Warm superdeformed nuclei:

S. Leoni University of Milano and INFN Warm superdeformed nuclei: Probes of Nuclear Structure and Tunneling Processes At the Onset of Chaos Oslo WS May 29

Outline: 1- INTRO: Warm Superdeformed Nuclei 2- Experimental Analysis 151 Tb & 196 Pb EUROBALL IV data 3- Theoretical Modelling Microscopic Monte Carlo simulation 4- OUTLOOK: Probes of Nuclear Structure & Potential Barriers

Compound Nucleus Chaos SD Warm Rotation strongly interacting bands I I-2 I+2 T= Regular bands Order Superdeformation at Finite Temperature Challenging topic experiment: focus on ~1% γ-decay theory: cranking at T coupled to tunneling to ND well L m ND ND SD tunneling SD to ND minima present status experiment: partial infos on 143 Eu, 152 Dy, 194 Hg theory: schematic OR many parameters

Aim of this work: Step forward in Experiment & Theory EXPERIMENT: Extensive Study of warm rotation in A=15 and 19: 151 Tb and 196 Pb Evaluation of several independent experimental oservables stringent test of γ-decay flow THEORY: Development of new Monte Carlo model Based on microscopic calculations Towards a parameter free model

1- The 151 Tb and 196 Pb experiments

Two High Statistics EUROBALL-IV Experiments 151 Tb and 196 Pb HECTOR BGO INNER BALL 21 detectors 8 Large BaF 2 for GDR analysis 3 Si + 17 Er 196 Pb + 4n Thin target, E beam = 148 MeV, L max 53 h Statistics: 8 days 2 1 8 <F Ge > = 3 <F γ > = 1 Goals: warm rotation in SD well (S. Leoni et al., in print in PRL) GDR in A = 19 (D. Montanari et al., in preparation) 27 Al + 13 Te 151 Tb + 6n Thin target, E beam = 155 MeV, L max 8 h Statistics: 17 days 9 1 9 <F Ge > = 5 <F γ > = 22 Goals: discrete spectroscopy in SD well (J. Robin et al., PRC77, 1438(28) search for linking transitions SD ND (J. Robin et al., PRC78(28)34319)

Discrete Spectroscopy Info s 151 Tb 196 Pb Intensity (%) 14 12 1 8 6 4 2 % 8,x1 6 6,x1 6 4,x1 6 2,x1 6, Yrast 8 1 12 14 16.8-1.6 MeV Intensity (%) 14 12 1 8 6 4 1.3 % 6 4 2 E γ Yrast 1 2 3 4 5 6 7 8.2-.8 MeV 2 2 2 4 6 8 1 12 14 Number of SD band 2 4 6 8 1 12 14 Number of SD band 151 Tb tentative assignment SD SD 196 Pb firm assignment 3698 462 ND ND J. Robin et al., Pys. Rev. C78(28)34319 A.N. Wilson et al., Phys. Rev. Lett. 95 (25)

Quasi-Continuum Spectroscopy: Warm Rotation E* 168 Yb RIDGES Discrete Unresolved Bands γ γ spectra & rotational planes x+y = 2z±δ I+1 I+1 I-2 I-2 I I I+2 I+2 I T= E2 Bump T I+8 I+6 I+4 I+2 I I+8 I+6 I+4 I+2 I γ spectra Total E2 Quasi-Continuum X Y Z

