Dynamical approach to synthesis of superheavy elementsseminar/RIBF-NPseminar/NP-Semi...29th October,...
Transcript of Dynamical approach to synthesis of superheavy elementsseminar/RIBF-NPseminar/NP-Semi...29th October,...
Dynamical approach to synthesis of superheavy elements
Y. Aritomo
Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology, Tokyo, Japan Flerov Laboratory of Nuclear Reactions, Dubna, Russia
the RIBF Nuclear Physics Seminars 169th
29th October, 2013
Fl
1. Introduction Superheavy Elements and Theoretical approaches 2. Model Dynamical model with Langevin equation Two center shell model
3. Results Evaporation residue cross section Mass distribution of Fission fragments
4. The way to synthesize new Superheavy elements by secondary beam
5. Summary
Contains
Lv Fl May 2012 IUPAC
104 105 106 107 108 109 110 111 112
flerovium livermorium
Periodic Table
Менделеев(1834-1907)
1869
Super Heavy Elements less stable
1. Introduction Nuclear Chart and Stability of Nuclei
Our Interests
・ Next magic number Z=82, N=126
・ Verification of ‘Island of Stability’
(predicted by macroscopic-microscopic
model in 1960’s)
・ Synthesis of new elements
Yu.Ts.Oganessian
0
5
10
Po
ten
tial
energ
y
(in M
eV)
Deformation
0.3.10 s.-6
1016
92U
years
Z=108
22 years later ....
0
5
10
92U
98Cf
Pote
nti
al e
ner
gy (i
n M
eV)
Deformation
Liquid DropModel
Z=108
1016
years
G. Flerov and K. Petrjzak
Leningrad 1940
N. Bohr and J.A. Wheeler (1939) Mayer and Jensen (1949) Magic numbers
Microscopic Theory
Models:
Macro-microscopic
Hartry-Fock-Bogolubov
Relativistic-mean-field
268106162
298114184
Quadrupole deformation β2
LD
Pote
ntial energ
y /
MeV
LD + shell
25098152
Fission barrier of Superheavy Elements
Shell correction energies in the
macroscopic-microscopic model
5
2
22 50.883 1 1.7826
C
S
E Z Ax
E N Z A
fissility parameter
Spherical nucleus
Surface energy
Coulomb energy
2 2 34SE r A
2 2
1 3
0
3
5C
e ZE
r A
Stability of Superheavy nuclei
Ys.Ts. Oganessian, Yu.A. Lazarev Treatise on Heavy-Ion Science vol.4 (1985)
1020
Z=107 104
102
LDM LDM
10
Experimental setup for synthesis of SHE
Lab Country City Accelerator Separator
FLNR Russia Dubna U400 U400M
DGFRS VASSILISSA
GSI Germany Darmstadt UNILAC SHIP TASCA
RIKEN Japan Wako RILAC GALIS
LBNL USA Berkeley 88-inch Cyclotron BGS
GANIL France Caen SPIRAL2's LINAC accelerator
S3 (Super Separator Spectrometer)
G.N. Flerov
(1913 -1990)
Yu.Ts. Oganessian
(1933-)
P. Armbruster
(1931-)
S. Hofmann
(1943-)
G. Muenzenberg
(1940-)
K. Morita
(1957-)
Fusion process in Superheavy mass region
FUSION
TRANSFER, QUASI-FISSION
Nuclear Molecule
Compound
Nucleus (CN)
Evaporation
Residue (ER)
FUSION-FISSION
Fission
Fragments 90~99%
„Cold“ and „Hot“ Fusion Reactions
Cold Fusion → doubly magic target nuclei: Pb, Bi;
E*(CN) = 10 – 20 MeV; evaporation of 1 – 2 neutrons;
up to now successful for Z ≤ 113
Hot Fusion → actinide targets (U, Cm, …) and 48Ca projectiles;
E*(CN) = 30 – 40 MeV; evaporation of 3 – 4 neutrons;
up to now successful for Z ≤ 118
reaction Q-value large
reaction Q-value small
Cold fusion reaction Hot fusion reaction 1994
110 Ds 62Ni + 208Pb 269110 + n (GSI)
111 Rg 64Ni + 209Bi 272111 + n (GSI)
1996
112 Cn 70Zn + 208Pb 277112 + n (GSI) named in Feb. 2010
1999
114 Fl 48Ca + 244Pu 292114 + 3n (FLNR) named in May. 2012
2000
116 Lv 48Ca + 248Cm 292116 + 4n (FLNR) named in May. 2012
2002
118 48Ca + 249Cf 294118 + 3n (FLNR)
2003
115 48Ca + 243Am 288115 + 3n 284113 + α (FLNR)
2004
113 70Zn + 209Bi 278113 + n (RIKEN)
2010
117 48Ca + 249Bk 294,293117 + 3-4n (FLNR)
Synthesis of New Elements Reports of new elements
2012
119 50Ti + 249Bk 296,295119 + 3-4n (GSI- TASCA)
20
Experimental data
Pb target
Actinide target
Evaporation residue cross sections
40
2. Model
1. 2-1. Estimation of cross sections
2. 2-2. Dynamical Equation
2* *
00
(2 1) ( , ) ( , ) ( , )2
ER cm CN
cm
T E P E W EE
10-22
10-20
10-19
~10-18
(s)
Reaction
Time
2* *
00
(2 1) ( , ) ( , ) ( , )2
ER cm CN
cm
T E P E W EE
Formation probability
Survival probability
Reaction time t < 10-22 s
10-22 < t < 10-18 s
~10-18 < t s
Quasi-fission 90~99 %
Fusion-fission
Tℓ
1st
stage
2nd
stage
3rd
stage
Touching probability
W
Recent Development of Theoretical Models
Tl PCN Wsuv
Antonenko, Admiyan,
Nasirov, Cherepanov,
Volkov, Giardina, Scheid
Simple WKB 1D di-nucleus confi.
