Study on Sub-barrier Fusion
Reactions and Synthesis of
Superheavy Elements Based on
Transport Theory
Zhao-Qing Feng
Institute of Modern Physics, CAS
Contents
• Introduction
• Improved isospin dependent quantum
molecular dynamics model
• Study on dynamics of fusion reactions
near Coulomb barrier
• Production cross sections of the
superheavy nuclei based on dinuclear
system model
• Summary
1. Introduction
• 60s, 20 century, Shell model prediction:
“stability island” around Z=114,N=184
• Experiments
GSI: 110-112
Dubna: 113-116
Riken: 113
IMP: 105, 107 (new nuclei)
• Theoretical models for the description
of superheavy nuclei:
Dinuclear system model (Adamian et al. NPA 633 (1998)
409, Li et al. EPL 64(2003)750, Feng et al. CPL 22 (2005) 846)
Fluctuation-dissipation model (Aritomo et al. PRC 59
(1999) 796)
Nucleon collectivization model (Zagrebaev et al. PRC
65 (2001) 014607)
Macroscopic dynamical model (S. Bjornholm and W.J.
Swiatecki, NPA 391(1982) 471)
Improved isospin dependent quantum
molecular dynamics model (Wang et al. PRC69 (2004)
034608), Feng et al. NPA 750 (2005) 232
2. Improved isospin dependent
quantum molecular dynamics model
• Purpose: to study fusion mechanism near
Coulomb barrier
• Improved aspects including:
1. Yukawa term is replaced by introducing
density dependent surface term derived from
self-consistently Skyrme interaction. (Wang et al.
PRC 65 (2002) 064608)
2. Introducing surface symmetry term. (Wang et al.
PRC 69 (2004) 034608)
3. Nucleon’s fermionic nature is improved by
using phase space constraint method. (M. Papa et
al. PRC 64 (2001) 024612)
4. Coulomb exchange term is included in
the model. (Wang et al. PRC 67 (2003) 024604)
5. Shell effect is considered in the model.
(Feng et al. NPA, 750 (2005) 232 )
6. Switch function method is introduced in
the model, which can effectively prevent
some unphysical nucleus emissions in the
process of projectile and target
appoarchng. (Feng et al. HEP&NP,2005,29(1) 41 )
2.1 Introduction on the improved isospin
dependent quantum molecular dynamics
model
• In the improved model, the effective interaction
potential energy is denoted as
U  U coul  U vol  U sym  U surf  U eff  U shell
U coul
e2

4
1
(1  tiz )(1  t jz )erf (rij / 4 L ) 

i
j  i ri j
1/ 3
3 3
e  
4 
2
U vol

4/3
p

dR
 ij
 ij








2 i j i  0
 1 i 
 j i  0






 


Csym
 ij 
3  ri  rj
U sym 
tizt jz
1  k sym 
 


2 i j i
0
2L  2L



  2

g surf
3  ri  rj  ij
 
  
U surf 

2 i j i  2 L  2 L    0



ij 


U eff  g   


i  j i
0 
  2
 (ri  rj ) 
1
ij 
exp 

3/ 2
4 L 
4L 

Csymk sym
 2  
 (r )  (r )dr
U surf -sym  
20



2


 
• Switch function method is introduced, which can
prevent some unphysical nucleons emission. So the
surface interaction energy of the system is written as
surf
surf
surf

U syst
 U proj
 U tsurf
S

U
arg
comp (1  S ).
S is called as switch function
S  C0  C1
R  Rlow
R  Rlow 2
R  Rlow 3
 C2 (
)  C3 (
) 
Rup  Rlow
Rup  Rlow
Rup  Rlow
R  Rlow 4
R  Rlow 5
C4 (
)  C5 (
)
Rup  Rlow
Rup  Rlow
Taking coefficients must satisfy the continuity of the
surface energy and its first derivative!
C0
C1
C2
0
0
0
C3
10
C4
C5
-15
6
Parameter set in the model
/MeV /MeV  Csym/MeV ksym/fm2 gsurf/MeVfm2 g /MeV 0/fm-3
-356.0
303.0
7/6
32.0
0.08
8.0
10.0
0.165
Parameter set taken by Wang et al.
The ground state properties, static (dynamical) barriers
fusion (capture) excitation function as well as neck
dynamical behaviour et al. can be described very well
using the improved model.
2.2 Consideration of shell effect in ImIQMD
• As we know that shell effect is the diversity of shell
model (shell structure) and macroscopic model (bulk
property). Thus, the shell correction energy can be
obtained from the variance of shell levels and
uniformed levels, which is written by
Eshell
~
 E  E.
Using Strutinsky method (NPA 95 (1967) 420), the
shell correction energy is written as



