A new statistical scission-point model fed with microscopic ingredients Sophie Heinrich CEA/DAM-Dif/DPTA/Service de Physique Nucléaire CEA/DAM-Dif/DPTA/Service

A new statistical scission-A new statistical scission-point model fed with point model fed with

microscopic ingredientsmicroscopic ingredients

A new statistical scission-A new statistical scission-point model fed with point model fed with

microscopic ingredientsmicroscopic ingredients

Sophie HeinrichSophie Heinrich

CEA/DAM-Dif/DPTA/Service de Physique NucléaireCEA/DAM-Dif/DPTA/Service de Physique Nucléaire

CEA DAM/DPTA/SPN/MED/Sophie Heinrich ESNT Workshop May 9-12 2006

Workshop on the Theories of Workshop on the Theories of Fission and Related PhenomenaFission and Related PhenomenaESNT Workshop May 9- 12,ESNT Workshop May 9- 12, 2006 2006

Workshop on the Theories of Workshop on the Theories of Fission and Related PhenomenaFission and Related PhenomenaESNT Workshop May 9- 12,ESNT Workshop May 9- 12, 2006 2006


A new statistical scission-point A new statistical scission-point modelmodel

PreamblePreamble

A new statistical scission-point A new statistical scission-point modelmodel

PreamblePreamble

Our goalOur goal::

To reconsider the original Wilkins scission-point model (1976)in order to provide some fission fragments properties,

sustaining it with microscopic ingredients,and avoiding ad hoc parameters.

(Thesis work)

ObservationsObservations::

Wide amplitude process

Dramatic importance of shell effects of the fission fragments.

Reorganization of the nucleus internal structure

System’s “history” is simulated by a statistical statistical equilibriumequilibrium at the

scission pointscission point.Static Approach


Fundamental HypothesisFundamental HypothesisFundamental HypothesisFundamental Hypothesis

Many reachable observables

We have:• Experimental data with new insight (exotic nuclei, super heavy nuclei) and wide energy range (SPIRAL , GSI, …)

• A need of predictions for nuclear data(used directly or as a guide for reaction models)

Why a renewal of the static approach ?Why a renewal of the static approach ? Why a renewal of the static approach ?Why a renewal of the static approach ?


We should provide:• Fission fragments distributions (mass, energy …)

• Fragments properties (deformation, isospin …)

Without phenomenological ajustement.


• Huge increase in computer processing power (CCRT, Ter@tec)

• Very good microscopic description for individual (deformed) energy levels

• New level densities

• Better comprehension of scission-point features

Possible improvements to scission-point model

Why a renewal of the static approach ?Why a renewal of the static approach ? Why a renewal of the static approach ?Why a renewal of the static approach ?

Fission fragments distributions are entirely determined at ScissionScission PointPoint by the energy available in the system of the complementary fragment pairs...

If scission point can be precisely characterized, there is no If scission point can be precisely characterized, there is no more ajustable parameter !more ajustable parameter !

Heavy fragment Light fragment

Tips distance

H L


Scission-point ModelScission-point ModelScission-point ModelScission-point Model

Energy at the scission point =

Individual microscopic energy (Individual microscopic energy (HF + Gogny forceHF + Gogny force)) for each fragments

++ Nuclear interactionNuclear interaction between the 2 fragments

++ Coulombian interactionCoulombian interaction between the 2 fragments

Available Energy of the system =

E( compound system before fission ) – E( scission )E( compound system before fission ) – E( scission )

)(* )( relEdispo EE Available energy:

Relative probability of a given fragment pair :Relative probability of a given fragment pair :

dEhhll

hlhZ

lZ

hA

lA

llE)*,(),(

),,,,,(

),(*

0

Phase space:

hlT

τZZAAV

hlhl ddZZAAPl h

coll

hlhlhlpot

1

0

1

0

),,,,,,(

min min

)exp(),,,(

Wilkins et al.CEA DAM/DPTA/SPN/MED/Sophie Heinrich ESNT Workshop May 9-12 2006

Basic equation Basic equation Basic equation Basic equation

If we can precisely evaluate If we can precisely evaluate DD at the scission point, at the scission point, there is no more adjustable parameters.there is no more adjustable parameters.

Heavy fragment

Light fragment

Tips Distance DD

H L


Scission-point ModelScission-point ModelScission-point ModelScission-point Model

Evolution of 228Th distributions

D = 1fm

to 10fm

How to choose D ???


Tips-Distance EffectTips-Distance EffectTips-Distance EffectTips-Distance Effect

Fusion path

Potential barrier

S P

Exit

Point

~ D


Fission PathFission PathFission PathFission Path

Z Axis (fm)

radi

us

(fm

)

Q20

Selection of the Exit Points :

Strong modification of total binding energy Hexadecapolar moment drop Nucleon density at the neck < 0.01 nuc.fm-3 :


Correlation between Scission-point and Correlation between Scission-point and Exit-pointExit-pointCorrelation between Scission-point and Correlation between Scission-point and Exit-pointExit-point

D ~ 4 to 6fm

Fit on 2 ellipsoids


Mass and charge distributionsMass and charge distributions

228 Thorium228 Thorium

D = 5fm

Excitation energy of fissioning nucleus = 10MeV

Direct access to mass and charge yields.

