電気的に励起された

岩田順敬 ( 東大理 )

Cedric Simenel (CEA/Saclay)

原子核の時間発展

Thanks toThanks to::

大塚孝治 ( 東大理、東大 CNS 、理研 )

Michael Bender (CEA/Saclay)

Electric excitation for fissions

target

E1 excitation

E2 excitation

Electric excitation

Induced fission

Real time evolution

Photo-induced fission

Let us break 16O !Ideas for“The way of giving some energies for the ground state”Induced fission (electrical excited initial state)

TDHFTDHF (with excitation)

Full Diabatic

E2 excitation

E1 excitation

Deformed initial state

Constraint HF + TDHFConstraint HF + TDHF

+ Adiabatic

J. W. Negele et al., Phys. Rev. C. J. W. Negele et al., Phys. Rev. C. 1717, 3 (1978), 3 (1978)

Initial state on the saddle point

InteractionInteraction

0)()( tHitdt tTDHF LagrangianTDHF Lagrangian

'),'(),',(2

22

drtrtrrVm

i iij

it

j

jj drdrtrtrrrrrVtrrV '''''),'''(),''()''',','',(~

),',( *

→ → One body evolutionOne body evolution

Antisymmetrized potential

TDHF equationTDHF equation (←Time dependent variational principle)(←Time dependent variational principle)

SkyrmeVV ExtV

TDHF Equation with Excitations

Electric Electric excitationexcitation

SLy4d

SLy4d : SLy4d : Chabanat - Bonche - Hansel, (1995)

)(ˆˆ0ttQkVExt

Amplitude Time t0

Instantaneous

)0()(ˆexp)( 0 0 i

t

ExtidVh

iTt

Time-ordering

Excitation part

””One body time evolution” (final One body time evolution” (final form)form)

Electric Excitations ( E1 & Electric Excitations ( E1 & E2 Excitation )E2 Excitation )

0h : Hamiltonian with nuclear force

Nfor

N

Pfor

PD N

x

Z

x

A

ZNQ̂

2222 ˆˆˆ2

16

5ˆiii zyxQ

The initial state we calculate the HF ground stateHF ground state of Oxygen 16

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

-20 -15 -10 -5 0 5 10 15 20-20

-15

-10

-5

0

5

10

15

20

E2 excitation

E1 excitation

time

“The boundary condition” is chosen to be Dirichlet zero on the edge of 3D box

The initial and the boundary value problem for TDHF equation

Ev8 :Ev8 :

P. Bonche et al., Comp. Phys. Com. 171, 49 (2005)P. Bonche et al., Comp. Phys. Com. 171, 49 (2005)

space

E2 excitation

HF|

GQR|

The most dominant transition in each case is considered to be as follows:

Energy

E2 excitation causes <Q2> deformation

HFe Qik || 2ˆ

0

Excited initial state Excited initial state ((small amp. & GQR dominancesmall amp. & GQR dominance))

GQRikqHFHFQik |||)ˆ1( 22

GQReikqHFt tQik ||)(| /ˆ

2

2 Time evolutionTime evolution

)/sin(2)(|ˆ|)( 2

22tkqtQt

q

QQ22 oscillation oscillation

E2 excitation

Excitation energy: 16MeV

The lower and the upper energy estimate for the induced fission energy of quadrupole type

E2 excitation

Nonlinearity existsNonlinearity exists::a small difference in excitation leads a large difference !a small difference in excitation leads a large difference !

Gap

262MeV

288MeV

86MeV

22MeV

16O1 time step = 0.45 fm/c

-20-15-10 -5 0 5 10 15 20

-20

-15

-10

-5

0

5

10

15

20

-20-15-10 -5 0 5 10 15 20

-20

-15

-10

-5

0

5

10

15

20

-20-15-10 -5 0 5 10 15 20

-20

-15

-10

-5

0

5

10

15

20

E2 excitation

-20-15-10 -5 0 5 10 15 20

-20

-15

-10

-5

0

5

10

15

20

192MeV

fission

oscillation

-20-15-10 -5 0 5 10 15 20

-20

-15

-10

-5

0

5

10

15

20

-20-15-10 -5 0 5 10 15 20

-20

-15

-10

-5

0

5

10

15

20

-20-15-10 -5 0 5 10 15 20

-20

-15

-10

-5

0

5

10

15

20

288MeV

time = 180.0 fm/c

16O 8Be + 8Be

HF|

GDR|

GQRGDR|

E1 excitation

Two mode coupling state

We will measure the deformation by <Q2>

The most dominant transition in each case is considered to be as follows:

