1. Fusion-Fission Dynamics for Super-Heavy Elements Bülent Yılmaz 1,2 and David Boilley 1,3 Fission of Atomic Nuclei Super-Heavy Elements (SHE) Measurement of fission time of SHE @ GANIL Kewpie2: A cascade code Fission time of SHE: isomeric structure effects Conclusions Advances in Nuclear Physics, Istanbul, 01/07/2008 1 GANIL,Caen,France 2 Ankara U.,Ankara,Turkey 3 Caen U.,Caen,France

2. Symmetric fission process Surface tension vs. Coulomb repulsion q V ( q ) scission B f saddle initial state LDM fission time E ? Advances in Nuclear Physics, Istanbul, 01/07/2008

3. q V ( q ) scission B f saddle initial state LDM fission time E ? Symmetric fission process Advances in Nuclear Physics, Istanbul, 01/07/2008 1- Statistical Models: 2- Dynamical Models: ¡ f = ! gs 2 ¼ 0 @ s 1 + µ ¯ 2 ! s d ¶ 2 ¡ ¯ 2 ! s d 1 A e ¡ B f = T diffusion over the fission barrier by Langevin or Fokker-Planck equations (q,p) space

4. Symmetric fission process q V ( q ) scission B f saddle initial state E ? Advances in Nuclear Physics, Istanbul, 01/07/2008 sample stochastic events

5. neutron gamma proton alpha Deexcitation Scheme of Hot Compound Nucleus... Evaporation Residue Fission Fragments Advances in Nuclear Physics, Istanbul, 01/07/2008

6. Super-Heavy Elements Heaviest nuclei Synthesis by heavy-ion fusion reactions Existance of critical initial center of mass energy Low production cross section (picobarn) No liquid drop potential barrier Stability by shell correction energies Reaction mechanism leading to SHE Advances in Nuclear Physics, Istanbul, 01/07/2008

7. Island of stability predicted due to shell closure Nuclear Chart Z=114 N=184 Z=120 Z=124 ? Advances in Nuclear Physics, Istanbul, 01/07/2008

8. long fission times measured with crystal blocking technique Measurement of fission time of SHE @ GANIL M. Morjean et al, EPJD 45, 27 (2007). 238 U + Ge @ 6.1 MeV/u %10 of the capture events has t f > 10 ¡ 18 s A. Drouart et al, AIP Conf. Proc. 1005, 215 (2008). 238 U + Ni @ 6.6 MeV/u with Z = 124 MeV E ? = 70 208 Pb + Ge @ 6.2 MeV/u ( > 10 ¡ 18 s ) D. Jacquet et al, AIP Conf. Proc. 853, 239 (2006). with E ? = 67 MeV Z = 120 long fission times observed no hint of long fission time Z = 114 New probe into SHE stability: M. Morjean et al, accepted to PRL Advances in Nuclear Physics, Istanbul, 01/07/2008

9. Kewpie2: A Cascade Code d P 0 d t = ¡ ¡ t ; 0 P 0 d P 1 d t = ¡ n ; 0 P 0 ¡ ¡ t ; 1 P 1... d P k d t = ¡ n ; k ¡ 1 P k ¡ 1 ¡ ¡ t ; k P k P k ! A ¡ k Z X Populations: + Bohr-Wheeler fission rate with Strutinsky and Kramers corrections Weisskopf neutron rate Mean Fission Time Kewpie2: A. Marchix, PhD Thesis (2007). Kewpie: B. Bouriquet, Comp. Phys. Com. 159, 1 (2004). Fission Time Distribution Bateman equations ¡ t ; k = ¡ f ; k + ¡ n ; k t f = 1 P t o t ( 0 ) ¡ P t o t ( 1 ) Z 1 0 t µ ¡ d P t o t d t ¶ d t = k max X k = 0 Z 1 0 t ¡ f ; k P k ( t ) d t Advances in Nuclear Physics, Istanbul, 01/07/2008

10. Kewpie2: A Cascade Code How can we reach 10% of long-fission events? with a constant potential B f P ( t f > 10 ¡ 18 s ) = 0 : 3 % at at P ( t f > 10 ¡ 18 s ) = 84 % B f = B n = 2 = 3 B f = B n = 6 MeV B f ' j ¢E s h e ll j Advances in Nuclear Physics, Istanbul, 01/07/2008

11. Using Moller and Nix shell correction energies, the statistics of the long fission times calculated by Kewpie2 are far smaller than what is observed experimentally for Z=120 and Z=124 nuclei. Kewpie2: A Cascade Code How can we reach 10% of long-fission events? with a damped potential according to Ignatyuk’s presription E d = 18 : 5 MeV B f ( E ? ) ' j ¢E s h e ll j exp µ ¡ E ? E d ¶ ¢E s h e ll = 12 up to 5 isotopes with arbitrarily fixed shell correction energies along the deexitation chain up to next 2 isotopes ¢E s h e ll = 10 ¢E s h e ll = 7 for the others P ( t f > 10 ¡ 18 s ) = 9 % Advances in Nuclear Physics, Istanbul, 01/07/2008

12. Isomeric Structure Are the observed long fission times due to high fission barriers or/and isomeric potential structures? some possible double-bump (isomeric) shapes single-bump shape Advances in Nuclear Physics, Istanbul, 01/07/2008

13. B f In order to understand the consequences of the potential structure beyond the saddle point two potential shapes has been considered. optimizes fission time Isomeric Structure some possible double-bump (isomeric) shapes single-bump shape t ( 2 ) f ¼ 3 £ t ( 1 ) f no evaporation Advances in Nuclear Physics, Istanbul, 01/07/2008

14. Langevin Equations for the deformation coordinate _ q ( t ) = p = M h ² ( t ) ² ( t 0 ) i = 2 M ¯ T ± ( t ¡ t 0 ) _ p ( t ) = ¡ V 0 ( q ) ¡ ¯ p + ² ( t ) h ² ( t ) i = 0 + Dynamical Model Monte-Carlo neutron evaporation scheme using Weisskopf rate formula q B q 0 q S q B q S q 0 scission saddle scission initial position double-bump potential single-bump potential ¯ = 2 £ 10 21 s -1 E ? = 70 MeV M = m 0 A = 4 ~ ! = 1 B n = 6 Advances in Nuclear Physics, Istanbul, 01/07/2008

15. fission time for Z=124-like nuclei Preliminary Advances in Nuclear Physics, Istanbul, 01/07/2008

16. fission time for Z=124-like nuclei E ? = 0 E ? = 5 M e V E ? = 20 M e V E ? = 2 M e V ¢E s h e ll = 10 M e V double-bump potentialsingle-bump potential ¢E s h e ll B f ( E ? ) = V 1 · 1 ¡ exp µ ¡ E ? E d ¶¸ + V 2 exp µ ¡ E ? E d ¶ V 2 V 1 Advances in Nuclear Physics, Istanbul, 01/07/2008

17. Preliminary fission time for Z=124-like nuclei Advances in Nuclear Physics, Istanbul, 01/07/2008

18. Conclusions Very large barriers are still necessary to explain the long fission time Thank You In future, if we have more precise measurement of fission time and distribution we cannot forget about the isomeric states. This study will be continued with more realistic model... Advances in Nuclear Physics, Istanbul, 01/07/2008