fusion-fission dynamics for super-heavy elements bülent yılmaz 1,2 and david boilley 1,3 fission...
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Fusion-Fission Dynamics for Super-Heavy Elements
Bülent Yılmaz1,2 and David Boilley1,3
• 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
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, 01/07/2008
1- Statistical Models:
2- Dynamical Models:
¡ f =! gs
2¼
0
@
s
1+µ
¯2! sd
¶2
¡¯
2! sd
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
saddleinitial 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
Fissio
n Fra
gmen
ts 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
n
1 1,A Z
2 2,A Z
1A
2A 1 2A A
1 2Z Z
2A 2A
1A 1A
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=120Z=124
?
Advances in Nuclear Physics, Istanbul, 01/07/2008
long fission times measured with crystal blocking technique
Measurement of fission time of SHE @ GANIL
M. Morjean et al, EPJD 45, 27 (2007).
238U + Ge @ 6.1 MeV/u
%10 of the capture events has tf > 10¡ 18s
A. Drouart et al, AIP Conf. Proc. 1005, 215 (2008).
238U + Ni @ 6.6 MeV/u
with Z = 124 MeVE ? = 70
208Pb + Ge @ 6.2 MeV/u
(> 10¡ 18s)
D. Jacquet et al, AIP Conf. Proc. 853, 239 (2006).
with E ? = 67 MeVZ = 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
dP0
dt = ¡ ¡ t;0P0
dP1
dt = ¡ n;0P0 ¡ ¡ t;1P1
.
.
.dPk
dt = ¡ n;k¡ 1Pk¡ 1 ¡ ¡ t;kPk
Pk ! A ¡ kZXPopulations:
+
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
tf =1
Ptot(0) ¡ Ptot(1 )
Z 1
0tµ
¡dPtot
dt
¶dt
=km a xX
k=0
Z 1
0t¡ f ;kPk(t)dt
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
Bf
P (tf > 10¡ 18s) = 0:3% atat
atatP (tf > 10¡ 18s) = 84%
Bf = Bn=2= 3
Bf = Bn = 6
MeV
MeV
Bf ' j¢ Eshell 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
Ed = 18:5 MeV
Bf (E ?) ' j¢ Eshell j expµ
¡E ?
Ed
¶ ¢ Eshell = 12 MeV
MeV
MeV
up to 5 isotopes
with arbitrarily fixed shell correction energies along the deexitation chain
up to next 2 isotopes¢ Eshell = 10
¢ Eshell = 7 for the others
P (tf > 10¡ 18s) = 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 ¼3£ t(1)
fno evaporation Advances in Nuclear Physics, Istanbul, 01/07/2008
Langevin Equations for the deformation coordinate
_q(t) = p=M
h²(t)²(t0)i = 2M ¯T±(t ¡ t0)
_p(t) = ¡ V0(q) ¡ ¯p+²(t)
h²(t)i = 0 +
Dynamical Model
Monte-Carlo neutron evaporation scheme using Weisskopf rate formula
qBq0 qS qB qSq0
scission
saddle saddle
scission
initial position initial
position
double-bump potentialsingle-bump potential
¯ = 2£ 1021s-1 E ? = 70MeV M = m0A=4 ~! = 1MeV Bn = 6MeV
Advances in Nuclear Physics, Istanbul, 01/07/2008
fission time for Z=124-like nuclei
PreliminaryPreliminary
Advances in Nuclear Physics, Istanbul, 01/07/2008
fission time for Z=124-like nuclei
E ? = 0
E ? = 5MeV
E ? = 20MeV
E ? = 2MeV
¢ Eshell = 10MeV
double-bump potential single-bump potential
¢ E shell
B f (E ?) = V1
·1¡ exp
µ¡
E ?
Ed
¶¸+ V2 exp
µ¡
E ?
Ed
¶
V2
V1
Advances in Nuclear Physics, Istanbul, 01/07/2008
PreliminaryPreliminary
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
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