~ [ N / 2]
Eshell  E  E  2  ei  2  e g (e)de
i 1

 (e  ei ) 2   e  ei 
 f 

g (e) 
exp  

2

  i

   
1
• The smoothed level density is usually given by
Gaussian distribution width   1.2.
In the calculation, 3rd-order Laguerre polynomial is
used. The Fermi energy is obtained by
N 2

 g (e)de.

The shell levels are calculated by using deformed
two center shell model. (R.A. Gherghescu, Phys. Rev. C 67
(2003) 014309)
• In ImIQMD, the Shell correction energy is denoted by
U
IQMD
shell

Eshell
 
dr .
2
a1  exp r  R  / a 
Using canonical equation, the force can be obtained as
 IQMD Eshell
exp r  R  / a  
Fshell 
r,
2 0
a 1  exp r  R  / a 
One can obtain the force of each nucleon derived from
the shell correction energy as
i

ei  ei
exp ri  R  / a 
Fshell 
r
2 0
a
1  exp ri  R  / a 
From energy density functional, we can also know that
shell effect mainly embodies the surface of the nucleus!
(M. Brack, C. Guet, H.B. Hakansson, Phys. Rep. 123 (1985) 276)
• Considering the Woods-Saxon distribution form of
the nuclear density , it is more self-consistently by
denoting the shell correction energy as
 
IQMD
U shell   Eshell dr .
0
 IQMD
Eshell
Fshell  
 ,
0
i
ei  ei
Fshell  
 i
0
DTCSM levels
It is very important to fill these
levels in ImIQMD. In our
calculation, we label each nucleon
according to angular momentum
and single particle energies,
which are obtained respectively

by
2




p


z
Li   (ri  pi ) z , ei  i   i    i 
2m
0
 0 
48
Ca+
U
smoothed proton levels
DTCSM proton levels
Ca
g(e)
80
f5/2
f7/2
50
s1/2/ d3/2
40
d5/2

30
p1/2
p3/2
20
s1/2
10
proton levels

smoothed neutron levels
DTCSM neutron levels
50
30
20
f 7/2
d3/2
s1/2
d5/2
p1/2
p3/2
10
s1/2
0.0
0.4
0.8
1.2
1.6
0.0
0.4
0.8
1.2
1.6
0.0
0.4
0.8
1.2
1.6
0.0
(R-Ri)/(Rt-Ri)
15
proton
Eshell
neutron
Eshell
10
Eshell
Eshell/MeV
E/MeV
40
5
0
-5
-10
0.0
0.5
1.0
(R-Ri)/(Rt-Ri)
1.5
0.4
0.8
1.2
1.6
EFermi=41.77MeV
E/MeV
60
EFermi=42.54MeV
70

238
smoothed levels
48
3. Dynamical study on fusion
reactions near Coulomb barrier
• Based on improved isospin dependent quantum
molecular dynamics model, the static and dynamical
Coulomb barrier, fusion/capture cross sections,
neck dynamical behaviour et al. are studied
systematically.
3.1 Dynamical barrier
V ( R)  E pt ( R)  E p  Et
Here, Ept, Ep and Et are the total, projectile and target
energy respectively, the kinetic energy part is
approximated by using Thomas-Feimi model as
2/3
2
2
 3  i 
3 


