EVIDENCE FOR TRANSIENT EFFECTS IN FISSION AND

IMPORTANCE FOR NUCLIDE PRODUCTION

B. Jurado1,2, K.-H. Schmidt1, A. Kelić1, C. Schmitt1, J. Benlliure3, A. Junghans4

1GSI, Darmstadt, Germany2GANIL, Caen, France

3University Santiago de Compostela, Spain4RFZ, Rossendorf, Germany

ContentsContents IntroductionIntroduction

What are transient effects in fission?What are transient effects in fission?

How to observe experimentally transient How to observe experimentally transient effects?effects?

Quantitative results for transient effectsQuantitative results for transient effects

Importance of transient effects for nuclide Importance of transient effects for nuclide productionproduction

ConclusionsConclusions

Dynamical description of the deexcitation process of a heavy nucleus:

Collective deg. freedom

Intrinsic deg. freedom

Dissipation: (T,q)

Langevin/Fokker-Planck eq.

Transport theories

Single Langevin Single Langevin trajectories in phase trajectories in phase

space space

+ +

EvaporationEvaporation

Evaporation code Evaporation code

+ +

ΓΓff(t), (t), Fokker-Planck Fokker-Planck eq.eq.

Two equivalent views of the process:

Transient effects in fissionTransient effects in fission

Evolution of the probability distributiont = 0 s t = 1·10-21 s t = 3·10-21 s

Transient time τf(β, A, Z, T)

To observe transient To observe transient effects…effects…

Small deformation and high E*Small deformation and high E*

Appropriate observablesAppropriate observables

Peripheral heavy-ion collisions at relativistic Peripheral heavy-ion collisions at relativistic energiesenergies

Small shape distortionSmall shape distortionLow angular momentum < 20 ħLow angular momentum < 20 ħHigh intrinsic excitation energies E* High intrinsic excitation energies E* ~ ∆A~ ∆AInverse KinematicsInverse Kinematics

??

Fusion-fission reactionsFusion-fission reactions

Experimental set-up Experimental set-up for fission studies in inverse for fission studies in inverse kinematicskinematics

238U (1 A GeV)

Z1+Z2 = 92

238U (1 A GeV) + (CH2)n

E*initial

Y fiss (Z1 + Z2)

New observables: Partial fission cross sectionsNew observables: Partial fission cross sections

Tfiss

Z1 + Z2 = 89

E*initial

z2 = Tfiss/Cz

New observables: Partial fission cross sectionsNew observables: Partial fission cross sections

Z1+Z2 = 92

Realistic description of the time-dependent fission-decay width

= 51021s-1

T= 3 MeVA = 248

f(t) =Num. Sol. FPE(K.-H. Bhatt, et al., Phys. Rev. C 33 (1986) 954)

f(t) = Step functionf(t) ~ (1-exp(-2.3t/f))

f(t) = Analytical approximation (B. Jurado, et al., Phys. Lett. B 553 (2003) 186)

f(t) = f(t)/ħ

The modelUpdated version of GSI code ABRABLA:

ABRASION

If T< 5 MeV

If T > 5 MeV

SIMULTANEOUSBREAK-UP

Freeze out T = 5 MeV

(W. A. Friedman, PRL, 60 (1988) 2125

W. Nörenberg et al. Eur. Phys. J A 9 (2000) 327

K.-H. Schmidt et al., Nucl. Phys. A 710 (2002) 157)

EVAPORATION / FISSION

af/an

(Ignatyuk)

Bf

(Sierk)

Total fission cross sections Total fission cross sections

fnucl 238U(1 A GeV) + Pb

Experiment2.160.14

b

No transient effects

3.33 b

f(t) step

= 21021 s-1 2.00 b

f(t) ~1-exp(-t/) = 41021 s-1

2.04 b

f(t) FPE

= 21021 s-1 2.09 b

The value of β depends on the description for f(t)

Total fission cross sections are not sensitive to the shape of f(t)

Sensitivity to the shape of Sensitivity to the shape of f(t)238U (1 A GeV) + (CH2)n

Experimental data

f(t) step, = 21021 s-1

f(t) ~1-exp(-t/), = 41021 s-1

f(t) FPE, = 21021 s-1

Sensitivity to the dissipation Sensitivity to the dissipation coefficient βcoefficient β238U (1 A GeV) + (CH2)n

Experimental data

Transition-state model

Kramers = 4·1021s-1

= 2·1021s-1

= 0.5·1021s-1

= 5·1021s-1

= 2·10= 2·102121ss-1-1

f f (1.7±0.4)(1.7±0.4)1010-21 -21 ss

(Data from J. Taieb et al., Nucl. Phys A 724 (2003) 413-430)

Influence on nuclide production…Influence on nuclide production…

Experimental Data

No transient effects

Transient effects β =1·1021s-1

238U (1 A· GeV) + p

Calculation

INCL-ABLA

Calculation

INCL-ABLA

(PhD. J. Pereira, Univ. Santiago de Compostela)

208P (1 A GeV) + p

Experimental data

Transition state model

= 21021 s-1

ConclusionsConclusions Experimental observation of transient effectsExperimental observation of transient effects

All observables described by a constant value of

= 21021s-1 f ≈ (1.7±0.4)10-21 s

Transient effects in fission strongly influence nuclide Transient effects in fission strongly influence nuclide productionproduction

Very realistic analytical approximation for Very realistic analytical approximation for f f (t)(t)