new clues on fission dynamics from systems of intermediate fissility

22th Winter Workshop on Nuclear DynamicsLa Jolla, 2006

1

New Clues on Fission Dynamics from Systems of Intermediate

FissilityE.V., A. Brondi, G. La Rana, R. Moro, M.Trotta, A. Ordine, A. Boiano

Istituto Nazionale di Fisica Nucleareand 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. Nadtochy

Department of Theoretical Physics, Omsk State University, Omsk,Russia

V.A. Rubchenya

Department of Physycs, University of Jyvaskyla, Finland


2

Fusion-Fission Reactions @10MeVA

Light particles and emission can provide a moving picture of the time evolution Multiplicity is a sensible

observable for time scales

Multiplicity is a sensible observable for time scales


3

Fission Dynamics in Systems of Intermediate Fissility

Prologue: FISSION TIME SCALE

Excess of pre-scission n, p, with respect to statistical model predictions

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

0 d ssc time

Equilibrium Saddle-Point Scission-Point


4

16O + 197Au

Excitation Energy (MeV)

40 60 80

4

3

2

1

1.06

1.00

af /an

Neutr

on

Mult

iplic

ity Statistical Model

= (35 ± 15) x 10-21 s

D. J. Hinde et al.

p

n

f

Statistical Model

< d f = 0

> d f = BW

/

D. J. Hinde et al.,PRC45 (1992)


5

- Inclusion of d (step function)

< d f = 0

> d f = BW

- Fission Barriers from A. J. Sierk Phys. Rev. C33 (1986)

- an from Toke and Swiatecki, Nucl. Phys. A372 (1981)

Calculations performed for different values of af / a and d:

0.94 < af / a < 1.12

0 < d < 40 x 10-21 s

-Different sets of transmission coefficients: default, OM, IWBCM

- Inclusion of d (step function)

< d f = 0

> d f = BW

- Fission Barriers from A. J. Sierk Phys. Rev. C33 (1986)

- an from Toke and Swiatecki, Nucl. Phys. A372 (1981)

Calculations performed for different values of af / a and d:

0.94 < af / a < 1.12

0 < d < 40 x 10-21 s

-Different sets of transmission coefficients: default, OM, IWBCM

Multiplicity Analysis with SM


6

Modified Statistical Model

TE ff /10ln2/ 20

2

121BW

fKramersf f

Kramersff tt /exp1

202/

Fission as a diffusion process (Kramer Prescription) :

1. the presence of nuclear viscosity reduces the fission rate BW

2. the full BW fission rate is never attained.

nuclear viscosity parameter < 1 underdamped > 1 overdamped

reduced dissipation coefficient

f transient buildup time of the flux over the barrier


7

Time Scales

n f = (35 ± 15) x 10-21 s D. J. Hinde et al.

f = (120 ± 10) x 10-21 s L. M. Pant et al.

n, p, d = 10 x 10-21 s ssc = 50 x 10-21 s J. P. Lestone et al.

p, d 0 H. Ikezoe et al.

GDR d = 30-200 x 10-21 s Shaw et al., Thoennessen et al.

Dynamical fission time scale: f = d + ssc

Dynamical fission time scale: f = d + ssc

The determination of the fission time scale and of the average deformation relies on Statistical Model calculations.

The determination of the fission time scale and of the average deformation relies on Statistical 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


8

Collective Transport Models

1. Lagrange equation (deterministic)

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

Dissipation from TKE, n multiplicity

Dynamics of fission consists in the study of the gradual change of the shape of a fissioning nucleus.

The shape is characterized in terms of collective variables (i.e. elongation parameter, the neck radius, mass asymmetry of exit fragments). The internal degrees of freedom (not collective) constitute the surrounding “heat bath”.The time evolution of these collective variables (interaction the “heat bath” ) describes the fission dynamics.


9

…but..

Nucleus E* (MeV) s Exp. Observ. ref.200Pb 60-100 3 Mn(pre) Pf L + K178W – 251Es 40-100 2neck 30sci

Mn(pre) Pf L + K

181,185,187Ir 164 5-8 Mn(pre) FP181,185,187Ir 164 22 Mn(pre) WF158Er 70-140 6 Mn(pre) KG + SM158Er 70-140 14 Mn(pre) SML224Th 64 20 ± 6 MGDR KG + SM175Ta 123 20 MGDR KG + SM90Sr - 278110 70-160 0.5 TKE KG + SM141Eu 90 20 Mn(pre), Mp(pre) M(pre)

Mn(ER), Mp(ER) M(ER) fiss

KG + SM

L+K: Langevin and Kramer; FP: Fokker-Plank; KG: Kramers-Grangé; SM: Statistical Model; WF: wall formula.


