Fusion-Fission Dynamics for Super-Heavy Elements

1. 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 Fusion-Fission Dynamics for Super-Heavy Elements Bülent Yılmaz1,2 and David Boilley1,3 1 GANIL,Caen,France2 Ankara U.,Ankara,Turkey 3 Caen U.,Caen,France Advances in Nuclear Physics, Istanbul, 01/07/2008

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

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

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

5. Deexcitation Scheme of Hot Compound Nucleus Fission Fragments Fission Fragments . . . gamma neutron proton Evaporation Residue alpha 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. Nuclear Chart Island of stability predicted due to shell closure Z=124 ? Z=120 Z=114 N=184 Advances in Nuclear Physics, Istanbul, 01/07/2008

8. ? ? E E 6 7 0 7 Z Z Z 1 1 1 2 1 2 4 4 0 = = = = = 1 8 1 8 ¡ ¡ ( ) 1 0 1 0 t > > s s f Measurement of fission time of SHE @ GANIL long fission times measured with crystal blocking technique with 238U + Ge @ 6.1 MeV/u MeV %10 of the capture events has M. Morjean et al, EPJD 45, 27 (2007). with MeV 238U + Ni @ 6.6 MeV/u long fission times observed D. Jacquet et al, AIP Conf. Proc. 853, 239 (2006). 208Pb + Ge @ 6.2 MeV/u no hint of long fission time A. Drouart et al, AIP Conf. Proc. 1005, 215 (2008). New probe into SHE stability: M. Morjean et al, accepted to PRL Advances in Nuclear Physics, Istanbul, 01/07/2008

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

10. 1 1 8 8 ¡ ¡ ( ( j = j ) ) % % P P B B B B B B ¢ E 1 1 0 0 2 6 3 8 0 4 3 t t > > ' s s = = = = = = f f f f f f h l l n n s e : Kewpie2: A Cascade Code How can we reach 10% of long-fission events? with a constant potential at MeV at MeV Advances in Nuclear Physics, Istanbul, 01/07/2008

11. 1 8 ¡ ( ) % P E ¢ ¢ ¢ E E E 1 8 1 5 0 1 7 1 0 2 9 t > s = = = = = d f h h h l l l l l l s s s e e e : µ ¶ E ? ( ) j j ? B E ¢ E ¡ ' e x p f h l l s e E d Kewpie2: A Cascade Code How can we reach 10% of long-fission events? with a damped potential according to Ignatyuk’s presription 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. with arbitrarily fixed shell correction energies along the deexitation chain MeV up to 5 isotopes MeV up to next 2 isotopes MeV MeV for the others 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? single-bump shape some possible double-bump (isomeric) shapes Advances in Nuclear Physics, Istanbul, 01/07/2008

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

14. 2 1 = ¯ ~ ? M E B A 2 1 7 6 0 1 0 4 £ q q q q q q ! m = = = = = S S B B 0 0 0 n 0 0 0 h ( ( ) ) ( ) i h ( ( ) ( ) i ) = ( ( ) ) ¯ ¯ ± V M M T _ _ 2 0 t t t t t t t t ¡ ¡ + ¡ p ² ² q ² q p p ² = = = = Dynamical Model Langevin Equations for the deformation coordinate Monte-Carlo neutron evaporation scheme using Weisskopf rate formula + MeV MeV MeV s-1 double-bump potential single-bump potential saddle saddle initial position initial position scission scission 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. ¢ E h l l s e ? ? ? ? E E V ¢ E V E E M M M V V V M V 2 2 5 0 0 1 0 e e e e = = = = = h l l 1 2 s e · µ ¶ ¸ µ ¶ ? ? E E ( ) ? B E V V 1 ¡ ¡ + ¡ e x p e x p = f 1 2 E E d d fission time for Z=124-like nuclei double-bump potential single-bump potential Advances in Nuclear Physics, Istanbul, 01/07/2008

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

18. Conclusions • Very large barriers are still necessary to explain the long fission time • 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... Thank You Advances in Nuclear Physics, Istanbul, 01/07/2008