1

A. Brondi, G. La Rana, R. Moro, M.Trotta, E. Vardaci, A. Ordine, A. BoianoIstituto Nazionale di Fisica Nucleare

and Dipartimento di Scienze Fisiche dell’Università di Napoli, I-80125 Napoli, Italy

M. Cinausero, E. Fioretto, G. Prete, V. Rizzi, D. ShettyIstituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Legnaro

I-36020 Legnaro (Padova), Italy

M. Barbui, D. Fabris, M. Lunardon, S. Moretto, G. ViestiIstituto Nazionale di Fisica Nucleare

and Dipartimento di Fisica dell’Università di Padova, I-35131 Padova, Italy

F. Lucarelli, N. GelliIstituto Nazionale di Fisica Nucleare

and Dipartimento di Fisica dell’Università di Firenze, I-50125 Firenze, Italy

P.N. NadtochyDepartment of Theoretical Physics, Omsk State University, Omsk,Russia

V.A. RubchenyaDepartment of Physycs, University of Jyvaskyla, Finland

New Clues on Fission Dynamics from Systems of Intermediate Fissility

Excess of pre-scissionn, p, α with respect to statistical model predictions

Dynamical effect: path from equilibrium to scission slowed-down by the nuclear viscosity

0 τd τssc time

Equilibrium Saddle-Point Scission-Point

Evidences of dynamical effects

Two theoretical approaches: Modified S.M., Dynamical models à t, viscosity

Modified Statistical Model

( )TE ff /10lnγτ =

( )

−+Γ=Γ γγ 2

121BWf

Kramersf ( ) ( )[ ]f

Kramersff tt τ/exp1 −−Γ=Γ

Fission as a diffusion process (Kramer Prescription) :

- the presence of nuclear viscosity reduces the fission rate ΓBW

γ à viscosity parameter

Time scale and dissipation from pre- and post-scission lp multiplicities

Γ= /hτ τ < τd Γf = 0 τ > τd Γf = ΓBW

Dynamical models

1. Lagrange equation (deterministic)

2. Transport equations (stochastic): Fokker-Planck and Langevin equations

Dissipation from TKE, n multiplicity

Evolution of the nuclear shape described by the collective variables.

In the stochastic approach the collective variables fluctuate because of the coupling to the internal degrees of freedom, which constitute the surrounding “heat bath” (Brownian motion).

Open Questions in Fission Dynamics

1. Fission time scale: ∼ 0-200 x 10-21 s;

2. Strength (β: ∼(2-30)x1021 s-1) and Nature of dissipation: one-body or two-body;

3. Dependence of the viscosity on the temperature and on the shape.

1. Fission time scale: ∼ 0-200 x 10-21 s;

2. Strength (β: ∼(2-30)x1021 s-1) and Nature of dissipation: one-body or two-body;

3. Dependence of the viscosity on the temperature and on the shape.

The determination of the fission time scale and of the viscosityrelies on Model calculations.The determination of the fission time scale and of the viscosityrelies on Model calculations.

Use as many observables as possible to constraint the relevant

model parameters

Use as many observables as possible to constraint the relevant

model parametersGOAL: To reproduce many observables with one set of input parameters

GOAL: To reproduce many observables with one set of input parameters

FER σσ ≥More constraints on the model’s parameters(σER, lp multiplicities in ER channel)

χχ~~0.600.60 χχ>0.60>0.60

Systems of Intermediate Fissility(χ ≅ 0.5 - 0.6)

sscpre ττ >>

è higher cross sections for lcp emission

è deformation effects on lcp emission

è no much data on these systems

è higher cross sections for lcp emission

è deformation effects on lcp emission

è no much data on these systems

Target

8πLP layout

34.0°

116 Si- CsI Telescopes

(E-DE & TOF)126 Si- CsI Telescopes

(E-DE & PSD)

4 PPACs

ERring G

4.7°60cm15cm

FF

ring A

particle – FF, ER coincidencesparticle – FF, ER coincidences

Studied Systems

G. La Rana et al., EPJ A16 (2003) 199

E. Vardaci et al., Phys.Atomic Nuclei 66, (2003) 1182, Nucl.Phys. A734 (2004) 241

τd

Fast Fission

R. Lacey et al., Phys. Rev. C37 (1988) 2540

W. Parker et al., Nucl. Phys. A568 (1994) 633

?93168Yb18O + 150Sm

0152132Ce32S + 100Mo

?122132Ce32S + 100Mo

5194147,9Tb40Ar + natAg4128147,9Tb40Ar + natAg8135149Gd121Sb + 27Al

2790141Eu32S + 109Ag

τd (10-21 s)Ex (MeV)CNSystem

M.S.M.