Energy

E1 excitation also causes <Q2> deformation

HFt |)(|

Time evolutionTime evolution

1)/cos(2)(|ˆ|)( 22

2 tqqktQt

qqd

QQ22 oscillation oscillation

GQRGDReGDReikq tiktik

d

qd || //

Important state of this case

C. Simenel and Ph. Chomaz. Phys. Review C, C. Simenel and Ph. Chomaz. Phys. Review C, 6868. (2003). (2003) ．．

E1 excitation

The exchange of the dominant excitation for <Q2>

<Q2> [fm2]

E* [MeV]

q0

2* kE

02* qQaE

2

02* qQbE

E1 excitation:

E2 excitation: )0,(*,02

qEQ Initial state

)/,/(),0,(*, 2

002ababqqEQ

trivial

)0(),0( ba RR

b/a 2

16O

15MeV

E1

E2

Small amp.

b/a

TDHF Results of Electric Oscillation caused by E1 excitation

16OE1 Excitation (18MeV) is given

<QD> evolution <Q2> evolution

Existence of a singular point

16O 157MeV

274MeV

71MeV

18MeV

423MeV

~800MeV

E1 excitation

Singular point

0*/)(ˆ EtQfixedD

is observed in TDHF calculation

There exists a singular point

around here

More precisely,

242MeV –309MeV

TDHF Results of Electric Oscillations

Center of oscillation

Damping oscillation

0)()(.

tf-tfcrit

)( t def

E1 excitation

criticalcritical

16O

274MeV424MeV

157MeV71MeV

605MeV

Converging to excited oxygen

Separating into fragments

At the criticalAt the critical, “Dominant transition exchange” is switched on !?

Above the critical, damped oscillationdamped oscillation can be seen in <Q2> motion.

E1 excitation

274MeV

Broken

Excited state

605MeV

time = 270.0 fm/c

-30 -20 -10 0 10 20 30-30

-20

-10

0

10

20

30

-30 -20 -10 0 10 20 30-30

-20

-10

0

10

20

30

-30 -20 -10 0 10 20 30-30

-20

-10

0

10

20

30

-30 -20 -10 0 10 20 30-30

-20

-10

0

10

20

30

-30 -20 -10 0 10 20 30-30

-20

-10

0

10

20

30

-30 -20 -10 0 10 20 30-30

-20

-10

0

10

20

30

-30 -20 -10 0 10 20 30-30

-20

-10

0

10

20

30

CHF calculation for 16O

~35MeV

QQ22 Constraint Constraint

is given is given

CHF result for the initial state of TDHF calculation

Real time evolutionTDHF

How about the dynamics of the fission fragment ?

-40-30-20-10 0 10 20 30 40

-40

-30

-20

-10

0

10

20

30

40

-40-30-20-10 0 10 20 30 40

-40

-30

-20

-10

0

10

20

30

40

-40-30-20-10 0 10 20 30 40

-40

-30

-20

-10

0

10

20

30

40

-40-30-20-10 0 10 20 30 40

-40

-30

-20

-10

0

10

20

30

40

Excited state with 35MeV35MeV

from the ground state

CHF

time = 540.0 fm/c

time = 0.0 fm/s

SummarySummaryE1 excitationE1 excitation

PerspectivePerspective Based on this result, we will go for “unstable nuclei”“unstable nuclei”

E2 excitationE2 excitation

CHF + TDHF calculationCHF + TDHF calculation

280MeV ( 17.5 MeV/A )280MeV ( 17.5 MeV/A )

35MeV35MeV 　　+ adiabatic (initial state)+ adiabatic (initial state)

full diabaticfull diabatic

Excitation energy [MeV]280~3003515

16O

Exchange Exchange of E1 & E2 of E1 & E2 CHFCHF

Induced Induced fission(TDHF)fission(TDHF)

Diff.profile for E1 & E2

gap oscillation or not