151 Tb Analysis SD gated γ spectrum E2 Bump SD gated γ γ 1 st Ridge Rot-Plane 2 nd Ridge Total γ γ 1 st Ridge counts counts [x1 3 ] counts [x1 3 ] counts [x1 3 ] 3 25 2 15 1 5 75 125 175 15 1 5 2 15 1 E γ 2 E γ = 1 kev 25 4 E γ = 2 kev 7 5 3 2 E γ = 1 kev -1 1 E γ1 -E γ2 [kev] Intensity [%] Intensity [%] Intensity [%] Intensity [%] Number Intensity Discrete Bands Analysis Techniques Counts 1 3 E2 SD gated Fluctuations 1 2 1 1 1 (2) Neve 1. Spectrum Intensity: N = µ 2 1 1 3 SD gated Ridge 1 2 1 1 1 1 3 2. Ridge 1 2 1 1 1 1 3 1 2 1 1 1 8 independent observables Yrast Spin N path 75 5 number of 25 bands 14 ± 2 N path 1 75 5 25 1 path µ 1 Spin P SD gated Ridge 2. Ridge Properties 1. Ridge of γ-decay flow I yrast = 2 % 1. Ridge 75 1 observed of SD nucleus 5 27 ± 8 25 3 4 5 6 7 Spin population 2. Spectrum Fluctuations: N path 12 ± 5 2 3 4 5 6 7

196 Pb Analysis SD gated γ spectrum E2 Bump SD gated γ γ 1 st Ridge Rot-Plane 2 nd Ridge Total γ γ 1 st Ridge counts [x1 3 ] counts [x1 3 ] counts [x1 3 ] Counts [x1 3 ] 8 6 4 2 8 6 4 6 5 4 15 1 5 5 75 1 125 E γ 2 E γ = 8 kev 4 E γ =16 kev 2 E γ = 8 kev -8 8 E γ1 -E γ2 [kev] Intensity [%] Intensity [%] Intensity [%] Intensity [%] 1 3 1 2 1 1 1 1 3 1 2 1 1 1 1 3 1 2 1 1 1 1 3 1 2 1 1 1 8 independent observables Intensity E2 SD gated E2 + M1 SD gated Ridge Yrast 2. Ridge 1. Ridge I yrast = 1.3 % 1 2 3 4 5 Spin N path N path N path 2 75 Number Discrete Bands Counts Fluctuations N N (2) eve path = µ 2 1 µ 1 P 4 SD gated Ridge 5 25 75 5 25 2. Ridge 1. Ridge 1 2 3 4 5 Spin 8 ± 3 12 ± 4 3 observed 2 ± 9

2- The Interpretation of the DATA a Monte Carlo simulation of the γ-decay based on microscopic calculations: Towards a parameter free model

2 E2 ND E1 E2 SD E1 extrapolated ρ SD, B(E2), barriers E* [MeV] ND tunneling SD Γ rot microscopic levels, B(E2), barriers 15 γ-decay in ND well: Γ rot I-2 I I+2 SD parametrized ρ ND, B(E2) ρ [MeV -1 ] 1 7 1 6 1 5 1 4 1 3 1 2 1 1 1 196 Pb 1 ND Hartree-Fock-BCS S. Goriely ADNDT 77, 311(21) 1-1 2 4 6 8 U [kev] γ-decay in SD well: microscopic + extrapolated 1 2 3 4 5 6 Spin

Microscopic calculations entering the Monte Carlo: 1. Interacting cranked shell model K. Yoshida, M. Matsuo, NPA612(1997)126 2. Microscopic Barriers & Tunneling Actions K. Yoshida, M. Matsuo and Y. Shimizu, NPA696, 85(21)

at T H = H def - ωj x + V res Configuration mixing

151 Tb microscopic calculations Cranked shell model at T E2 fragmentation U [MeV] 3 2 1 H = H def ωj x + V res yrast (,+) π = - 1 2 3 4 5 6 7 8 3 π = + n b 1 1 35 3 4.5 + n b = 2 onset of damping U onset 1 2 3 4 5 U [MeV] I-2 I U [MeV] 2 1 Width [kev] 25 2 15 1 5 Γ rot I-2 I Γ rot Γ µ 1 2 3 4 5 6 7 8 Spin 3 4 5 6 7 Spin K. Yoshida, M. Matsuo, NPA612(1997)126

