fusion-fission process in super heavy mass region...reaction mechanism of fusion-fission process in...
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Reaction mechanism of fusion-fission process in superheavy mass region
Y. Aritomo1, K. Hagino2, K. Nishio1, and S. Chiba1
1Japan Atomic Energy Agency, Tokai, Japan2 Department of Physics, Tohoku University, Sendai, Japan
「微視的核反応理論による物理」YITP, Kyoto, Japan, 1-3 August, 2011
1. ModelCoupled-channels method + Dynamical Langevin calculation
Trajectory analysis Langevin equationTwo center shell model
2. Results36S+238U and 30Si+238U
Mass distribution of Fission fragmentsCapture Cross-sectionFusion Cross-section
3. Mechanism of Dynamical processPotential energy surface on scission lineAnalysis of trajectory behaviorAnalysis of probability distribution
4. Summary
36S + 238U30Si + 238U
Exp. by
K. Nishio
et al.
Zcn=106 Zcn=108
Phenomenalism
Dynamical Model based on Fluctuation-dissipation theory
(Langevin eq, Fokker-Plank eq, etc) Classical trajectory analysis
We can obtain…. Fission, Synthesis of SHE
Mass and TKE distribution of fission fragments ACN : 200~300
Neutron multiplicity
Charge distribution
Cross section (capture, mass symmetric fission, fusion)
Angle of ejected particle, Kinetic energy loss ( two body)
Conditions
Nuclear shape parameter
Potential energy surface (LDM, shell correction energy, LS force)
Transport coefficients (friction, inertia mass) Liner Response Theory
Dynamical equation (memory effect, Einstein relation)
What we can obtain under the conditions
1. Model
1. 1-1. Potential
2. 1-2. Dynamical Equation
1-3. Simulation of Experiment and Cross Sections
Estimation of cross sections
Capture Cross Section
Fusion Cross Section
Coupled-channel method
Dynamical calculation
Langevin eq.
CN
Formation probability PCN
計算処方の概観
Time-evolution of nuclear shape
in fusion-fission process
1. Potential energy surface
2. Trajectory described by
equations
Model: Outlook of calculation methods
two-center parametrization
(Maruhn and Greiner,
Z. Phys. 251(1972) 431)
),,( z
Nuclear shape
δ=0
(δ1=δ2)
Trajectory which enters
into the spherical region
= fusion trajectory
( , , )q z
2
0
( 1)( , , ) ( ) ( , )
2 ( )
( ) ( ) ( )
( , ) ( ) ( )
DM SH
DM S C
SH shell
V q T V q V q TI q
V q E q E q
V q T E q T
T : nuclear temperature
E* =aT2 a : level density parameter
Toke and Swiatecki
ES : Generalized surface energy (finite range effect)
EC : Coulomb repulsion for diffused surface
E0shell : Shell correction energy at T=0
I : Moment of inertia for rigid body
Φ(T) : Temperature dependent factor
MeV 20
exp)(2
d
d
E
E
aTT
Potential Energy
qi : deformation coordinate （nuclear shape）
two-center parametrization (Maruhn and Greiner, Z. Phys. 251(1972) 431)
pi : momentum
mij : Hydrodynamical mass (inertia mass）
γij: Wall and Window (one-body) dissipation （friction ）
)(2
1 11
1
tRgpmppmqq
V
dt
dp
pmdt
dq
jijkjkijkjjk
ii
i
jiji
ijjk
k
ik
ijjii
Tgg
tttRtRtR
process) (Markovian noise white:)(2)()( ,0)( 2121
),,( z
)(2
1 1*
int qVppmEE jiij
energy excitation : energy, intrinsic : *
