1. Quasi-continuum studies in superdeformed 151Tb and 196Pb nuclei
G. Benzoni
Outline:
SD decay out at T=0 and T≠0
The experiments
Analysis
Results
Perspectives
INFN sezione di Milano e
Universita’ degli Studi di Milano

2. SD bands are found in many nuclei A = 30,60,80,130,150,160,190
Typical intensity pattern:
loss of intensity at low energies
Rigid body
Super deformed band
superfluid
Counts * 103
196Pb
SD band
Decay-out
Feeding
Plateau
Intensity %
Eg [keV] SD ND
quantum tunneling
btw SD and ND minima
phase transition normal  superfluid system

3. 196Pb Evidences of discrete linking transitions in few nuclei SDND
3698
4062
196Pb
High-energy transitions
Low intensity
 ~ 10-4% channel
Highly fragmented decay
 high level density
A.N. Wilson et al., Phys. Rev. Lett. 95 (2005)
Need for AGATA-like arrays
What can we do already now ???
study of average properties of SD discrete excited bands
 analysis of quasi-continuum spectra

4. Rotational motion at finite temperature (T≠0) 0 < U < 1-2 MeV
168Yb
 RIDGE
 VALLEY
2:1
I+2 I
I-2
Regular bands
T0
Ridges: unresolved discrete regular bands
(Eg1 –Eg2) (keV)
Counts
Do SD ridges have same properties as discrete SD yrast band ???
A.Bracco and S.Leoni, Rep.Prog.Phys. 65 (2002) 299

5. Two different nuclei in comparison 151Tb and 196Pb
Euroball, Strasburgo (Fr)
HECTOR
Thin target, Ebeam = 155 MeV
27Al + 130Te  157Tb*
30Si + 170Er  200Pb*
Thin target, Ebeam = 150 MeV
BGO INNER BALL
Ridges analysis:
- Moment of inertia  ridge ≈ yrast
Intensity of SD ridge
FWHM of SD ridge
Comparison with cranked shell model calculations + decay out
Number of paths (discrete bands)

6. 151Tb 196Pb Up to now full analysis performed only in 143Eu
 proved the need to include tunneling effects
S. Leoni at al. PLB 498(2001)137
196Pb
Need other cases in different/similar mass regions
151Tb
152Dy
Spin
N(2)path
192Hg
To be also compared to 192Hg and 152Dy for which theory is available

7. Ridge consists of many discrete bands
Ridges in coincidence with SD yrast band
1600
1200
800
400
-50 50
-100
<Eg> = 532 keV
(Eg1 –Eg2) (keV)
100
Counts
<Eg> = 1280 keV
151Tb
196Pb
MeV
MeV
151Tb
Eg [keV]
Intensity %
150
300
151Tb
FWHM [keV]
Ridge
<FWHM> = 11.7 keV
Discrete trans SD ND
Eg [keV]
FWHMridge ≈ 4×FWHMyrast
Intensityridge ≈ 3x Intensityyrast
Ridge consists of many discrete bands

8. Npath  number of discrete unresolved bands forming the ridge
Fluctuation analysis
Npath  number of discrete unresolved bands forming the ridge
151Tb
Mean Npath = Tb
45 196Pb tot matrix
15 and 25 in direct coincidence
Npath decreasing at low energies
Theory overestimates Npath

9. Statistical model of decay-out
ND SD
Spacing of SD states
ACTION
Transmission coeff. SD
Calculated along the tunneling path ND
Probability to “fly out” from SD minimum
EM decay width
Spacing of ND states
152Dy
Pout
Eexc
Vigezzi et al., PLB 249(1990)163.
Gu and Weidenmuller, NPA660(1999)197
Yoshida, Matsuo and Shimizu NPA 696 (2001)

10. No decay-out rND  Cr rND S  Cmass S decay-out Results for 151Tb
143Eu
151Tb
Cranked shell model T ≠ 0
Npath
Eg [keV]
 comparison with theory including tunneling not yet ready
Rescaled curve of 143Eu already gives good agreement
No decay-out
decay-out
Results for 196Pb
Theory  Iout =12 
Exp.  Iout = 6  (Eexc = 0 MeV )
Need to use renormalization factors
rND  Cr rND
S  Cmass S
Cr = 2e-4
Cmass = 3
(pairing)

11. Conclusions Perspectives Acknowledgments…
Investigation of SD excited bands in 151Tb and 196Pb
SD ridge structures found in both nuclei
Npath ~ Tb
~ Pb in tot matrix
Comparison with cranked shell model calculations including tunneling
Good agreement for 196Pb…still to finalise for 151Tb
additional info on pairing (Cmass) and level density (Cr)
Perspectives
MONTECARLO simulation to study decay flux in coincidence with SD yrast
Comparison with existing analysis on 192Hg
(T.L.Khoo and A.Lopez-Martens)
Acknowledgments…

12. M.Matsuo, Y.R.Shimizu and E.Vigezzi for CSM calculations
Participants to the experiments
G.Benzoni, S.Leoni, A.DeConto, D.Montanari, A.Bracco, N.Blasi, F.Camera, B.Million, O.Wieland
Dipartimento di Fisica, Universita’ degli Studi di Milano and INFN sezione di Milano, Via Celoria 16, Milano, Italy
Maj, M.Kmiecik
Niewodniczanski Institute of Nuclear Physics, Krakow, Poland
B.Herskind
The Niels Bohr Institute, Blegdamsvej 15-17, 2100, Copenhagen
G.Duchene, J.Robin, Th.Bysrki, F.A.Beck,
Institut de Recherches Subatomiques, 23 rue du Loess,F-67037, Strasbourg, France
P.J.Twin
Oliver Lodge Laboratory, University of Liverpool, P.O. Box 147, Liverpool L69 7ZE, UK
A.Odahara, K.Lagergren
KTH,Royal Institute of Technology,Physics Department, Frescativägen 24,S , Stockholm, Sweden
M.Matsuo, Y.R.Shimizu and E.Vigezzi for CSM calculations
(Niigata University) (INFN Milano)

13. 196Pb Intensity of SD ridge vs. intensity of yrast SD 151Tb 196Pb
300
600
900 2 6 10
 8.5 keV
Ridge SD ND
FWHM [keV]
Discrete trans
196Pb
Intensity of SD ridge vs. intensity of yrast SD
Eg [keV]
Intensity %
150
300
151Tb
196Pb

14. Actions  decreasing at increasing spin decreasing at increasing Eexc
 Easier to “fly out”
Different behaviour for 151Tb and 196Pb
Decay-out properties (Iout, Eout) expected to be different
Pout