196 Pb microscopic calculations Cranked shell model at T U [MeV] 1,,5, H = H def ωj x + V res Pb: CSM calculations yrast (+,) π = - (-,) (-,1) EXP U onset 4 3 2 1 151 Tb versus 196 Pb b) 151 Tb 196 Pb U [MeV] 1,,5 π = + (+,) (+,1) N band 3 2 1 a) 196 Pb 151 Tb, yrast (+,) 1 2 3 4 5 Spin [h] K. Yoshida, M. Matsuo, NPA612(1997)126 1 2 3 4 5 6 7 Spin [h]

microscopic calculations for decay-out at T K. Yoshida, M. Matsuo and Y. Shimizu, NPA696, 85(21) ND SD Γ t M hωsd = 2π 1 2 DSD hω SD (1+ e 2 S 1 ) action integral S ( E ) = ds 2M ( V ( q( s)) E ) path along tunneling path driven by pairing S S 2 15 1 5 12 1 8 6 4 2 151 Tb (,+) U =. MeV.4.6 U =. MeV.4.8 1. 1.2 1.4 1.6 196 Pb.2 (,+) 1.8 1 2 3 4 5 6 Spin.8 1.6 2.4 2.8 3.6 4.4 5.2 extension of model used for SD yrast 152 Dy

Microscopic Calculations in SD well Energy levels, E2 strengths, actions S Microscopic Monte Carlo Simulation: 1. Drastic reduction of Number of parameters: - entry distribution - E1 strength in SD & ND well - level density in ND well 2. Quantitative analysis of Spectrum Intensity and Fluctuations

The simulation parameters 27 Al + 14 Te @ E lab =152 MeV 1. The Entry Distribution: it is NOT a real parameter (it can be measured or calculated) dσ/di [arb. un.] 1 8 6 4 CN fusion (Grazing code) 151 Tb (Cascade) n 2 n 2 4 6 8 1 Spin Entry 151 Tb E * [MeV] 4 3 2 1 ND SD E2 E1 E2 E1 tunneling γ SD yrast counts [arb.un.] 6 4 2 <I> = 58 h ± 8 h <U> = 8.3 ± 2.5 MeV 2 I=3 I=4 15 1 5 ND yrast 5 1 15 2 U [MeV] 5 1 15 2 U [MeV] 1 2 3 4 5 6 7 8 Spin A. Winther, Nucl. Phys. A594, 23(1995) F. Pulhofer, Nucl. Phys. A28, 267 (1977)

The simulation parameters 2. The E1 decay strength: the tail of the GDR E2 ND E1 E2 SD E1 T f GDR = Sum of 3 Lorentzian 3 ( E1) = H1 n K E1 B( E1) Eγ T(E1) [s -1-1 ] 4x1 19 19 3x1 19 19 f GDR 2x1 19 19 1x1 19 19 tunneling ND SD Hindrance factor ~ 1-2 (tuned to reproduce the intensity of the yrast band) K.E.G. Lobner, Phys. Lett. 26B, 369(1968) G. Leander, PRC38, 728(1988) 5 1 15 2 25 3 3 E γ [MeV]

151 Tb: simulated γ-spectra Counts [arb. un.] counts [x1 3 ] 6 4 2 7 5 3 Total γ γ matrix 2 E γ = 1 kev 2 E γ = 1 kev SIMUL DATA -1 1 E γ1 -E γ2 [kev] Counts [arb. un.] counts [x1 3 ] 15 1 5 15 1 5 SD gated matrix 2 E γ = 1 kev 2 E γ = 1 kev -1 1 E γ1 -E γ2 [kev] counts counts 15 1 5 375 125 175 25 2 15 1 5 E2 SD gated 75 125 175 E γ SIMUL DATA Analysis of Simulated Spectra: Spectrum Intensity (population) Fluctuations (number of bands)