Ekin 

5 2m i  2 
The static nucleus-nucleus interaction potential
300
48
200
Vb
h
Ca+
208
Pb
w
V/MeV
100
0
Total
Prox.
Kinetic
Skyrme
Symmetry
Surface
Coulomb
Effective
-100
-200
-300
4
8
12
R/fm
16
20
Static barriers, prox. (W.D. Myers et al., PRC 62 (2000) 044610)
300
300
48
Vb/MeV
250
208
Ca+
ImIQMD
Prox.
200
238
Ca+
U
200
150
150
100
100
50
50
5
10
15
20
25
120
5
10
15
20
25
15
20
25
120
16
16
208
O+
100
Vb/MeV
48
250
Pb
Pb
80
80
60
60
40
40
20
238
O+
100
U
20
5
10
15
R/fm
20
25
5
10
R/fm
Dependence on the projectile-target combinations
leading to the same compound nucleus formation 258Rf
350
350
124
300
Vb/MeV
134
Sn+
Xe
86
ImIQMD
Prox.
250
250
200
200
150
150
100
172
Kr+
300
Er
100
5
10
15
20
25
300
5
10
15
20
25
20
25
140
24
50
Ti+
250
234
Mg+
208
Pb
U
120
Vb/MeV
200
100
150
80
100
50
60
5
10
15
R/fm
20
25
5
10
15
R/fm
The static and dynamical interaction potentials calculated
by using the ImIQMD for the reaction sytems40,48Ca+40,48Ca.
40
40
40
48
48
48
Ca+ Ca,Vb=56.28MeV
70
50
Ca+ Ca,Vb=54.42MeV
60
Ca+ Ca,Vb=50.61MeV
Ca+ Ca,Vb=48.70MeV
40
40
Ca+ Ca,Vb=47.23MeV
48
Ca+ Ca,Vb=45.68MeV
48
48
b= 0 fm
50
Vb/MeV
40
40
20
30
30
16
12
Vshell/MeV
Vb/MeV
40
20
10
Ec.m.=50MeV (below the static barriers)
20
8
4
0
0
2
4
6
8
10
R/fm
0
0
4
8
12
R/fm
16
20
8
10
12
14
R/fm
16
18
Dependence of dynamical barriers on incident energy
250
Vb=198.5 MeV (Prox. 2000)
48
Ca+
238
Vb=177.7 MeV (Adiabatic barrier)
U
Vb=203.8 MeV (waist to waist )
Vb=187.0 MeV (pole to pole)
Vb=182.6 MeV (Ec.m.=220 MeV)
Vb=174.4 MeV (Ec.m.=200 MeV)
200
Vb/MeV
Vb=169.8 MeV (Ec.m.=190 MeV)
Vb=167.6 MeV (Ec.m.=180 MeV)
Vb=166.4 MeV (Ec.m.=175 MeV)
150
100
4
8
12
16
R/fm
20
24
Dependence of fusion barrier on projectile neutron
number leading to the same element formation
340
340
320
320
Z=110
238
300
260
240
Vb/MeV
220
200
30
40
50
60
Ca+ U
232
Ti+ Th
226
Cr+ Ra
210
Fe+ Rn
210
Ni+ Po
208
Zn+ Pb
202
Ge+ Hg
194
Se+ Pt
192
Kr+ Os
186
Sr+ W
180
Zr+ Hf
176
Mo+ Yb
164
Pd+ Dy
152
Sn+ Sm
300
232
Ca+ Th
226
Ti+ Ra
208
Ni+ Pb
202
Zn+ Hg
194
Ge+ Pt
192
Se+ Os
186
Kr+ W
176
Zr+ Yb
160
Pd+ Gd
150
Sn+ Nd
280
180
20
Z=112
70
340
280
260
240
220
200
180
20
30
40
50
60
70
360
244
Ca+ Pu
238
Ti+ U
232
Cr+ Th
226
Fe+ Ra
210
Ni+ Rn
210
Zn+ Po
208
Ge+ Pb
202
Se+ Hg
188
Kr+ Pt
192
Sr+ Os
186
Zr+ W
180
Mo+ Hf
176
Ru+ Yb
168
Pd+ Er
166
Cd+ Dy
160
Sn+ Gd
Z=114
320
300
280
260
240
220
200
20
30
40
50
60
70
80
Z=116
340
248
320
Ca+ Cm
238
Cr+ U
226
Ni+ Ra
210
Ge+ Po
202
Kr+ Hg
192
Zr+ Os
180
Ru+ Hf
168
Cd+ Er
166
Sn+ Dy
152
Xe+ Sm
300
280
260
240
220
200
20
Nproj
30
40
50
60
70
80
3.2 Neck dynamical behaviour
Time evolution of N/Z at neck region for 40,48Ca+ 40,48Ca
4.5
4.5
Ec.m.=50MeV below the barriers for b=0fm
4.0
3.5
40
2.5
2.5
2.0
1.5
1.5
1.0
1.0
0
50
100
150
-1
t/(fmc )
200
40
Ca+ Ca
48
Ca+ Ca
48
48
Ca+ Ca
3.0
2.0
0.5
40
40
N/Z
N/Z
3.5
40
Ca+ Ca
40
48
Ca+ Ca
48
48
Ca+ Ca
3.0
Ec.m.=60MeV above the barriers for b=0fm
4.0
250
0.5
0
50
100
150
-1
t/(fmc )
200
250
5.0
208
Ca+
4.0
Pb
N/Z(Ec.m.=190MeV)
N/Z(Ec.m.=200MeV)
3.5
N/Z
N/Z dependence on
incident energy at neck
region for system
48Ca+208Pb
48
4.5
3.0
2.5
2.0
1.5
1.0
0
20
40
60
80
100
120
140
T/(fm/c)
60
48
238
Ca+
50
40
Ntrans
Nucleon transfer in neck
region for reaction
system 48Ca+238U
U, Ec.m.=200 MeV
48
p( Ca)
48
n( Ca)
238
p( U)
238
n( U)
30
20
10
0
200
250
300
350
T/(fm/c)
400
450
500
Neck radius development in the process of neck formation
8
Rneck/fm
6
4
48
48
208
Ec.m.=200 MeV
2
238
Ca+ U, Ec.m.=190 MeV
Ca+ Pb
Waist to Waist
pole to pole
Ec.m.=180 MeV
0
0
100
200
t/(fm/c)
300
0
100
200
t/(fm/c)
300
400
3.3 The calculation of fusion/capture
cross sections
 fus ( E )  2
bmax
 p fus ( E, b)bdb
Fusion excitation functions for 40,48Ca+40,48Ca
0
1000
1000
40
40
40
Ca+ Ca
Experimental data taken in
Refs M. Trotta et al., Phys.
Rev. C 65 (2001) R011601
H.A Aljuwair et al., Phys.
Rev. C 30 (1984) 1223
100
fus/mb
fus/mb
100
48
Ca+ Ca
10
exp
ImIQMD
IQMD
1
10
exp(M. Trotta et al.)
exp(H. A. Aljuwair et al.)
IQMD(Wang et al.)
ImIQMD(this work)
(b)
IQMD(this work)
1
(a)
0.1
0.1
48
50
52
54
56
58
60
62
64
66
68
70
48
50
52
54
56
Ec.m./MeV
1000
60
62
64
66
68
70
1000
48
48
Ca+ Ca
100
fus/mb
100
fus/mb
58
Ec.m./MeV
10
exp
ImIQMD
IQMD
1
10
40Ca+40Ca
40Ca+48Ca
48Ca+48Ca
1
(c)
(d)
0.1
0.1
48
50
52
54
56
58
60
Ec.m./MeV
62
64
66
68
70
48
50
52
54
56
58
60
Ec.m./MeV
62
64
66
68
70
Positive Q value will lead to the enhancement of subbarrier fusion cross sections
3
fusion cross section
10
18
58
O+ Ni
16
60
O+ Ni
2
10
1
10
30
35
40
45
50
55
Ec.m./MeV
40,48Ca+124,116Sn, 16,18O+42,40Ca, 9,11Li+208,206Pb
PRC 67 (2003) 061601R.
suggested by V.I. Zagrebaev
Capture cross sections for heavy systems
3
10
48
3
208
10
Ca+ Pb
48
238
Ca+ U
cap/mb
cap/mb
2
10
1
10
2
10
exp
ImIQMD
exp
ImIQMD
0
1
10
170
175
180
185
Ec.m./MeV
190
195
200
10
180
190
200
210
220
Ec.m./MeV
Experimental data taken from E.V Prokhorova et al., nuclexp/0309021 and W.Q Shen et al., Phys. Rev C 36 (1987) 115
230
240
3
10
2
10
cap/mb
M. Dasgupta et al., Nucl. Phys A
734 (2004) 148
K. Nishio et al., Phys. Rev. Lett
93 (2004) 162701
16
1
10
16
208
O+ Pb
exp
ImIQMD
238
O+ U
exp
ImIQMD
0
10
70
80
90
100
110
75
80
Ec.m./MeV
90
95
Ec.m./MeV
3
10
48
244
Ca+
Pu
2
10
/mb
M. G. Itkis, Yu. Ts. Oganessian,
E. M. Kozulin et al.,
Proceedings on Fusion
Dynamics at the Extremes,
Dubna, 2000, edited by Yu. Ts.
Oganessian and V. I.
Zagrebaev page 93.
85
exp
ImIQMD
1
10
0
10
190
195
200
205
210
Ec.m./MeV
215
220
225
230
Preliminary consideration on the calculation of the
evaporation cross sections based on ImIQMD
Formation probability at excitation energy E* is written
as
P
PCN ( E*) 
0
 E  E *
1  exp  0

