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THE SPY MODEL: HOW A

MICROSCOPIC DESCRIPTION OF THE

NUCLEUS CAN SHED SOME LIGHT

ON FISSION

| PAGE 1

S. Panebianco, N. Dubray, S. Hilaire, J-F. Lemaître, J-L. Sida

CEA - Irfu/SPhN, Saclay, FranceCEA – DIF, Arpajon, France

FUSTIPEN topical meeting

October 13th 2014GANIL, Caen (FR)

INTRODUCTION

Why a scission-point model?

N-body problem

Nuclear structure

High spin exotic nuclei

Viscosity and friction

Non-adiabatic dynamics

Intrinsic vs collective DoF

Event-odd effects

Shell effects

Deformations

Fission is the ideal nuclear physics laboratory and is still a challenge for theory and experiments

INTRODUCTION

Why a scission-point model?

N-body problem

Nuclear structure

High spin exotic nuclei

Viscosity and friction

Non-adiabatic dynamics

Intrinsic vs collective DoF

Event-odd effects

Shell effects

Deformations

Fission is the ideal nuclear physics laboratory and is still a challenge for theory and experiments

Two main approaches are used to model the fission process:

Models based on phenomenology • Based on experimental data• Describe well know properties• Low predictive power far from data• Low computing cost

Models based on microscopy• Only few parameters (N-N interaction)• Less precise agreement with data• High predictive power far from know regions• High computing cost

INTRODUCTION

Why a scission-point model?

N-body problem

Nuclear structure

High spin exotic nuclei

Viscosity and friction

Non-adiabatic dynamics

Intrinsic vs collective DoF

Event-odd effects

Shell effects

Deformations

Fission is the ideal nuclear physics laboratory and is still a challenge for theory and experiments

Scission-point modelB. D. Wilkins et al., Phys. Rev. C 14 (1976) 1832

• Strong hypothesis are needed:• Static• CN formation neglected• All fragment properties are freezed

• Energy balance at scission : LDM+shell corections (Strutinski)+pairing corrections• Parameters needed (intrinsic and collective temperature)• Very low computing cost

INTRODUCTION

Why a new scission-point model?

N-body problem

Nuclear structure

High spin exotic nuclei

Viscosity and friction

Non-adiabatic dynamics

Intrinsic vs collective DoF

Event-odd effects

Shell effects

Deformations

Fission is the ideal nuclear physics laboratory and is still a challenge for theory and experiments

SPY : a new scission-point model based on microscopic ingredients

Scission-point model• Strong hypothesis are needed:

• Static• CN formation neglected• All fragment properties are freezed

• Very low computing cost

Microscopic data• Precise treatement of nuclear structure• No parameters needed• Only way to explore unkown regions• Microscopic data are tabulated (fast!)

E

1

2

3

deformation

THE SCISSION-POINT DEFINITION

THE SCISSION-POINT DEFINITION

E

1

2

3

deformation

d

Z1, N

1,b

1Z

2, N

2,b

2

- Thermodynamic equilibrium at scission is assumed → statistical equilibrium among system degrees of freedom- Isolated fragments → microcanonical statistical descriptionÞ all states at scission are equiprobable

THE SCISSION-POINT DEFINITION

E

1

2

3

deformation

d

Z1, N

1,b

1Z

2, N

2,b

2

The system configuration is defined by the two fragments DoF :- proton and neutron numbers (Z

1, N

1, Z

2, N

2)

- quadrupolar deformations ( b1 , b

2)

- intrinsic excitation energy (E1* , E

2*)

Two quantities are needed to calculate average observables : - available energy for each configuration : E

avail

- state density of the two fragments: r1 , r

2

THE ENERGY BALANCE AT SCISSION

- Available energy calculation for each fragmentation (500-1000)

236U* ® 132Sn + 104Mo→ fragments individual energyfrom HFB calculation with Gogny D1S interaction (Amedee data base)S. Hilaire et al., Eur. Phys. Jour. A 33 (2007) 237

→ interaction energy(nuclear + Couloub interactions)J. Blocki et al., Annals of Physics 105 (1977) 427S. Cohen et al., Annals of Physics 19 (1962) 67