576 ± 5070 ± 70,038(0,005)

0,055(0,007)

0,56 (0.09)

0,90 (0.14)

σER [mb] σff [mb] MαpreMp

preMαERMp

ER

200 MeV 32S + 100Moà132Ce:

particle-ER coincidences

1. The SM code Lilita_N97 (no fission included) reproduces the angular distribution

2. It overestimates p and α multiplicities by the same factor 1.8

3. It well reproduces the energy spectra shapes of p and α

A B C D E F G

10-3

10-2

10-4

10-1

0 40 80 120

Lilita_N97exp

alpha

dM/d

Ω (

ster

-1)

A B C D E F G

expLilita_N97

10-2

10-1

10-30 40 80 120

proton

Detector # Detector #

dM/d

Ω (

ster

-1)

10-2

10-1

A B C D E F G10-3

0 40 80 120Detector #

expPACE

expPACE

A B C D E F G10-4

0 40 80 120

Detector #

10-3

10-2

10-1

proton alpha

particle-ER coincidences: PACE

1. The SM code PACE (fission included) reproduces the a.d.

2. It overestimates p (by 1.8) and α (by 3.1) multiplicities

3. No selection of input parameters improves the agreement

4. The energy spectra are generally too hard

Q & A

If the model does not work where it is supposed to work, why do we use it in another regime to estimate time scales ?

What are the effects of this inability of the model to predict correctly the particle

competition in the fission channel?

In principle, if the charged particle multip. are overestimated, the neutron multiplicity should be underestimated......(?)

Excitation Energy (MeV)

40 60 80

4

3

2

1

Neu

tron

Mul

tipl

icit

y StatisticalModel

1.06

1.00

af

/an

16O + 197AuThis means that the time delay may be overestimated if only neutrons are measured in the FF channel....

122 MeV 18O + 150Smà168Yb

0

0.5

1

1.5

2

2.5

3

3.5

0 5 10 15 20 25 30 35 40 45

n

p

α

Newton et al.Nucl.Phys.A483 (1988)

τd (x 10-21)

PreS

ciss

ion

Mul

tipl

icit

y

Overestimation of p and α

What do we do?

By using a more realistic approach we can try to put this picture together!

3D Langevin approach + Statistical Model

Karpov, Nadtochy et al.

Phys.Rev. C63, 2001

LILITA_N97 for light particle evaporation along trajectories

3D Langevin Eq.

)(2

2

tfTdtdq

mqV

dtqd

m ββ +−∂∂

−=)()()( 2 ttDtftf ijji ′−=′ δδ

TD β22 =

Inertia Tensor Wherner Wheleer

Friction Tensor

One body dissipation

q1 = elongation

q2 = neck size

q3 = mass asymmetry

597610.0200.0500.580.82Theor.

576 ±50

70 ±7

0,038 ±0,005

0,055 ±0,007

0,56 ±0.09

0,91 ±0.15

Exp.

σER(mb)

σFF(mb)

MαMpMαMp

Prescission channel

ER channel

200 MeV 32S + 100Mo

One body dissipation appears to be the dominant mechanism

200 MeV 32S + 100Mo: Fission Rate

t (x 10-21)

Fiss

ion

Rat

e L = 60

L = 50

L = 40

L = 0-20

Transient time: 15 - 25 x 10-21 s for L=50-60 h

Conclusions

The current implementations of the SM do not reproduce correctly particle competitions in the ER channel

The extraction of the fission time scale is affected by the reliability of the SM ingredients used

The SM is unable to reproduce a sizeable set of observable which involve the Fission and the ER channel

Dynamical models seem to be a promising approach capable of reproducing a more complete set of data

More tests and measurement need to be performed