Exp. versus Theory 151 Tb 196 Pb Analysis of Intensities exclusive quantities SD gated decay-flow E2+M1 SD gated γ spectrum E2 Bump SD gated γ γ 1 st Ridge inclusive quantities average decay-flow Rot-Plane 2 nd Ridge Total γ γ 1 st Ridge

SD gated quantities are sensitive to E1/E2 balance Enhanced octupole vibrations have been observed in A= 15 and A = 19 196 Pb, 19 Hg 194 Hg T(E1) [s -1 ] f GDR 4x1 19 3x1 19 2x1 19 1x1 19 SD E1 E1 5 1 15 2 25 3 enhanced GDR E γ [MeV] 151 Tb D. Rosbach et al. PLB513(21)9 T. Lauritsen et al., PRL89(22)28251 B(E1) ~ 1-4 -1-3 W.u. 1 to 1 times stronger Theory: Nilson + QRPA J. Kvasil, N. LoIudice et al., PRC75 (27)3436 T. Nakatsukasa et al., PLB343(1995)19 Standard GDR

Exp. versus Theory: Intensities 151 Tb 196 Pb exclusive quantities SD gated decay-flow E2+M1 enhanced GDR 151 Tb Standard GDR inclusive quantities average decay-flow other types of enhancement my be possible M1 s Good agreement with data in both A=15 and 19 region S. Leoni et al. PRL11(28)14252

Exp. versus Theory: Intensities 151 Tb 196 Pb exclusive quantities SD gated decay-flow E2+M1 inclusive quantities average decay-flow Good agreement with data in both A=15 and 19 region S. Leoni et al. PRL11(28)14252

Exp. versus Theory: Number of Discrete Bands I-2 I Cranking Onset of Damping (Chaos) n branch < 2 + decay-out (tunnel through potential barrier) 1 1-2 x1-4 + Population decay-flow (N path = 1/Σw i 2 ) W i I = 5,51 h 1 2 3 4 U [MeV] N path 1 75 5 25 151 Tb Yrast 1. Ridge 2 3 4 5 6 7 Spin - the flow bias strongly the population probability N Excited bands - TEST of nuclear structure & tunneling model over wide range of I and U N (2) eve path = µ 2 1 µ 1 P

N = N (2) eve path µ 2 1 µ 1 P N path N path N path 5 SD-gated 1. Ridge 25 e) 8 2. Ridge 6 4 2 1 5 151 Tb No decay-out c) 1. Ridge No decay-out a) 2 3 4 5 6 7 Spin [h] f) SD-gated 1. Ridge 196 Pb 2. Ridge No decay-out d) 1. Ridge No decay-out b) 1 2 3 4 5 Spin [h] 5 25 12 8 4 15 1 5 Good agreement with data in both A=15 and 19 region S. Leoni et al. PRL11(28)14252

OUTLOOK: Probes of Nuclear Structure and Tunneling 1. Strength of two-body interaction 2. Mass parameter in action S 3. ND level density Sensitivity mostly in A = 19 region

Probes of Nuclear Structures 1. Sensitivity to two-body interaction Strength Cranked shell model at T H = H def ωj x + V res V res (1,2) = v T δ(x 1 -x 2 ) 1 2 3 4 5 Spin [h] 1 196 196 Pb1 st Ridge 194 75 Pb.5 v Hg T N N (2) eve path = µ 2 1 µ 1 b) P Number of discrete SD bands S. Leoni et al. Submitted to PRC 5 25 v T 1.5 v T 3 h 4 h 5 h 1 Regular bands of chaotic nature v T A. Lopez-Martens, PRL1(28)1251

Probes of Nuclear Structures 2. Sensitivity to Mass Parameter in Action S ND SD Γ t = hωsd 2π DSD hω SD (1+ e 2 S 1 ) 196 Pb action integral along tunneling path S E ) = ds 2M ( V ( q( s)) E ) path ( M 1 2 driven by pairing M C m M S. Leoni et al. Submitted to PRC