  
Where E0 is the critical excitation energy depending on
the reaction system,  is the barrier distribution width,
we can take it as
  (B  B ) / 2
s
d
So the evaporation cross section can be denoted by
bmax
 evap  2  bp fus ( E, b)PCN ( Ec.m. )Wsur ( Ec.m. , b)db
0
4. Production cross sections of the
superheavy nuclei based on dinuclear
system model
• In dinuclear system mdoel, evaporation cross
section is denoted by
 c ( Ec.m. )    2 (2 J  1)T ( Ec.m. , J )PCN ( Ec.m. , J )Wsur ( Ec.m. , J )
J
Cap.
Q-fission
Fission
Schematic illustration of the fusion process
•   2 /( 2Ec.m. ) , T(Ec.m.,J) is usually taken 0.5.
A
• Fusion probability PCN ( J )   P( A1 , E1 ( J ), int ( J )) dA1
BG
0
• The mass distribution probability P(A1,E1,t) is given by master
equation
dP( A1 , E1 , t )
 WA , A' [d A1 P( A1' , E1' , t )  d A' P( A1 , E1 , t )]
1
1
1
dt
A1'
which is solved numerically in the model.
If only considering the competition of neutron emission and
fission, the survival probability Wsur with emitting X neutrons can
be written as
*
x 