Statistical method
Statistical model
Aritomo, Ohta
Experimental data,
Gross-Kalinovski
3D two-center shell model
3D-Langevin eq.
Langevin with Statistical
model
Bouriquet, Shen, Kosenko,
Boilley, Abe
Gross-Kalinovski 2D two-center LD model
2D-Langevin eq.
Statistical model
(KEWPIE)
Ohta Simple WKB Empirical function derived
from results with
3D-Langevin
Statistical model
Zagrebaev, Greiner Quantum
(CC or empirical model)
3D two-core model
Master eq.
Zagrebaev, Greiner,
Aritomo, Karpov,
Noumenko
Unified model
3D two-center shell model
3D-Langevin eq.
Statistical model
Statistical model
Swiatecki, Wilczynska,
Wilczynski
Empirical method 1D-Diffusion model
Analytical formula
Statistical model
Misicu, Gupta, Greiner Deformation and
Orientation
Ichikawa, Iwamoto, Moller,
Sierk
Deformation and
Quadrupole zero-point
vibrational energy
V.I. Zagrebaev, et al. Phy. Rev. C. 65. (2001) 014607
Fission width
Bohr and Wheeler (1939)
Statistical model (transition state method)
initial state and final state
Kramers (1940)
Dynamical model
friction as diffusion process
*
*
* 0
1 ( )
2 ( )
exp2
BE UBW
f B
B
dK E U KE
UT
T
Stationary solution
Fission width
~
Recent Development of Theoretical Models
Tl PCN Wsuv
Antonenko, Admiyan,
Nasirov, Cherepanov,
Volkov, Giardina, Scheid
Simple WKB 1D di-nucleus confi.
Statistical method
Statistical model
Aritomo, Ohta
Experimental data,
Gross-Kalinovski
3D two-center shell model
3D-Langevin eq.
Langevin with Statistical
model
Bouriquet, Shen, Kosenko,
Boilley, Abe
Gross-Kalinovski 2D two-center LD model
2D-Langevin eq.
Statistical model
(KEWPIE)
Ohta Simple WKB Empirical function derived
from results with
3D-Langevin
Statistical model
Zagrebaev, Greiner Quantum
(CC or empirical model)
3D two-core model
Master eq.
Zagrebaev, Greiner,
Aritomo, Karpov,
Noumenko
Unified model
3D two-center shell model
3D-Langevin eq.
Statistical model
Statistical model
Swiatecki, Wilczynska,
Wilczynski
Empirical method 1D-Diffusion model
Analytical formula
Statistical model
Misicu, Gupta, Greiner Deformation and
Orientation
Ichikawa, Iwamoto, Moller,
Sierk
Deformation and
Quadrupole zero-point
vibrational energy
Nuclear shape is described by
Two center parametrozation
2* *
00
(2 1) ( , ) ( , ) ( , )2
ER cm CN
cm
T E P E W EE
Formation probability
Survival probability
Reaction time t < 10-22 s
10-22 < t < 10-18 s
~10-18 < t s
Quasi-fission 90~99 %
Fusion-fission
Tℓ
1st
stage
2nd
stage
3rd
stage
Touching probability
σcap ? PCN
W
Tℓ
Uncertainty
of the 2nd stage
2. Model
1. 2-1. Potential
2. Two-center shell model
3.
2-2. Equation trajectory calculation
),,( z
Overview of Dynamical Process in reaction 36S+238U
10
1. Potential energy surface
2. Trajectory described by
equations
two-center parametrization
(Maruhn and Greiner,
Z. Phys. 251(1972) 431)
),,( z
Nuclear shape
(δ1=δ2)
( , , )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
δ=0
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
Fission barrier recovers at low excitation energy
298114
2. Model
1. 2-1. Potential
2. Two-center shell model
3.
