Can we constrain the fusion hindrance?
David BOILLEY and Hongliang LÜ (吕宏亮 )
GANIL and Normandie Université
Yasuhisa ABE (阿部恭久 )RCNP, Osaka:( 大阪大学核物理研究センター )
Caiwan SHEN (沈彩万 )Huzhou Teachers’ College:(湖州师范学院 )
Anthony MarchixCEA/DSM Saclay
2
Reaction to form SHE
Experimental fusion hindrance
K.-H. Schmidt & W. Morawek Rep. Prog. Phys. 54 (1991) 949
Reseparation
Coulomb barrier
Quasi-fission
Inner barrier
Fission
SHE
Unknown inner barrier
Naik, Loveland et al, Phys. Rev. C 76, 054604
6
One – two orders of magnitude!
Naik, Loveland et al, Phys. Rev. C 76, 054604
What’s the problem?
• The best known part has the same discrepancies than the less known part!
• Is it due to uncertainties?
Experiments
Models
Experimental uncertainties
Max
imum
val
ue o
f σ1n
Z
Survival probability
• Bf < Bn => Fission dominates:
• Parameters entering the fission width have a great influence
• Fission barrier is most sensitive parameter• Nuisance parameters:
– Damping energy: – Friction coefficient:
Nuisance parameters
Fission barriers
• In the past:
• Nowadays:– Tables: Moller et al
Various models
Various models (2)
Fission barriers (MeV)
Reaction Möller Ivanyuk
208Pb(50Ti,1n)257Rf 5.65 4.47
208Pb(54Cr,1n)261Sg 5.91 4.57
208Pb(58Fe,1n)265Hs 6.26 5.22
Summary
Partial conclusions
• Fusion hindrance and fission barriers are both unknown
• How to progress?– Measurement of fission barriers:
• Heaviest nucleus is No
– Microscopic models:• Only the Coulomb barrier
Fusion by diffusion
• Effective barrier to have half of the particles to over pass the saddle
Y. Abe, D. B., B.G. Giraud and T. Wada, Phys. Rev. E61, 1125 (2000)D. B., Y. Abe and JD Bao, Eur. Phys. J. A18, 627 (2003)
Potential lanscape
Importance of the neck
The value of the neck parameter differs from authors
Neck dynamics
V()=f.
10
We solved theSmoluchowski equation
Neck equilibrates very quickly <> 0.1
Position of the inner barrier
Fusion hindrance for symmetric reactions
Borderline between hindered and non hindered reactions
Dynamical coupling
• Rapid neck evolution affects the initial value of the other parameters:– To the asymmetry parameter:
– To the radius:• Initial shift that increases hindrance
Test on a simple case
Exact solution for a saddle made with 2
parabolas
Conclusions
• Theoretical uncertainty are larger than experimental ones
• Uncertainty analysis helps to pin down important parameters
• Beyond parameters, reduction to small number of degrees of freedom should be done carefully
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