected γ-ray plus charged-particleenergy consistent with the Q-value for this channel [10]. Totals of 775 mil-lion and 827 million particle–γ–γ–γ and higher fold coincidence events wererecorded in the first and second experiments, respectively.Svensson printed on November 15, 2018 31000 2000 3000 4000 5000050001000015000Eγ (keV)Countsx 2 36Ar11861630 1970 + 1975216024442602 28212948335234484166 - 511406641664950 - 5114950Fig. 1. Gamma-ray spectrum obtained by summing coincidence gates set on allmembers of the superdeformed band (circles). Diamonds indicate linking transi-tions connecting the band to low-spin states in 36Ar.3. Results and DiscussionThe γ-ray spectrum from the thin-target experiment obtained by sum-ming coincidence gates set on all members of the superdeformed band iden-tified in 36Ar is shown in Fig. 1, and a partial decay scheme for 36Ar ispresented in Fig. 2. As shown in Fig. 2, the high-energy γ rays indicated bydiamonds in Fig. 1 link the SD band to previously known low-spin states,and thereby fix the absolute excitation energies of the SD levels. The spec-trum of the SD band obtained with a single gate on the 4950 keV γ ray,shown in the upper inset of Fig. 2, illustrates the quality of the coincidencedata for these linking transitions. Angular distribution measurements es-tablish stretched quadrupole character for the high-energy linking γ raysand for all of the in-band transitions. The lower insets in Fig. 2 presenttwo examples of such measurements, which determine the spins, and, underthe reasonable assumption that the transitions are E2 rather than M2, theparities, of the SD states from 2+ to 16+. Although γ decay by a 622 keVtransition to the previously known (0+) state at 4329 keV [11] was not ob-served in this experiment, this state is presumed to be the SD bandheadbased on the regular rotational spacing.4 Svensson printed on November 15, 20181000 2000 30000200400600Eγ (keV)CountsGate: 4950 keV0 60 120 180500600700Angle (degrees)Relative YieldEγ = 4166 keV0 60 120 180250300350Angle (degrees)Relative YieldEγ = 3352 keVFig. 2. Partial decay scheme for 36Ar showing the superdeformed band (left). Theupper inset shows a spectrum of the band obtained with a single gate set on the4950 keV linking transition. Angular distributions relative to the beam axis arepresented for the 3352 keV and 4166 keV linking transitions in the lower insets.We have performed both configuration-dependent [12] cranked Nilsson-Strutinsky (CNS) and large-scale s1/2d3/2-pf spherical shell model (SM)calculations with the diagonalization code Antoine [13] for the 36Ar SDband. As detailed in Ref. [6], these calculations provide a good descriptionof the energetic properties of the band and enable its firm assignment to aconfiguration in which four pf -shell orbitals are occupied. Here we focusprimarily on the quadrupole properties of the band.Svensson printed on November 15, 2018 50.0 0.1 0.2 0.3 0.4 0.5 0.60.00.10.20.30.40.50 4 8 12 160100200300400ε2 cos(γ + 30o)ε 2 sin(γ + 30o)36ArAngular Momentum (h)0+, 2+8+16+γ = 0oγ = -30oγ = 30oγ = 60oB(E2) (e 2fm 4 )Cranked Nilsson-StrutinskyShell Model (s1/2d3/2)4(pf)4Prolate Rotor (β2 = 0.45)(a)Fig. 3. Calculated trajectory in the (ε2,γ) deformation plane for the SD band in36Ar. The inset shows the corresponding B(E2) values from the cranked Nilsson-Strutinsky (circles) and shell model (diamonds) calculations. The B(E2)’s for afixed prolate deformation β2 = 0.45 are also shown for comparison (squares).The predicted equilibrium deformations for the SD band from the CNScalculations are shown in Fig. 3. At low spin, a prolate shape with deforma-tion ε2 = 0.40, which remains approximately constant up to I = 8h̄, is cal-culated. At higher spins, the nucleus is predicted to change shape smoothly,becoming increasingly triaxial until the band terminates in a fully alignedoblate (γ = 60◦) state at Iπ = 16+. Assuming the rotor model with theinitial state deformations, the B(E2; I → I − 2) values corresponding tothis shape trajectory are shown by the circles in the inset of Fig. 3. Alsoshown in this Figure are the B(E2) values from the SM calculations. Bothcalculation indicate a large collectivity at low spin which decreases as theband termination is approached. However, the shell model calculations areseen to predict somewhat smaller B(E2) values for the intermediate spinstates, but somewhat larger values close to termination.In order to test the quadrupole properties