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
18
Embed
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.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
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...