Outline of involved deformations.

CEA DAM/DPTA/SPN/MED/Sophie Heinrich Journées de physique nucléaire 2006

222->228222->228ThoriumThorium

K-H. Schmidt et al.

N=132

N=134

N=136

N=138

Competition between the symmetric and the asymmetric fission for isotopes from A=222 to A=228.


Mean Values Mean Values Mean Values Mean Values

hl

E

ddd

Ehhll

hZ

lZ

hA

lAP

ll

)*,(),(...

),,,(

),(*

0............

X


Total Kinetic Energy : <VTotal Kinetic Energy : <Vcoulcoul + V + Vnucnuc>>Total Kinetic Energy : <VTotal Kinetic Energy : <Vcoulcoul + V + Vnucnuc>>

5UZ

A

A

Average kinetic energy for one fragment


Average TKE of a specific fragment pairAverage TKE of a specific fragment pair Average TKE of a specific fragment pairAverage TKE of a specific fragment pair

We can pick a specific fragment pair …

… and calculate the TKE of the system distribution.


Average deformation and excitation Average deformation and excitation energiesenergies

Average deformation and excitation Average deformation and excitation energiesenergies

A

Z

A

Average deformation of one fragment

Average excitation energy of one fragment with respect to the mass

Saw-tooth curve

Spherical/deformed and proton/neutron shell effects are well reproduce (Gogny force works fine).

Most probable configurations: reliable predictions for nuclear data with a parameter coming from microscopic calculation.

Peak width too short: needs dynamical consideration.


What have we learned ?What have we learned ?What have we learned ?What have we learned ?

Many observables are available : mean TKE, mean excitation energy,... and can be used for further evaluations (number of emitted neutron, …)

We still suffer from a lack of description about what happens before the scission-point (prescission energy, emission of particules,…).

Rethink the whole definition of scission point.

Include temperature microscopic calculation (no more shell effect).


Still to be done :Still to be done :Still to be done :Still to be done :

Try out microscopic level densities.

J.L. Sida J.L. Sida (PhD Director)(PhD Director)H. GoutteH. GoutteJ.F. BergerJ.F. BergerM. GirodM. GirodS. HilaireS. Hilaire

P. RomainP. RomainB. MorillonB. MorillonP.MorelP.MorelM. DupuisM. DupuisF. ChappertF. Chappert


Cast & Crew :Cast & Crew :Cast & Crew :Cast & Crew :


Level Density : G S MLevel Density : G S MLevel Density : G S MLevel Density : G S M

Generalized Superfluid ModelGeneralized Superfluid Model : : Critical energy, critical temperature, …etc, corresponding to phase transition between normal and superfluid phase.

Level DensityLevel Density ::

02 ETaE critcritcrit

4/504/1

)(2

)(12

)2(1 )(

0

EEaE e

EEa

oc

2

2

11)(~

aTe

WAaaaT

E > Ecrit

:

E < Ecrit :

DE e

S

oc

)2(1 )(

2

21

1)(~critcrit

Ta

critTa

eWAaaa

critcrit

First interpretation : liquid drop fission…

Equal mass fragments :

Actually, we often observe a heavy and a light fragment…

We need to consider quantum effects


Experimental resultsExperimental resultsExperimental resultsExperimental results

Multi-valley symmetric valley asymmetric valley

Time dependant Time dependant Potential Energy SurfacePotential Energy Surface

Time dependant Time dependant Potential Energy SurfacePotential Energy Surface

ElongationAsymmetry

En

erg

y

Exit Points Héloïse Goutte

CEA/DAM Theoretical Nuclear Structure Lab.


Dynamical CalculationsDynamical CalculationsDynamical CalculationsDynamical Calculations


Microscopic Description of the Microscopic Description of the NucleusNucleus

Microscopic Description of the Microscopic Description of the NucleusNucleus

1 Nucleus = N nucleons with strong interaction

Force N-N ? No direct calculationfrom QCD

N body physics

Can be resolved up to N = 10 - 12For N >> 10 : approximation needed

Shell Model• Effective residual interaction• Valence space• Symmetry conservation

Mean field Approach• No core• Separation between internal structure and collective excitation(mean field and beyond)

Naked force

Effective force

Zero rangeFinite range

Phenomenological Effective Force

Documents

A new statistical scission-point model fed with microscopic ingredients Sophie Heinrich CEA/DAM-Dif/DPTA/Service de Physique Nucléaire CEA/DAM-Dif/DPTA/Service