shown in Fig. 3, we havemeasured state lifetimes throughout the 36Ar SD band by Doppler-shift at-tenuation techniques. These measurements rely on changes in the velocities6 Svensson printed on November 15, 20180 1 2 3 4 5 6 7 8-3-2-10123vz/c (%)v x/c (%)36Ar Recoil VelocityDistributionθ = 30ovo/c = 4.18%Fig. 4. Initial recoil velocity distribution in the vx–vz plane for36Ar nuclei in the2α-gated data set, as reconstructed from the measured alpha-particle momenta.The beam is in the z-direction, and the recoil velocity for a compound nucleusformed at the center of the target was vz/c = 4.18%.of the recoiling 36Ar nuclei as they pass through the target and, in the caseof the second experiment, the Au target backing. It is therefore essential tohave a good understanding of the initial recoil velocity distribution for theevents in the particle-gated data set. In the 24Mg(20Ne,2α)36Ar reaction,the evaporation of two alpha particles from the compound 44Ti nucleus pro-duces a very broad recoil distribution for the 36Ar nuclei. Furthermore, thealpha-particle detection efficiency is strongly angle dependent. The alphasemitted forward (relative to the beam direction) in the center-of-mass (CM)frame receive an energy boost in the lab frame from the CM motion, andare detected more efficiently than those emitted at backward angles, whichhave lower energies in the lab system. A result of requiring 2α detection isthus to bias the experimental data set towards events in which the alphaparticles were emitted in the forward direction, and consequently the 36Arrecoil velocity was reduced compared to that of the compound system. Thiseffect is clearly seen in Fig. 4, which shows the experimental recoil velocitydistribution for the 36Ar nuclei reconstructed from the measured energiesSvensson printed on November 15, 2018 702040608010002040602050 2100 2150 2200 2250020406080Eγ (keV)Counts22082160 keVθ = 35oθ = 90oθ = 145oFig. 5. Doppler-shift attenuation lineshape analysis for the 2160 keV 8+SD → 6+SDtransition. The stopped peak at 2208 keV is the 3−1 → 2+1 transition in36Ar.and directions of the detected alpha particles. In order to obtain meaningfullifetime measurements, it was necessary to modify the Lineshape code [14]to incorporate this experimentally determined initial recoil velocity distri-bution. The excellent fits to the γ-ray lineshapes that were obtained by thismethod are illustrated with the 2160 keV 8+ → 6+ SD transition in Fig. 5.A complete description of the lifetime measurements for the 36Ar SDband is given in Ref. [15]. Here we summarize the resulting B(E2) valuesin Fig. 6. The CNS calculations are seen to provide a good description ofthe measured low-spin B(E2) values, but underpredict the high-spin col-lectivity. This result is expected as these calculations do not include theeffects of shape fluctuations about the equilibrium deformations, which willremove the artificial vanishing of the B(E2) at the terminating state arisingfrom the prediction of an exactly oblate equilibrium deformation. The SMcalculations provide an excellent description of the spin-dependence of the8 Svensson printed on November 15, 20180 4 8 12 160100200300400500Angular Momentum (h)B(E2) (e2fm4 )ExperimentCranked Nilsson-StrutinskyShell Model (s1/2d3/2)4(pf)4Fig. 6. Measured B(E2; I → I − 2) values for the SD band in 36Ar comparedwith the results of cranked Nilsson-Strutinsky (dashed line) and (s1/2d3/2)4(pf)4spherical shell model (solid line) calculations. The inner error bars represent thestatistical uncertainties, while the outer error bars show the effects of systematic±10% shifts in the stopping powers.B(E2) values, including the substantial remaining collectivity at the ter-minating state, but systematically underestimate the experimental valuesby approximately 20%. In order to further investigate these effects, it isinteresting to compare the microscopic structures of the wavefunctions forthe SD band from the two calculations.Figure 7 shows the occupancies of spherical j-shells in the SD bandfrom the CNS and SM calculations. We note that the relatively constantoccupancies at low spin confirm the concept of a rotational band built ona fixed intrinsic configuration. At higher spins, the increasingly rapid oc-cupancy changes reflect the changes in the intrinsic deformation shown inFig. 