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