Fusion hindrance and SHE D. Boilley GANIL and Univ. Caen CEA, Saclay: On the prediction for the SHE production RCNP, Osaka: B. Giraud ( 大阪大学核物理研究センター ) Yasuhisa Abe GANIL, Caen: ( 阿部恭久) Anthony Marchix Kazimierz Dolny, Sept. 20011 Yoann Lallouet Huzhou Teachers’ College: ( 湖州师范学院 ) Ankara university: Caiwan Shen ( 沈彩万 ) Bülent Yilmaz
Questions for theoreticians Can we guide the experiments ? What is the shell correction energy ? Difficulties On the prediction for the SHE production Models cannot be extrapolated from lighter systems Fusion hindrance Kazimierz Dolny, Sept. 20011 Extremely low cross sections Few data with few information
Blocking technique in crystals Introduction Premier point On the prediction for the SHE production Chapitre 1 Section 1 … Kazimierz Dolny, Sept. 20011 F. Goldenbaum et al., PRL 82 (1999) 5012
Direct evidence for long fission times Mesurements at GANIL by crystal blocking techniques Fission barriers Z = 124 A = 312 From P. MÖLLER et al., At least 12 % of the capture At. Dat. And Nucl. Dat. Tab. 59 (1995) 185 events with a life time longer than On the prediction for the SHE production 10 -18 s Quasi-elastic (target) Z = 120 A = 296 At least 10 % of the capture events with a life time longer than 10 -18 s Kazimierz Dolny, Sept. 20011 Z = 114 A = 282 Very low statistic or no events with a life time longer than 10 -18 s 1 � f � 10 � 21 s M. Morjean et al, Eur. Phys. J. D45 (2007) 27 & PRL101, 072701 (2008)
KEWPIE 2 Main ingredients Formalism: Weisskopf or Hauser- Feshbach Bohr-Wheeler Level density: Bohr-Mottelson with On the prediction for the SHE production angular dependence Level density parameter: Töke-Swiatecki Suppression of shell Kazimierz Dolny, Sept. 20011 energy corrections according to Ignatyuk dP Collective n P f + � i n ) P i i � 1 ( t ) � ( � i i ( t ) dt = � i � 1 enhancement included A. Marchix, PhD thesis, Univ. Caen (2007)
Simplified model Fission vs neutron Bf=Bn evaporation Bn=6 MeV & Bf Fission time constant along the chain On the prediction for the SHE production Long fission times mean: B f ≈ B n Pre-scission neutrons Long fission time events occur after Kazimierz Dolny, Sept. 20011 evaporation of several neutrons We cannot extract Bf of each isotope D.B. et al, IJMP E17 (2008) 1681-1693
What about Δ E shell ? a ground = a .(1 + (1 � e � E */ E d ). � E shell ) E * B f � e � E */ E d . � E shell On the prediction for the SHE production Experimental results for Z=120 and 124 cannot be reproduced with Möller’s table Kazimierz Dolny, Sept. 20011 Very large Δ E shell for the first isotopes of the evaporation chain Potential structure effects ?
On the prediction for the SHE production Preliminary E* = 20MeV E E* = 2MeV E ? = 0 = 5MeV Structure effect 2 Kazimierz Dolny, Sept. 20011
On the prediction for the SHE production Residue cross sections Kazimierz Dolny, Sept. 20011
KEWPIE 2 Specificity It is not a Monte-Carlo code to calculate very low probabilities It is based on a discretisation in bins of the energy spectra: On the prediction for the SHE production Kazimierz Dolny, Sept. 20011
Residue cross sections Important parameters of KEWPIE2 Shell correction energy -> correction factor � E shell = f . � E Moller Damping Energy E d On the prediction for the SHE production a ground = a .(1 + (1 � e � E */ E d ). � E shell ) E * Originally, Ed =18.5 MeV B f � e � E */ E d . � E shell Kazimierz Dolny, Sept. 20011 Reduced friction β =2.10 21 s -1 A. Marchix, PhD thesis, Univ. Caen (2007)
Results Fitting the residue cross sections gives very strong constraint on Δ E shell … • Precision of 1 MeV On the prediction for the SHE production … if we know the fusion cross section Kazimierz Dolny, Sept. 20011
Reaction Reseparation Quasi-fission Fission On the prediction for the SHE production Kazimierz Dolny, Sept. 20011 Inner barrier Coulomb barrier SHE How to assess the fusion model?
Experimental fusion hindrance On the prediction for the SHE production Kazimierz Dolny, Sept. 20011 K.-H. Schmidt & W. Morawek Rep. Prog. Phys. 54 (1991) 949
On the prediction for the SHE production Position of the inner barrier Kazimierz Dolny, Sept. 20011
Importance of the neck The value of the neck parameter differs from authors On the prediction for the SHE production Kazimierz Dolny, Sept. 20011
Neck dynamics V( ε )=f. ε On the prediction for the SHE production ε 0 1 We solved the Smoluchowski equation Kazimierz Dolny, Sept. 20011 Neck equilibrates very quickly < ε > ≈ 0.1
On the prediction for the SHE production Fusion hindrance for symmetric reactions Kazimierz Dolny, Sept. 20011
On the prediction for the SHE production Fusion hindrance for symmetric reactions Kazimierz Dolny, Sept. 20011
On the prediction for the SHE production Influence of the shift Kazimierz Dolny, Sept. 20011
On the prediction for the SHE production Borderline between hindered and non hindered reactions Kazimierz Dolny, Sept. 20011
Adiabatic approximation Fast degree of freedom V( ε )=f. ε (neck) vs slow degree of freedom (r) Tensor coupling Shift of the initial condition in r ε On the prediction for the SHE production 0 1 Larger hindrance due to dynamical coupling! Kazimierz Dolny, Sept. 20011
On the prediction for the SHE production solution for a saddle made parabolas with 2 Exact Test on a simple case Kazimierz Dolny, Sept. 20011
On the prediction for the SHE production http://www.ensarfp7.eu/workshops/fushe2012/ Advertisement Kazimierz Dolny, Sept. 20011
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