(
E
, J)
*
*
n
i


Wsur ( ECN , x, J )  P( ECN , x, J ) 
*
*
i 1  ( E , J )   ( E , J ) 
f
i
 n i
i
Energy and angular-momentum dissipation are described by
Fokker-Planck equation
f p f u f
l f

2

2



  v p f   2 D p f   vl f   2 Dl f 
t  r r p rel 
p
p
l
l
Based on dinuclear system model, the production cross
sections of superheavy nuclei in cold fusion reactions
are studied systematically.
350
258
ABG
20
Rf
50
208
Ti+ Pb
124
Xe+ Sn
58
208
Fe+ Pb
130
136
Xe+ Xe
134
Bfus=29.96MeV
0
Vcn/MeV
U/MeV
300
Bfus=14.29MeV
10
250
-10
200
Hpocket
-20
150
-30
-1.0
-0.5
0.0
0.5
1.0

10
12
14
16
18
R/fm
• In the DNS model, the compound nucleus formation is governed
by the driving potential.
U ( A1 , R)  U LD ( A1 )  U LD ( A2 )  U LD ( A)  U C ( A1 , R)  U N ( A1 , R)
• Height of the pocket are
6.39 MeV (0.61) 4.80 MeV (0.56)
1.70 MeV (0.04)
1.71MeV (0.02)
20
Feng, Jin, Fu et al., Chin. Phys. Lett., 22(4), 2005, 846
7
Bcoul
10
Bin=6 MeV
136
10
5
50
208
Bin=6 MeV
4
10
259
Xe+ Sn Rf+n
6
10
124
3
10
257
Ti+ Pb Rf+n
58
208
265
Fe+ Pb Hs+n
4
10
Bin=14 MeV
Bin=14 MeV
2
10
10
2
10
exp
vibr+transfer
this work(4.49MeV(Moeller))
this work(3.84MeV(DTCSM))
vibr+transfer
vibr+transfer
this work(4.49MeV(Moeller))
this work(4.12MeV(Moeller))
1
10
0
10
-1
10
-2
/pb
/pb
3
134
124
257
136
124
259
Xe+ Sn Rf+n
1
10
0
10
-1
10
Xe+ Sn Rf+n
10
-2
exp
vibr+transfer
this work(5.27MeV(Moeller))
this work(2.88MeV(DTCSM))
vibr+transfer
vibr+transfer
this work(5.27MeV(Moeller))
130
136
265
Xe+ Xe Hs+n
10
176
180
184
188
192
280
284
288
292
208
212
216
Ec.m./MeV
220
224 304
308
312
Ec.m./MeV
Production cross sections for asymmetric and nearly
symmetric reaction systems, comparison
with coupled channel model which has included
nucleon transfer and surface vibration is also shown.
(V.Yu. Denisov Prog. Part. Nucl. Phys. 46 (2001) 303)
316
320
Improvement of dinuclear system model
• In order to describe correctly the capture process,
barrier distribution function method is included in the
model. (P.H. Stelson, PLB 205 (1988) 190, V.I. Zagrebaev et al., PRC 65 (2001)
014607) The transmission coefficient is denoted as
T ( E c . m. , J )   f ( B )
1
 2 