10

From the theoretical point of view the predictions vary almost by two or three orders of magnitude. Most of the theories predict indeed an overdamped motion ( > 2x1021 s-1)

…but..


11

The role of isospin in the dissipation

W. Ye, Eur. Phys. J. A18 (2003) 571

N/Z

1.25

1.40

1.52

N/Z

1.49

1.40

1.32


12

Open Questions in Fission Dynamics

1. Fission time scale;

2. Strength 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;

2. Strength and Nature of dissipation: one-body or two-body;

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


13

FRE More constraint on the model’s parameters(ER, lp multiplicities in ER channel)

~~0.600.60 >0.60>0.60

Systems of Intermediate Fissility 0.5 - 0.6)

sscpre

deformation effects on lcp emission

no much data on these systems

deformation effects on lcp emission

no much data on these systems


14

Target

8LP layout

34.0°

116 Si- CsI Telescopes

(E-DE & TOF)126 Si- C

sI Telescopes

(E-DE & PSD)

4 PPACs

ring G

4.7°60cm15cm

FF

ring A


15

The 8LP setup

MAX ENERGY Wall: up to 64 AMeV Ball : up to 34 AMeV

TRIGGERS Fission Fragments in ring E/F/G Evaporation Residues (4 PPAC- PPAC)

CORSET (under construction)

ENERGY THRESHOLDS 0.5 AMeV for p and 2-3 AMeV for 12C


16

What observables ?

particle – FF coincidences

particle – ER coincidences

particle – FF coincidences

particle – ER coincidences

8LP + Trigger for ER and FF


17

Systems Studied

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

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

d

Fast Fission

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

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

System CN Ex (MeV) d (10-21 s)

32S + 109Ag 141Eu 90 2718O + 150Sm 168Yb 93 ?32S + 100Mo 132Ce 122 ?121Sb + 27Al 149Gd 135 840Ar + natAg 147,9Tb 128 440Ar + natAg 147,9Tb 194 532S + 100Mo 132Ce 152 0


18

200 MeV 32S + 100Mo132Ce: Fragment-Fragment

Correlations

Ring F-G

Ring G-G

E1

E2 E2

E1


19

Fragment-Fragment-Particle Coincidences

Particle Energy Spectra can arise from several sources: in order to extract the pre- and post-scission integrated multiplicity it is necessary to unfold the contribution of these sources.

Three main sources:- Composite

System prior to scission- The two fission

fragments

The Statistical code GANES is used to unfold the spectra and extract the multiplicities.


20

In-Plane Multiplicity Spectra

12 in-plane correlation angles

CS

F1

F2

43o

78o

102o

120o

137o

156o

204o

223o

241o

258o

282o 299o

Elab (MeV)

d2 M/ddE

(

ster

-1 M

eV-1)

=78° =102° =120°=43°

=156° =204° =223°=137°

=258° =241° =282° =299°

200 MeV 32S + 100Mo132Ce


21

ring Gring G

= in-plane angle out-of-plane angle

d2 M/ddE

ster

-1 M

eV-1)

Elab (MeV)

= 35.4°

= 24.9°

= 9.2°

= 335.1°

= 324.6°

= 318.9°

= 41.1°

= 350.8°

200 MeV 32S + 100Mo132Ce

CS

F1

F2

Out-Of-Plane Multiplicity Spectra


22

ring Ering E


Elab (MeV)

= 74.2°

= 66.6°

= 38.8°

= 293.4°

= 285.8°

= 77.0°

= 321.2°

d2 M/ddE

(

ster

-1 M

eV-1)

= 283.0°

200 MeV 32S + 100Mo132Ce

CS

F1

F2



23

d2 M/ddE

(

ster

-1 M

eV-1)

Elab (MeV)

= 113.0°

= 140.8°

= 247.0°

= 254.5°

= 257.3°

= 102.7°

= 219.2°

= 105.5°

200 MeV 32S + 100Mo132Ce


ring Dring D

CS

F1

F2



24

MpER M

ER Mppre M

pre ff [mb] ER [mb]

0,90 (0.14)

0,56 (0.09)

0,055

(0,007)

