Rotational Damping and

1
Rotational Damping and Order-to-Chaos transition
in Exotic Nuclei

• Introduction Warm Rotating Nuclei
• ND nuclei
• Spin, Temperature and Shell effects
• SD nuclei
• decay-out and compound/ergodic bands

S. Leoni - Milano University and INFN Milano
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Reaction employed Fusion evaporation 5 MeV/A
Experimental apparatus Ge Ball (AGATA)
particle detectors
spectrometer if Ilt109 pps requested
signals g-energy Eg g-multiplicity Mg ? I g-sum
energy SEg ? E particle identification and
particle energy
EUROBALL IV
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Quasi-Continuum Studies mostly employ fusion
evaporation reactions
Stable beams fission limits the maximum angular
momentum of the nucleus Neutron rich beams
population of larger angular momenta
fission barrier increases with neutron number
Ba (Z56)
I70 ?
Swiatecki-Myers
86Kr 48Ca
Bf MeV
94Kr 48Ca
Bn8 MeV
A
Yb (Z70)
I70 ?
Bf MeV
Bn8 MeV
132Sn 48Ca
48Ca 124Sn
A
P.Fallon ActaPhys.Pol.B36(2005)1003
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Warm Rotating Nuclei
Order-to-Chaos
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1. Rotational Damping Spin Dependence
E2 strength
Dw0
fine structure of rotational damping
I-2
I32 h
damped
S. Leoni et al., PRL93(2004)022501 F. Stephens et
al., PRL88(2002)142501 M. Matsuo et al.,
PLB465(1999)1
discrete
Spiral2 reaction 132Sn(_at_ 560MeV)48Ca?
176Yb(76?)4n
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2. Rotational Damping Temperature effect
Stable48Ca(_at_ 215MeV)124Sn?168Yb(63?)4n Spiral2
132Sn(_at_ 560MeV)48Ca? 176Yb(76?)4n For a
precise selection of initial U Spiral2 74Kr(_at_
325MeV) 58Ni ?128Nd(51?)4p
Motional narrowing Gm gtgt 2Dw0 evolution of the
system towards complexity
168Yb
I40 h
B. Lauritzen et al., NPA457(1986)61.
Døssing, Vigezzi, NPA587(1995)13.
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3. Rotational Damping Shell effects
Grot 2(2Dw0)
for U 2 MeV
168Yb I40h,U2MeV
106
98
neutron
Stable 48Ca 124Sn?168Yb4n Spiral2 132Sn
48Ca? 176Yb4n
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Spiral 1 case Te isotopes
Te isotopes I40h,U2MeV

• EXOGAMVAMOS Proposal (Milano et al.)
• discrete spectroscopy not known I ? 20 h
• Quasi-Continuum Grot
• 1Danalysis only
• due to low beam intensity I ? 106 pps

Stable 64Ni 54Cr ?114Te4n Frattini et al.,
PRL83(1999)5234 Spiral144Ar 82Se ? 122Te4n
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4. SD nuclei A190

• Fission Barrier increases with A
• inner barrier WI increases with A

190Hg
192Pb
E
SD band
192Hg
194Pb
Inner barrier
194Hg
196Pb
I
196Po
198Po
Libert et al., PRC60(1999)054301

• larger cross section for SD population
• spin limit 50? ? 60 ?
• SD intensity higher than 1-2

Spiral2 reaction (?) 50,52Ca150Nd?
196,198Hg(60?)4n
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Quasi-Continuum Decay-Out

• ESD increases with A
• ESD depends on model

Pt
Hg
Pb
Heenen et al., PRC57(1998)1719
Lauritzen et al., PRC62(2000)044316
Test of predictive power of mean-field theory
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5. SD Nuclei Ergodic Bands
regular rotational decay NOT fragmented between
chaotic states
Gm gtgt d gtgt Grot
B. R. Mottelson, Nucl. Phys. A557 (1993) S.
Åberg, Z. Phys. A358 (1997)
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SD states in A190
Highly def states in A110
Population of heavier Hgs Spiral2
50,52Ca150Nd? 196,198Hg(60?)4n Stable 48Ca
150Nd?194Hg(50?)4n
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Conclusions Most interesting reactions for
Quasi-Continuum studies in Exotic Nuclei ND
nuclei 132Sn(_at_ 560MeV)48Ca? 176Yb(76?)4n spin,t
emperature, shell effects 74Kr(_at_ 325MeV) 58Ni
?128Nd(51?)4p temperature effects SD
nuclei 50,52Ca150Nd? 196,198Hg(60?)4n
SD decay-out, ergodic bands 94Kr 26Mg?
114Cd(70?)6n ergodic bands
Milano, Argonne, Berkley, Kyoto, Orsay,
Oslo Benzoni, Bracco, Leoni, Vigezzi, Khoo,
Deleplanque, Matsuo, Lopez-Martens, Siem
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Observation limit Stable Eg 1.4 MeV ? 50
? RIB Eg 1.5 MeV ? 58 ?
Gates at 1.3 MeV and 1.4 MeV
Gates at 1.4 MeV and 1.5 MeV
Counts (nor to 106 gates)
Counts (nor to 106 gates)
Gamma-ray Energy (MeV)
Gamma-ray Energy (MeV)
M.Deleplanque et al.
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Yb nuclei the case for motional narrowing

• lmax 64 h in 168Yb, 76 h in 176 Yb

• Extend observable region of Eg from 1.4 MeV to
  1.5 MeV

Gates at 1.3 MeV and 1.4 MeV
Gates at 1.4 MeV and 1.5 MeV
Counts (nor to 106 gates)
Counts (nor to 106 gates)
Gamma-ray Energy (MeV)
Gamma-ray Energy (MeV)

• Look for motional narrowing

D. Ward et al., Phys. Rev. C66 (2002) 024317,
and W.D. Myers et al., Acta Phys. Polonica B27
(1996) 99.
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Compound Damping Width
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