Eavail= EHFB1 (Z1, N1,b1)+EHFB2 (Z2,N2,b2)

+ Ecoul (d ,Z1, N1,b1,Z2, N2,b2)+Enucl (d ,Z1, N1,b1, Z2,N2,b2)

- ECN if Eavail<0 : fragmentation is allowed

WHAT THE MICROSCOPY BRINGS

- Available energy calculation for each fragmentation (500-1000)

CNnuclcoulHFB2HFB1avail E - EE+EE E ++=

THE STATISTICS AT SCISSION

2avail2avail1212211 EEx1Exx,,,N,Z,N,Z δρρ=ββπ

• The probability of a given fragmentation is related to the phase space available at scission• The phase space is defined by the number of available states of each fragment, i.e. the intrinsic state density• The energy partition at scission is supposed to be equiprobable between each state available to the system (microcanonical)• Therefore the probability of a configuration is defined as:

with x the fraction of energy available to excite fragment 1

21212211

1.3

0.6

1.3

0.6

2211

212211

1

0

212211

dd,,N,Z,N,ZN,Z,N,ZP

dxx,,,N,Z,N,Z,,N,Z,N,Z

ββββΠ=

ββπ=ββΠ

• Hence, the probability of a fragmentation is easily calculated:

THE STATISTICS AT SCISSION

For the time being, a Fermi gas level density is used (CT model)

4/54/1

2

122

1 )(

UaU e

aU

F

3/2AAa b 282769.0 ,0692559.0 b

aUaI /0A. Koning et al., Nucl. Phys. A 810 (2008) 13

No dependence on deformation

SOME EXPECTED RESULTS

Fission yields of 235U(nth,f) and 252Cf(sf)

J. F. Lemaître et al., Proc. «Fission 2013», Caen (France), 28-31/05/2013.

SOME EXPECTED RESULTS

Kinectic Energy of fragments from 235U(nth,f)

J. F. Lemaître et al., Proc. «Fission 2013», Caen (France), 28-31/05/2013.

SOME REMARKABLE RESULTS

A REMARKABLE POWER OF DESCRIPTION

Charge yields from Ac to U isotopic chains

SPY vs GSI data (Nucl. Phys. A 665, 221)J. F. Lemaître et al., Proc. «Zakopane 2014», 31/08-07/09/2014

A REMARKABLE PREDICTION POWER

Peak multiplicity over the whole nuclear chart

J. F. Lemaître et al., Proc. «Zakopane 2014», 31/08-07/09/2014

WHAT THE MICROSCOPY BROUGHT

The integration of microscopic description of the nuclei in a statistical scission point model shows that shell effects drive the mass asymetry

However, these effects are energy (temparature) and deformation dependent and still too pronounced (i.e., 132Sn plays as a strong attractor)

J. F. Lemaître et al., paper in preparation for PRC

WHAT THE MICROSCOPY CAN STILL BRING

But : nuclear structure affects also state density:• Include microscopic state density from combinatorial on HFB

nucleonic level diagram

SOME PRELIMINARY RESULTS

Fission yields of 235U(nth,f) and 252Cf(sf)Fragment nuclear structure is present on:

Individual energy (HFB – Gogny D1S) State density (Fermi gas)

SOME PRELIMINARY RESULTS

Fission yields of 235U(nth,f) and 252Cf(sf)Fragment nuclear structure is present on:

Individual energy (HFB – Gogny D1S) State density (Fermi gas)

PERSPECTIVES

The integration of microscopic description of the nuclei in a statistical scission point model showed that shell effects drive the mass asymetry

However, these effects are energy (temparature) and deformation dependent and still too pronounced (i.e., 132Sn plays as a strong attractor)

The ongoing developments consist of:• Explore the richness of microscopic state density from HFB• Include collectivity on both HFB energy and states density• Include HFB data at finite temperature (Gogny D1M)