3. For the pf shell, the occupancies predicted by the two calculationsare very similar, indicating the dominance of the quadrupole deformationin determining the structure of the wavefunction for this highly collectiverotational band. The full treatment of all correlations, in particular pair-ing, in the shell model leads only to a small increase in the occupancies ofthe upper pf shell orbitals relative to the dominant deformation-inducedmixing of the spherical j-shells reflected in the CNS occupancies. For theSvensson printed on November 15, 2018 901230 4 8 12 160123Angular Momentum (h)Orbital Occupation (π + ν)(a) Cranked Nilsson(b) Shell Model: (s1/2d3/2)4(pf)4d5/2 holess1/2d3/2f7/2p3/2 f5/2p1/2s1/2d3/2f7/2p3/2f5/2p1/2Fig. 7. Occupancies of spherical j-shells in the 36Ar superdeformed band from (a)cranked Nilsson-Strutinsky and (b) (s1/2d3/2)4(pf)4 shell model calculations.sd shell, dimensionality considerations required a truncation of the shellmodel space to s1/2d3/2. The CNS calculations, however, indicate that thed5/2 orbital is only ∼ 90% full in the SD band. It is worth noting thatthe intrinsic quadrupole moment Q0 = 113 e fm2 deduced for the SD bandfrom the (s1/2d3/2)4(pf)4 SM calculation is already 80% of the maximumpossible in the full (sd)16(pf)4 space (as attained in the unrealistic SU(3)limit). Nevertheless, a ∼ 5–10% increase in Q0 due to the d5/2-hole compo-nent of the wavefunction is plausible, and would account for the ∼ 10–20%underestimate of the B(E2) values by the current shell model calculations.Further study of the role of the d5/2 orbital in the structure of this highlycollective band, perhaps through Monte Carlo Shell Model techniques [16],would clearly be desirable.10 Svensson printed on November 15, 20184. ConclusionsA superdeformed rotational band has been identified in the light N = Znucleus 36Ar. The linking of this band to previously known low-spin states,combined with lifetime measurements throughout the band, have estab-lished absolute excitation energies, spins, and parities, as well as in-bandand out-of-band B(E2) values for the SD states. With effectively completespectroscopic information and a model space large enough for substantialcollectivity to develop, yet small enough to be approached from the shell-model perspective, the 36Ar SD band offers many exciting opportunities forfurther studies of the microscopic structure of collective rotational motionin nuclei.5. AcknowledgementsThis work has been partially supported by the Natural Sciences andEngineering Research Council of Canada, the U.S. D.O.E. under ContractsDE-AC03-76SF00098, W-31-109-ENG-38, and DE-FG05-88ER40406, theSwedish Institute, NFR (Sweden), DGES (Spain) under Grant No. PB96-53,and IN2P3 (France).REFERENCES[1] J.P. Elliott, Proc. R. Soc. London 245, 128 (1958); 245, 562 (1958).[2] K. Kumar and M. Baranger, Nucl. Phys. A110, 529 (1968).[3] A.P. Zuker et al., Phys. Rev. C 52, R1741 (1995).[4] C. Vargas et al., Phys. Rev. C 61, 031301(R) (2000).[5] C. Bahri and D.J. Rowe, Nucl. Phys. A662, 125 (2000).[6] C.E. Svensson et al., Phys. Rev. Lett. 85, 2693 (2000).[7] I.-Y. Lee, Nucl. Phys. A520, 641c (1990).[8] M. Devlin et al., Nucl. Instrum. Methods Phys. Res. A 383, 506 (1996).[9] D.G. Sarantites et al., Nucl. Instrum. Methods Phys. Res. A 381, 418 (1996).[10] C.E. Svensson et al., Nucl. Instrum. Methods Phys. Res. A 396, 228 (1997).[11] P.M. Johnson, M.A. Meyer, and D. Reitmann, Nucl. Phys. A218, 333 (1974).[12] T. Bengtsson and I. Ragnarsson, Nucl. Phys. A436, 14 (1985);A.V. Afanasjev and I. Ragnarsson, Nucl. Phys. A591, 387 (1995).[13] E. Caurier, computer code Antoine, Strasbourg (1989).[14] J.C. Wells et al., Report ORNL-6689 (1991).[15] C.E. Svensson et al., Phys. Rev. C, in press.[16] M. Honma, T. Mizusaki, and T. Otsuka, Phys. Rev. Lett. 77, 3315 (1996);T. Otsuka, M. Honma, and T. Mizusaki, Phys. Rev. Lett. 81, 1588 (1998).

Fast rotation of the N = Z nucleus 36Ar

Svensson, C.E.

Aberg, S.

Appelbe, D.E.

Ball, G.C.

Carpenter, M.P.

Lipoglavek, M.

HAL-IN2P3

Fast rotation of the N=Z nucleus $^{36}$Ar

HAL Descartes

Svensson, CE

Macchiavelli, AO

Appelbe, DE

Austin, RAE

Baktash, C

Ball, GC

Carpenter, MP

Clark, RM

Deleplanque, MA

Diamond, RM

Janssens, RVF

Lane, GJ

Lee, IY

Paul, SD

Radford, DC

Sarantites, DG

Stephens, FS

Yu, CH

eScholarship - University of California

Fast Rotation of the N=Z Nucleus 36Ar

Fast Rotation of the N=Z Nucleus 36Ar

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Carolina Digital Repository

HAL-IN2P3

HAL Descartes

eScholarship - University of California