 B 
1  exp 
J ( J  1)  E 
2
2R ( J )

  ( J ) 
2
dB
2


The barrier distribution
 B  Bm  
exp  
 , B  Bm
function satisfies the

  1  

normalization condition, f ( B)  N 
2

which is usually taken

 B  Bm  
 , B  Bm
exp  
as a asymmetric
2  






Gaussian distribution
form.
 f ( B)dB  1
• Here Bm=(B0+Bs)/2, B0 and Bs are the height of the
Coulomb barrier and the saddle point respectively.
Gaussian distribution function 2= (B0-Bs)/2, 1 is
less than the value of 2 (usually 2 MeV). V. I.
Zagrebaev PRC64 (2001)034606
208
48
Ca+ Pb
350
200
300
200
V/MeV
250
Vb()/MeV
V(R,=0)/MeV
V0=180.6 MeV
V0=180.6 MeV
200
160
*
V
0
*Vs
150
160
RB=12.22 fm
10
12
R/fm
Vs=163.9 MeV
=0.81
=0.
14
-0.5
0.0
100
0.5

1.0
8
10
1.5
12
R/
1.5
1.0
14
fm
0.5
16
0.0
18
-0.5
20
22
-1.0

Capture cross section can be reproduced very well by
introducing the barrier distribution function method
3
10
48
3
208
10
Ca+ Pb
2
10
2
10
cap/mb
cap/mb
1
10
exp
T=0.5
vibrational coupling
ECCM
H-W formula
0
10
-1
10
1
10
48
238
Ca+ U
0
10
-2
-1
10
10
170
180
Ec.m./MeV
190
200
160
180
200
Ec.m./MeV
220
240
Comparison of calculated evaporation residue cross
sections with experimental data for 1,2,3,4 neutron
emission
3
10
3
208
48
Ca+ Pb
2
256-xn

capture
1n
2n
3n
4n
2n(Oganessian et al.)
calculated results
1
10
0
10
-1
/mb
10
-2
10
48
2n
1n
1
10
-xn

1n
2n
3n
4n
2
10
-3
10
206
Ca+ Pb
2n
10
/nb
10
3n
4n
0
10
3n
-4
10
4n
1n
-5
10
-1
10
-6
10
-7
-2
10
10
5
10
15
20
25
30
E*/MeV
35
40
45
50
55
15
20
25
30
35
40
45
50
55
60
E*/MeV
Experimental data taken from E.V Prokhorova et al., nucl-exp/0309021
Yu. Ts. Oganessian et al., Phys. Rev. C 64, 054606 (2001).
2n
10
/pb
Production cross sections of
superheavy nuclei 286-xn112,
292-xn114, 296-xn116 in 48Ca
induced reactions and
comparison with Dubna data
238
U
1
0.01
25
30
10
244
Pu
35
40
45
E*/MeV
50
2n
4n
2n
3n
0.1
(Yu.Ts. Oganessian et al., PRC 70 (2004)
064609)
10
4n
55
60
4n
248
Cm
3n
3n
5n
/pb
/pb
1
1
5n
0.1
0.1
0.01
0.01
25
30
35
40
45
E*/MeV
50
55
60
25
30
35
40
45
E*/MeV
50
55
60
Extension to multi-dimension degree of
freedom for the driving potential
• In the DNS model, we only consider the mass asymmetry degree
of freedom, so there is some difficulties for describing the mass
distribution of quasi-fission or fission, as well as reasonably
showing the formation process of the compound nucleus. We
need to consider the center of mass distance R and deformation
degree of freedom  et al. in the process of the superheavy
compound nucleus formation.
Y. Aritomo, M. Ohta, NPA 744 (2004) 3
5. Summary
• The isospin dependent quantum molecular dynamics
model is improved by introducing switch function
method for the surface term and considering shell
effect. Experimental fusion/capture cross sections
can be reproduced very well using the improved
model. Fusion barrier and neck dynamical behaviour
in fusion process are studied systematically.
• The dinuclear system model is improved by
introducing the barrier distribution function method,
dynamical deformation is considered in the capture
process. Evaporation residue cross sections can be
regenerated well for 1n,2n,3n 4n evaporation. Further
studies are in progress!