THE LESSON WE’VE LEARNT

THE LESSON WE’VE LEARNT

BACKUP

BACKUP

AVAILABLE ENERGY AT SCISSION: SYMMETRIC FRAGMENTATION

90Zr

180Hg fission @ E*=10MeV

SPY

BACKUP

AVAILABLE ENERGY AT SCISSION: ASYMMETRIC FRAGMENTATION

76Se104Pd

180Hg fission @ E*=10MeV

SPY

SOME UNEXPECTED RESULTS

The strange case of 180Hg

b-delayed fission of 180Tl (@ Isolde)Surprising asymmetric yields of 180Hg fission fully attributed to the nuclear structure of the fissioning nucleus

A. Andreyev et al., Phys. Rev. Lett. 105 (2011) 252502

P. Möller et al., Phys. Rev. C 85 (2012) 024306

SOME UNEXPECTED RESULTS

The strange case of 180HgSPY results for 180Hg fission @ E*=10MeV

S. Panebianco et al., Phys. Rev. C 86 (2012) 064601

Self-consistent HFB of 180Hg:most probable configuration(q20=256.12b ; q30=33.28b3/2)

d = 5.7 fm

SPYSPY

BACKUPTWO REFERENCE CASES

Itkis et al., Yad. Fiz. 53 (1991) 1225

198Hg fission @ E*=10 MeV

SPY

236U fission @ E*=8 MeV

SOME UNEXPECTED RESULTS

Microscopic data open the possibility to explore the whole nuclear chart

Mean deformation of heavy fragment Mean deformation of light fragment

Ypeak/Yvalley

SOME UNEXPECTED RESULTS

Microscopic data open the possibility to explore the whole nuclear chart

Mean deformation of heavy fragment Mean deformation of light fragment

Ypeak/Yvalley

132Sn

SOME UNEXPECTED RESULTS

Microscopic data open the possibility to explore the whole nuclear chart

Mean deformation of heavy fragment Mean deformation of light fragment

Ypeak/Yvalley

132Sn

SOME UNEXPECTED RESULTS

Microscopic data open the possibility to explore the whole nuclear chart

Mean deformation of heavy fragment Mean deformation of light fragment

Ypeak/Yvalley

SOME UNEXPECTED RESULTS

White : Solar r-abundance distributionRed : fission yields from SPYBlue : fission yields from empirical formula

Impact of SPY prediction on stellar nucleosynthesis (collab. with S. Goriely)

S. Goriely, Astron. Astrophys. 342, 881 (1999)T. Kodoma et al., Nucl. Phys. A. 239, 489 (1975)

SOME UNEXPECTED RESULTS

Impact of SPY prediction on stellar nucleosynthesis (collab. with S. Goriely)

Very unexpected four-humped mass distribution from A=278 isobars

SOME UNEXPECTED RESULTS

Impact of SPY prediction on stellar nucleosynthesis (collab. with S. Goriely)

Very unexpected four-humped mass distribution from A=278 isobars

Confirmed by full HFB calculation

S. Goriely, SP et al., to be published

PES of 278Cf

•The SPY model is “parameter free”

•The distance d is fixed at 5 fm

•The distance is chosen on the exit points selection criteria used on Bruyères microscopic fission calculations

BACKUP

ON THE SCISSION POINT DEFINITION

ElongationAsymmetry

En

erg

y

Exit Points

H. Goutte z (fm)

r (f

m)

Nucleon density at the neck < 0.01 fm3

Total binding energy drop ( 15 MeV) Hexadecupolar moment drop ( 1/3)

d=5fm

BACKUP

Wilkins VS SPY

Epot=E1ind+E2

ind+Ecoul+Enucl

Wilkins model SPY model

Individual energy Liquid drop+

Strutinski + pairing

HFB (Gogny D1S)http://www-phynu.cea.fr/HFB-Gogny.htm

S. Hilaire and M. Girod, EPJ A 33 (2007) 237

Energy balance Relative : Epot

Absolute : Eavail

= Epot

– ECN

(if < 0 ; fragmentation is allowed)

Temperature parameters

Collective (statistics) +

Intrinsic (shell effects)

No temperature States density for statistics

Deformation Only prolate Oblate + prolate

Distance d 1.2 - 1.4 fm 5 fm

Statistics Canonical Microcanonical

BACKUP

On the mean deformation energy

The deformation energy is directly related to the number of emitted

particles