Dynamical Approach to Synthesis of Superheavy Elements

Y. Aritomo

Department of Electric and Electronic Engineering, Faculty of Science and Engineering,Kindai University, Kowakae, Osaka, Japan

Long-term workshop on

“Computational Advances in Nuclear

and Hadron Physics” (CANHP2015)

YITP, Kyoto, Japan, 1st October 2015

Structure Light Nuclei

Reaction Superheavy Nuclei

Topics

1. Shell Correction Energy

Two-Center Shell Model

2. Dynamical Approach

Key Words

1. IntroductionSuper Heavy ElementsStability of Nuclei, Shell effectsSynthesis of SHE

2. Experimental methods

3. Theoretical calculation

Dynamical model (Fluctuation Dissipation model)Langevin equation

4. Calculation results

fusion-fission process

5. Further study

Contants

LvFlMay 2012 IUPAC

104 105 106 107 108 109 110 111 112

flerovium livermorium

Periodic Table

Менделеев(1834-1907)

1869

Super Heavy Elements less stable

Taka

Fuji

Our Interest

・ Next magic number Z=82, N=126

・ Verification of ‘Island of Stability’

（predicted by macroscopic-microscopic

model in 1960’s）

・ Synthesis of new elements

1. Introduction

N

Z

Nuclear Chart

Stability of nuclei

Yu. Ts. Oganessian

Experimental setup for synthesis of SHE

Lab Country City Accelerator Separator

FLNR Russia Dubna U400U400M

DGFRSVASSILISSA

GSI Germany Darmstadt UNILAC SHIPTASCA

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

Fragments90~99%

Experimental data

Pb target

Actinide target

Evaporation residue cross sections

40

2* *

00

(2 1) ( , ) ( , ) ( , )2

ER cm CN

cm

T E P E W EE

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

Cold fusion reaction Hot fusion reaction1994

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 ElementsReports of new elements

Heavy ion reaction

2. Model

1. 2-1. Estimation of cross sections

2. 2-2. Dynamical Equation

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

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

20

0

E

Ee

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

Taking into account the fluctuation around the mean trajectory

Thermal fluctuation of nuclear shape thermal fluctuation of collective motion

0.0

0.5

1.0

1.5

2.0

0

20

40

-0.5

0.0

0.5

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 equationFriction Random force

dissipation fluctuationordinary 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

236U E*=20 MeV

分裂過程

Mass

50 75 100 125 150 175

0

50

100

150

50 75 100 125 150 175

0

50

100

150

C

Mass

all on all off only 33 on only 22 on

50 75 100 125 150 175

140

揺動項なし Newton Eq 揺動項あり Langevin Eq.

Mass

50 75 100 125 150 175

0

50

100

150

50 75 100 125 150 175

0

50

100

150

C

Mass

all on all off only 33 on only 22 on

50 75 100 125 150 175

140

質量分布

6

Overview of Dynamical Process in reaction 36S+238U

10

Projectile dependence of fragment mass distributions

Experiments by K. Nishio et al. (JAEA)

Z=106 107 108 110 112

Calculated spectra for fusion-fission and quasi-fission

Experiments by K. Nishio et al. (JAEA)

4. Mechanism of Dynamical process

30Si+238U 36S+238U

200u74u

137u

178u90u

134u

Clarify the origin of the difference

MDFF at Low incident energy

15

(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

Time evolution of probability distribution

Try to clarify the origin of difference between the both cases

Probability distribution on the z-A plane

E* =

35.5 MeV

L=0, θ=0

30Si+238U

36S+238U

Probability distribution of total time on the z-δ plane

39.5 MeV

The relation between the touching point and the ridge line is very important to decide the process

fusion hindrance

Ridge line

steep

gentle Contact

point

200u74u

137u

36S + 238U30Si + 238U

178u90u

134u

FF and DQF

t > 50 x 10-21 sec

-0.2 < δ < 0.2 (peak 0)

QF via mono-nucleus

t < 30 x 10-21 sec

0.2 < δ < 0.5 (peak 0.4)

QF

t < 10 x 10-21 sec

0 < δ < 0.2 (peak 0)

FF and DQF

t < 30 x 10-21 sec

0 < δ < 0.4 (peak 0.2)

20

(1) Origin of the reaction process

(2) Building times

(3) Deformation of fragments

Fission Process

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

Experiment J.Katakura, JENDL FP Decay Data File 2011 and Fission Yields

calculation Y. Aritomo and S. Chiba, PRC 88, 044614(2013)

CalExp・

Exp. Phys.Rev. 141(1966)1146

236U* ( E* = 20MeV)

Mass distribution of fission fragments E* = 20 MeV

234U240Pu

Comparison between Cal. and Exp.

37

Fiss

ion

Yie

ld (

%)

Fragment Mass (u)

40–50 MeV

30–40 MeV

20–30 MeV

234Th 235Pa 236U 234Th 235Pa 236U

Cal. ED = 20 MeV Cal. ED = 30 MeV

Cal.

Exp.

E*

MeV 20

exp)(2

d

d

E

E

aTT

Compiled by K. Nishio and JAEA group

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 probability distribution

4. The relation between the touching point and the ridge line is very importantto decide the process fusion hindrance

And….

5. Summary

Collaborators

K. Hagino Department of Physics, Tohoku University

K. NishioAdvanced Science Research Center, Japan Atomic Energy Agency

S. ChibaResearch Laboratory for Nuclear Reactors, Tokyo Institute of Technology

V.I. Zagrebaev, A.V. KarpovFlerov Laboratory of Nuclear Reactions

W. GreinerFrankfurt Institute for Advanced Studies, J.W. Goethe University