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 GANIL Kewpie2: A cascade code Fission time of SHE: isomeric structure effects Conclusions Advances in Nuclear Physics, Istanbul, 01/07/ GANIL,Caen,France 2 Ankara U.,Ankara,Turkey 3 Caen U.,Caen,France

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

q V ( q ) scission B f saddle initial state LDM fission time E ? Symmetric fission process Advances in Nuclear Physics, Istanbul, 01/07/ Statistical Models: 2- Dynamical Models: ¡ f = ! gs 2 ¼ 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

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

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

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

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

long fission times measured with crystal blocking technique Measurement of fission time of GANIL M. Morjean et al, EPJD 45, 27 (2007). 238 U 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 MeV/u with Z = 124 MeV E ? = Pb 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

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

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

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

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

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

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 £ s -1 E ? = 70 MeV M = m 0 A = 4 ~ ! = 1 B n = 6 Advances in Nuclear Physics, Istanbul, 01/07/2008

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

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

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

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