Montecarlo simulation of the decay of warm superdeformed nuclei

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Montecarlo simulation of the decay of warm superdeformed nuclei E. Vigezzi INFN Milano Understanding the dynamics in the SD well: probing γ strength functions, energy barriers, level densities, residual interactions S. Leoni et al., PRL 11, 14252 (28); PRC; to be published

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 Statistics: 8 days 2 1 8 <F Ge > = 3 <F > = 1 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 Statistics: 17 days 9 1 9 <F Ge > = 5 <F > = 22 discrete spectroscopy in SD well (J. Robin et al., PRC77, 1438(28)) search for linking transitions SD ND (J. Robin et al., PRC78, 34319(29))

Quasi-Continuum Spectroscopy: Warm Rotation RIDGES Discrete Unresolved Bands E* 168 Yb 168 Yb I-2 I I+2 T= T I-2 I I+2 E2 bump I+1 spectra I I+8 I+6 I+4 I+2 I

Compound Nucleus Chaos Warm Rotation strongly interacting bands I I-2 I+2 SD T= Regular bands Order L m ND ND SD tunneling SD to ND minima

151 Tb Analysis SD gated spectrum E2 Bump SD gated 1 st Ridge Rot-Plane 2 nd Ridge Total 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 E = 1 kev 25 E = 2 kev 7 5 3 E = 1 kev -1 1 E 1 -E 2 [kev] Intensity [%] Intensity [%] Intensity [%] Intensity [%] Intensity 1 3 E2 SD gated 1 1 3 SD gated Ridge 1 1 3 2. Ridge 1 1 3 1 8 independent observables Yrast I yrast = 2 % 1. Ridge 3 4 5 6 7 N path N path N path Number of Discrete Bands Counts Fluctuations 75 5 25 1 75 5 25 1 75 5 25 N (2) path 14 ± 2 12 ± 5 27 ± 8 Neve P 2 1 1 SD gated Ridge 2. Ridge 1. Ridge 1 observed 2 3 4 5 6 7

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

Intensity [%] Intensity [%] Intensity [%] Intensity [%] Intensity 1 3 E2 SD gated 1 1 3 SD gated Ridge 1 1 3 2. Ridge 1 1 3 1 Yrast I yrast = 2 % 3 4 5 6 7 1. Ridge 151Tb 4% of the yrast intensity: The rest must come from damped bands 2-3 times higher than the yrast intensity: bands decay to ND well

at T Vnn = 34 MeV fm 3 Vnp= 5 MeV fm 3 H = H def - J x + V res Configuration mixing

E2 fragmentation rotational damping Width [kev] 35 3 25 2 15 1 5 rot I-2 I rot n branch 1 1 1 151 Tb n branch = 2 n branch = 2 onset of damping x 1/1 I = 5 + I = 4 + I-2 I 3 4 5 6 7 1 2 3 4 U [MeV] K. Yoshida, M. Matsuo, NPA612(1997)126

E2 ND E1 E2 SD E1 extrapolated SD, B(E2), barriers 2 E* [MeV] ND tunneling SD rot microscopic levels, B(E2), barriers 15 rot I-2 I I+2 SD 1 ND -decay in SD well: microscopic + extrapolated 3 4 5 6

Microscopic calculations for decay-out at T K. Yoshida, M. Matsuo and Y. Shimizu, NPA696, 85(21) ND SD M t 1 2 DSD 1 2 1 e action integral S ( E ) ds 2M ( V ( q( s)) E ) path along tunneling path 2S driven by pairing S S 2 15 1 5 12 1 151 Tb (,+) U =. MeV U =. MeV.4 196 Pb.2 (,+) 8.4.6 6.8 1. 4 1.2 1.4 2 1.6 1.8 3 4 5 6.8 1.6 2.4 2.8 3.6 4.4 5.2 extension of model used for SD yrast 152 Dy

Ingredients of the Monte Carlo simulation: Microscopic levels in SD well and actions: calculated up to 5 MeV above yrast (151 Tb) and 3 MeV (196Pb); extrapolated above. Inertial mass multiplied by.7 (151Tb) and 2.5 (196Pb) E2 transitions: calculated in the SD well; schematic parametrization in the ND well E1 transitions: GDR tail, with a scaling factor to reproduce yrast intensity Entry distribution: calculated Level density in the ND well: P. Demetriou and S. Goriely, NPA 695 (21) 95