Probes of Nuclear Structures 3. Sensitivity to level density in ND well ND level density S. Goriely et al. RIPL-2 (28) RIPL-2 RIPL-2 (21) Yrast Region of interest U 7 MeV RIPL-2

CONCLUSIONS: Warm Rotation in Superdeformed nuclei is a test bench for 1. cranked shell model at finite temperature 2. tunneling through potential barrier Experimental analysis 151 Tb & 196 Pb: Intensities and Fluctuations of Quasi-continuum spectra Data interpretation: Microscopic Monte Carlo simulation, almost parameter free Evidence for nuclear structure effects: enhanced E1 strength @ E γ = 1-2 MeV Sensitivity to V res, Inertial Mass and ND level density Ideal physics case for intense Stable/Radioactive beams & new generation detector arrays (AGATA & GRETA) Collaborators

Participants to the Experiments Milano University & INFN: A. Bracco, G. Benzoni, N. Blasi, S. Brambilla, F. Camera, F. Crespi, A. DeConto, S. Leoni, P.Mason, D. Montanari, B. Million, M. Pignanelli, O. Wieland IRES, Strasbourg: G.Duchene, J.Robin, D. Curien, Th.Bysrki, F.A.Beck et al., Krackow, Poland: A.Maj, M. Kmiecik, P.Bednarczyk, W. Meczynski, J. Styczen, et al. NBI, Copenhagen: B. Herskind, G. Hagemann, G. Sletten et al. Oliver Lodge Laboratory, University of Liverpool: P.J.Twin KTH, Stockholm: A.Odahara, K.Lagergren + EUROBALL collaborations Theory: E.Vigezzi (Milano University & INFN) M.Matsuo (Niigata University), Y.R.Shimizu (Kyushu University) et al.

194 Hg

Outlook: detailed analysis of other cases 1. The SD NUCLEUS 152 Dy So far investigated in details via a parameter dependent model T.Lautitsen et al., PRC75(27)6439 2. The PECULIAR case of 194 Hg 1 Regular bands of chaotic nature A. Lopez-Martens, PRL1(28)1251 chaotic intrinsic-motion regular rotational decay chaotic rotational decay Can theory reproduce this? ergodic bands rotational damping

n mix 14 12 1 8 6 151 Tb I π = 5 + -48 + -46 + 4 2 14 15 16 17 18 19 E [MeV] 4 151 Tb 196 Pb 194 Hg 194 Hg % 2 <2 2-4 n mix 4-6 >6

E2 strength α> Yb (Z=7) I=4h,U=2MeV highly aligned orbits 16 176 Yb Γ rot 98 168 Yb ω I no highly aligned orbits Γ µ Γ µ I-2 I-2 neutron Γ rot = 2(2 ω ) for U 2 MeV ω = ( ω N ) 2 + ( ω P ) 2

N path 1 5 No decay-out a) 1. Ridge 2 3 4 5 6 7 Spin [h] Ν path = 1/ΣW i 2 the flow bias strongly the population probability U SD [MeV] 1 2 1 8 6 4 2 1-1 1-2 1 1-2 1x1-4 d σ /d I ( 1 5 1 T b ) 1 5 1 T b e) 2 3 4 5 6 7 S p in [h ] N path 22 I = 5,51 h 1 2 3 4 U [MeV] ΣW i 2 W i

Exp. versus Theory I-2 I Cranking Onset of Damping (Chaos) n branch < 2 + decay-out (barriers and pairing) N path N path 75 5 25 1 75 5 25 Number of Discrete Bands 151 Tb 196 Pb SD gated Ridge SD gated Ridge 2. Ridge 2. Ridge 75 5 25 125 1 75 5 25 + Population decay-flow (N path = 1/Σw i^2 ) N path 1 75 5 25 Yrast 1. Ridge Excited bands 1. Ridge 125 1 75 5 25 2 3 4 5 6 7 1 2 3 4 5 Spin Spin Monte Carlo simulation: TEST of theory over wide spin range!