2-2. Equation Taking into account the fluctuation around the mean trajectory
Thermal fluctuation of nuclear shape
thermal fluctuation of collective motion
),,( z
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 equation Friction Random force
dissipation fluctuation ordinary differential equation
Einstein relation Fluctuation-dissipation theorem
0.0
0.5
1.0
1.5
2.0
0
20
40
-0.5
0.0
0.5
z
-0.5 0.0 0.5 1.0 1.5 2.0
-0.5
0.0
0.5
z
Fission process 240U E* < 20 MeV
Trajectory on potential energy surface
Overview of Dynamical Process in reaction 36S+238U
10
3. Results
Evaporation residue cross section
Mass distribution of fission fragments
Itkis et al.
Cal.
Calculation results 48Ca + 244Pu
Calculation
4. Way to synthesize new SHE
Ti, Cr, Fe etc. beams
Transfer reaction U+Th, U+Cm
Secondary beams
Cold fusion reaction Hot fusion reaction 1994
110 Ds 62Ni + 208Pb 269110 + n (GSI)
111 Rg 64Ni + 209Bi 272111 + n (GSI)
1996
112 Cn 70Zn + 208Pb 277112 + n (GSI) named in Feb. 2010
1999
114 Fl 48Ca + 244Pu 292114 + 3n (FLNR) named in May. 2012
2000
116 Lv 48Ca + 248Cm 292116 + 4n (FLNR) named in May. 2012
2002
118 48Ca + 249Cf 294118 + 3n (FLNR)
2003
115 48Ca + 243Am 288115 + 3n 284113 + α (FLNR)
2004
113 70Zn + 209Bi 278113 + n (RIKEN)
2010
117 48Ca + 249Bk 294,293117 + 3-4n (FLNR)
Synthesis of New Elements Reports of new elements
20
Yu. Ts. Oganessian and K. Morita
190
A=304
Possibility of synthesizing 298114
Model Calculation
3. Survival Process
118
117 293117 294117
116
115 287115 288115 289115 290115
114
113 282113 283113 284113 285113 286113
283Cn
278Rg 279Rg 280Rg 281Rg 282Rg
274Mt 275Mt 276Mt 278Mt
270Bh 271Bh 272Bh 274Bh
266Db 267Db 268Db 270Db
294118
290Lv 291Lv
286Fl 287Fl
282Cn
275Hs
267Rf
CN 278113
274Rg
270
Mt
266Bh
262Db
278113
274Rg
270Mt
266Bh
262Db
258Lr
254Md
254Fm
250Cf
2* *
00
(2 1) ( , ) ( , ) ( , )2
ER cm CN
cm
T E P E W EE
Trajectory calculation Two-center parametrization
Capture
Fusion
Survival
3-dim Langevin
Statistical model
f
n
To estimate survival probability
Dynamical model
dqtqPtEW );,();,(saddle inside
*
0
W ; survival probability
One-dimensional Smoluchowski equation
tqPq
TtqP
q
tqV
qtqP
t;,;,
;,1;,
2
2
T(t) : temperature statistical code SIMDEC
Cooling curve
statistical code
q ; separation distance
We assume the particle emissions are limited to neutron emission in the neutron-rich heavy nuclei.
friction reduced ;
mass inertia ;
ondistributiy probabilit ; ;,
tqP probability distribution
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 Φ(T)=exp{-aT2/Ed}, Ed=20 MeV
VLD(q)
MeV 20
exp)(2
d
d
E
E
aTT
)( )(),(
)()()(
),()(2
1)(),,(
0
2
TqETqV
qEqEqV
TqVqI
qVTqV
shellSH
CSLD
SHLD
MeV 20
exp)( *
d
d
E
E
ET
298114
Fission barrier recovers at low excitation energy
Neutron Separation energy Shell correction energy at G.S.
3. Survival process
Rapid cooling
Approaching to the closed shell
Bf (
MeV)
A=298
A=304
Smoluchowski equation
A=304
Bf (
MeV)
4. Summary 1. The possibility of synthesizing a doubly magic superheavy nucleus, 298114184, was
investigated on the basis of fluctuation dissipation dynamics.
2. Owing to the neutron emissions, we must generate more neutron-rich compound nuclei.
3. To calculate the survival probability, we employ the dynamical model.
4. 304114 has two advantages to achieving a high survival probability.
1 ) small neutron separation energy and rapid cooling
2 ) the neutron number of the nucleus approaches that of the double closed shell
obtain a large fission barrier
5. The systematical investigation compared with the statistical model and dynamical one is necessary. We must apply the dynamical model for known systems.
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
Collaborators S. Chiba Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology K. Hagino Department of Physics, Tohoku University K. Nishio Advanced Science Research Center, Japan Atomic Energy Agency V.I. Zagrebaev, A.V. Karpov Flerov Laboratory of Nuclear Reactions W. Greiner Frankfurt Institute for Advanced Studies, J.W. Goethe University