151 Tb: simulated -spectra Counts [arb. un.] counts [x1 3 ] 6 4 2 7 5 3 Total matrix E = 1 kev E = 1 kev SIMUL DATA -1 1 E 1 -E 2 [kev] Counts [arb. un.] counts [x1 3 ] 15 1 5 15 1 5 SD gated matrix E = 1 kev E = 1 kev -1 1 E 1 -E 2 [kev] counts counts 15 1 5 375 125 175 25 2 15 1 5 E2 SD gated 75 125 175 E SIMUL DATA

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

SD gated quantities are sensitive to E1/E2 balance Enhanced dipole transitions have been observed in A= 15 and A = 19 196 Pb, 19 Hg 194 Hg 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 than GDR tail Theory: J. Kvasil et al., PRC75 (27)3436 T. Nakatsukasa et al., PLB343(1995)19

Results are sensitive to the absolute value and to the spin-dependence of the calculated actions

Why to consider fluctuations? T. Dossing et al, Phys. Rep. 268 (1996) 1 Because they give a measure of the number of paths populating a certain region of the γ-γ spectrum. N path = 1/ Σ W i 2 Npath along the ridge gives a measure of the number of discrete bands as a function of angular momentum. But: each band is weighted by the square of its intensity. When all paths have the same probability, W i = 1/Ntrue and Npath= Ntrue

n mix 14 12 1 8 6 151 Tb I = 5 + -48 + -46 + 4 2 14 15 16 17 18 19 E [MeV] 194 Hg 194Hg: Bands survive in the mixing region. They are based on mixed states but are not damped (ergodic bands). Can they be populated and affect the fluctuation spectra?

Exp. versus Theory I Cranking Onset of Damping n branch < 2 N path 75 5 25 Number of Discrete Bands 151 Tb 196 Pb SD gated Ridge SD gated Ridge 75 5 25 I-2 + decay-out N path 1 75 5 25 2. Ridge 2. Ridge 125 1 75 5 25 + Population (N path = 1/w i2 ) N path 1 75 5 25 1. Ridge 1. Ridge 125 1 75 5 25 2 3 4 5 6 7 3 4 5 Strong suppression due to uneven population of the bands

194Hg : 1 Regular bands of chaotic nature A. Lopez-Martens et al., PRL1(28)1251

Conclusions Warm Rotation in Superdeformed nuclei is a test bench for cranked shell model at finite temperature & tunneling through potential barrier Experimental analysis 151 Tb & 196 Pb: Intensities and Fluctuations of Quasi-continuum spectra provide strong constraints on theoretical models Possibility of testing decay-out models over a wide spin range Data interpretation: Microscopic Monte Carlo simulation, reducing free parameters to the minimum Good overall agreement with data Indication of nuclear structure effects in the E1 strength at low excitation energy (~ 1 MeV) Collaboration

Participants to the Experiments Milano University & INFN: S. Leoni, A. Bracco, G. Benzoni, N. Blasi, S. Brambilla, F. Camera, F. Crespi, A. DeConto, 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., Krakow, 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: M.Matsuo (Niigata University), Y.R.Shimizu (Kyushu University), E.V.

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

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

151 Tb: simulated discrete SD bands population 1 4 = + YRAST 1 3 even spins 1 4 = - 1 3 even spins Intensity 1 Intensity 1 1-1 1-1 1-2 25 3 35 4 45 5 55 6 65 7 1-2 25 3 35 4 45 5 55 6 65 7 75 1 4 = + 1 4 = - 1 3 odd spins 1 3 odd spins Intensity 1 Intensity 1 1-1 1-1 1-2 25 3 35 4 45 5 55 6 65 7 1-2 25 3 35 4 45 5 55 6 65 7 75

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 Yrast 1 2 3 4 5 6 7 8.2-.8 MeV 2 2 2 4 6 8 2 14 Number of SD band 2 4 6 8 2 14 Number of SD band 151 Tb tentative assignment SD SD 196 Pb firm assignment 3698 462 ND ND J. Robin et al., submitted to PRC A.N. Wilson et al., Phys. Rev. Lett. 95 (25)