int EE
多次元ランジュバン方程式Multi-dimensional Langevin Equation
Newton equationFriction Random force
dissipation fluctuation
Two Center Shell Model
2
22
LS L0
ˆ ( ) ( ) ( )2
H V V Vm
r r p s r p
r
a2a1
r R=0.75 (1+ )0 2/3 r
z =z1 2=0r r r
z
z2a1 a2
b1
b2
a1 | |z1z2 a2
b2
|zmax1
| zmin2
| |z1
E0
E
e= /E0E
z
V V V
V0
b1
b1 b2
( )a ( )b ( )c
J. Maruhn and W. Greiner, Z. Phys, 1972
2 2 2 2
1 1 1
2 2 2 2 2 2
1 1 1 1 1
1
2 2 2 2 2 20 2 2 2 2 2
2
2 2 2 2
2 2 2
1 1
01
( ) 1 12
0
z
z
z
z
z z z
z c z d z g z
z z
V z m z c z d z g z
z z
z z z
r
r
r
r
r
r
r r
r
1
2
0
0
z z zz
z z z
Neck parameter is the ratio of smoothed potential
height to the original one where two harmonic
oscillator potential cross each other
ε = 1.0
0.35
0.0
224Th
Time dependent adiabatic fusion-fission potential
Time-dependent
weight function
V. Zagrebaev, A. Karpov, Y. Aritomo, M. Naumenko and W. Greiner, Phys. Part. Nucl. 38 (2007) 469
0.4
0.8 3.31.8 2.81.3 2.3 3.8
0.2
0.6
0.8
1.0
r/R0n
eck p
ara
me
ter
()e
2. Results
2-2.
1. Capture and Fusion Cross sections
2. Mass distribution of Fission Fragments
34, 36S+238U and 30Si+238U 2-2.
Touching probability CC method
Perform a trajectory calculation
starting from the touching distance between target and projectile
to the end each process.
Fusion box and Sample trajectory 36S+238U
E*= 40 MeV
L = 0
θ = 0
z-α
δ=0
z-δ
α=0
QF
FFFF?
QF
FF
DQF
Results 36S+238U MDFF and Cross sections
FF
process
Results 30Si+238U MDFF and Cross sections
3. Mechanism of Dynamical process
30Si+238U 36S+238U
200u74u
137u
178u90u
134u
Clarification of the mechanism of Fusion-fission process
MDFF at Low incident energy
0.4
0.8 3.31.8 2.81.3 2.3 3.8
0.2
0.6
0.8
1.0
r/R0
neck p
ara
me
ter
()e
(a) 1-dim Potential energy on scission line
30Si+238U
36S+238U
(b) Trajectory Analysis on Potential Energy Surface z-A plane
E* = 35.5 MeV
L=0, θ=0
30Si+238U
δ=0.22, ε=1.0
δ=0.22, ε=0.35
δ=0.22, ε=1.0
E* = 39.5 MeV
L=0, θ=0
36S+238U
Trajectory Analysis on Potential Energy Surface 30Si+238U
E* =
35.5 MeV
L=0, θ=0
Trajectory Analysis on Potential Energy Surface 36S+238U
E* =
39.5 MeV
L=0, θ=0
0.8 1.0 1.2 1.4 1.60.48
0.60
0.72
0.84
B
z0.8 1.0 1.2 1.4 1.6
0.48
0.60
0.72
0.84
B
z0.8 1.0 1.2 1.4 1.6
0.48
0.60
0.72
0.84
B
z
Trajectory Analysis using ALL trajectories
~40,000 points
(c) Trajectory Analysis “Probability Distribution”
E* =
35.5 MeV
L=0, θ=0
E* =
39.5 MeV
L=0, θ=0
3. Summary
1. In order to analyze the fusion-fission process in superheavy mass region, we apply the Couple channels method + Langevin calculation.
2. Incident energy dependence of mass distribution of fission fragments (MDFF) is reproduced in reaction 36S+238U and 30Si+238U.
3. The shape of the MDFF is analyzed using (a) 1-dim potential energy surface on the scission line (b) sample trajectory on the potential energy surface (c) probability distribution
4. The relation between the touching point and the ridge line is very importantto decide the process fusion hindrance
leading to synthesize SHE
4. Summary
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