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 Marchix CEA/DSM Saclay

Reaction to form SHE 2

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,

6 One – two orders of magnitude!

Naik, Loveland et al, Phys. Rev. C 76,

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 Maximum value of σ 1n Z

Survival probability B f 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) ReactionMöllerIvanyuk 208Pb(50Ti,1n)257Rf Pb(54Cr,1n)261Sg Pb(58Fe,1n)265Hs

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.   1 0 We solved the Smoluchowski 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