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% -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: Study of warm rotation in 151 Tb and 196 Pb Evaluation of several independent experimental oservables stringent test of -decay flow THEORY: Development of new Monte Carlo model Based on microscopic calculations Towards a parameter free model

196 Pb microscopic calculations Cranked shell model at T E2 fragmentation U (MeV) U (Mev) 2. 1.5 1..5. 2. 1.5 1..5. H = H def J x + V res = - yrast (,+) 3 4 5 6 red even green odd = + n branch Width [kev] 1 1 1 196 Pb n branch = 2 n branch = 2 rot I-2 onset of damping I = 3 +..5 1. 1.5 2. 2.5 U [MeV] 25 2 15 1 5 I x 1/1 rot I = 2 + 3 4 5 K. Yoshida, M. Matsuo, NPA612(1997)126 I-2 I

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

Exp. versus Theory Analysis of Intensities 151 Tb 196 Pb exclusive quantities SD gated decay-flow inclusive quantities average decay-flow Intensity [%] Intensity [%] Intensity [%] Intensity [%] 1 3 E2 SD gated 1 1 3 SD gated Ridge 1 1 3 2. Ridge 1 1 3 1 1. Ridge Yrast I yrast = 2 % 3 4 5 6 7 Intensity [%] Intensity [%] Intensity [%] Intensity [%] 1 3 1 1 3 1 1 3 1 1 3 1 E2+M1 E2 SD gated SD gated Ridge Yrast I yrast = 1.3% 2. 2Ridge 1. Ridge 3 4 5 SD gated spectrum E2 Bump SD gated 1 st Ridge Rot-Plane 2 nd Ridge Total 1 st Ridge

Exp. versus Theory Analysis of Intensities 151 Tb 196 Pb exclusive quantities SD gated decay-flow inclusive quantities average decay-flow Intensity [%] Intensity [%] Intensity [%] Intensity [%] 1 3 2. Ridge 1 1 3 1 1 3 E2 SD gated 1 1 3 SD gated Ridge 1 1. Ridge Yrast I yrast = 2 % 3 4 5 6 7 Intensity [%] Intensity [%] Intensity [%] Intensity [%] 1 3 1 1 3 1 3 1 1 3 1 E2+M1 Yrast I yrast = 1.3% E2 SD gated SD gated Ridge 2. 2Rid Ridge 1. Ridge 3 4 5 SD gated spectrum E2 Bump SD gated 1 st Ridge Rot-Plane 2 nd Ridge Total 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 ] 4x9 3x9 2x9 1x9 SD 5 5 2 25 3 E [MeV] 7 6 enhanced GDR T. Lauritsen et al., PRL89(22)28251 D. Rosbach et al. PLB513(21)9 B(E1) ~ 1-4 -1-3 W.u. 1 to 1 times stronger Theory: Nilson + QRPA J. Kvasil et al., PRC75 (27)3436 T. Nakatsukasa et al., PLB343(1995)19 T(E1) [s -1 ] 5 4 3 2 Standard GDR 151 Tb.5 1. 1.5 2. 2.5 E [MeV]

The E1 decay strength: the tail of the GDR f GDR = Sum of 3 Lorentzian ND SD T 3 ( E1) H1 n K E1 B( E1) E E2 E1 E2 E1 T(E1) [s -1 T(E1) [s -1 ] 4x9 19 3x9 19 2x9 19 1x9 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) 55 5 2 25 3 E [MeV]

n mix 14 12 1 8 6 151 Tb I = 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

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 ] 4x9 3x9 2x9 1x9 SD 5 5 2 25 3 E [MeV] 7 6 enhanced GDR T. Lauritsen et al., PRL89(22)28251 D. Rosbach et al. PLB513(21)9 B(E1) ~ 1-4 -1-3 W.u. 1 to 1 times stronger Theory: Nilson + QRPA J. Kvasil et al., PRC75 (27)3436 T. Nakatsukasa et al., PLB343(1995)19 T(E1) [s -1 ] 5 4 3 2 Standard GDR 151 Tb.5 1. 1.5 2. 2.5 E [MeV]

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