0,038(0,005)

70 ± 7 576 ± 50

200 MeV 32S + 100Mo132Ce:


25

Important to measure Mn

200 MeV 32S + 100MoFF


26

particle-ER coincidences

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

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

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

A B C D E F G

10-

3

10-

2

10-

4

10-

1

0 40 80 120

Lilita_N97exp

alpha

dM

/d

(ste

r-1)

A B C D E F G

expLilita_N97

10-

2

10-

1

10-

3 0 40 80 120

proton

Detector # Detector #


27

dM

/d

(ste

r-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 120Detector #

10-

3

10-

2

10-

1

proton alpha

particle-ER coincidences: PACE (1)

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

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

3. No selection of input parameters improves the agreement

4. The energy spectra are generally too hard


28

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 ?

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

With respect to what baseline number is the excess to be determined?With respect to what baseline number is the excess to be determined?

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

competition in the fission channel?

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......(?)

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

Mult

iplic

ity Statistical

Model

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....

This means that the time delay may be overestimated if only neutrons are measured in the FF channel....


29

122 MeV 18O + 150Sm168Yb

0

0.5

1

1.5

2

2.5

3

3.5

0 5 10 15 20 25 30 35 40 45

n

p

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

d (x 10-21)

Pre

Sci

ssio

n M

ult

iplic

ity


30

What do we do?

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

3D Langevin approach + Statistical Model

3D Langevin approach + Statistical Model

Karpov, Nadtochy et al.

Phys.Rev. C63, 2001

LILITA_N97 for light particle evaporation along trajectories


31

3D Langevin Eq. (1)

1. The shape is characterized in terms of collective variables (i.e. elongation parameter, the neck radius, mass asymmetry of exit fragments).

2. The internal degrees of freedom (not collective) constitute the surrounding ‘heat bath’.

3. The heat bath induces fluctuations on the collective variables

1. The shape is characterized in terms of collective variables (i.e. elongation parameter, the neck radius, mass asymmetry of exit fragments).

2. The internal degrees of freedom (not collective) constitute the surrounding ‘heat bath’.

3. The heat bath induces fluctuations on the collective variables

Langevin equations describe the time evolution of the collective variables like the evolution of Brownian particle that interact stochastically with a ‘heat bath’ (internal degrees of freedom).

Langevin equations describe the time evolution of the collective variables like the evolution of Brownian particle that interact stochastically with a ‘heat bath’ (internal degrees of freedom).

Dynamical approach of fission consists into the study of the gradual change of the shape of a fissioning nucleus.


32

3D Langevin Eq. (2)

)(tFvdt

dvM

)(2

2

tfTdt

dqm

q

V

dt

qdm

)()()( 2 ttDtFtF ijji

TD 22

Inertia Tensor Friction Tensor

q1 = deformation

q2 = neck size

q3 = mass asymmetry


33

Ecoll - the energy connected with collective degrees of freedom

Eint - the energy connected with internal degrees of freedom

Eevap- the energy carried away by the evaporated particles

PES

Time Evolution


34

fission events Evaporation residue events

- starting point (sphere) - saddle point

For each fissioning trajectory it is possible to calculate masses (M1 and M2) and kinetic energies (EK) of fission fragments, fission time (tf), the number of evaporated light prescission particles.

Samples of Trajectories

scission line


35

200 MeV 32S + 100Mo: Fission Rate

t (x 10-21)

Fis

sion

Rat

e L = 60

L = 50

L = 40

L = 0-20


36

ER channel Prescission channel

Mp M Mp M

FF

(mb)

ER

(mb)

Exp.0,91 ± 0.15

0,56 ± 0.09

0,055 ± 0,007

0,038 ± 0,005

70 ± 7576 ±

50

Theor. 0.82 0.58 0.050 0.020 61 597

200 MeV 32S + 100Mo

Transient time for fission, ranging from 15 to 20 x 10-21 at high angular momentum of the composite system, where fission is relevant

Transient time for fission, ranging from 15 to 20 x 10-21 at high angular momentum of the composite system, where fission is relevant


37

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 seems to be a promising approach capable of reproducing a more complete set of data

More tests and measurement need to be performed

new clues on fission dynamics from systems of intermediate fissility

Documents

statistical modelt td

fisica delluniversit

fission rate gbwthe

bw fission rate

time evolutionmultiplicity

gbw fission barriers

statistical model calculations

time scalesfission dynamics