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SPY: a microscopic statistical scission-point model to predict fission fragment distributions S. Panebianco 1 , N. Dubray 2 , H. Goutte 1 , S. Heinrich 2* , S. Hilaire 2 , J.-F. Lematre, J.-L. Sida 1 1 CEA Centre de Saclay, Irfu, 91191

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SLIDE 1

Stefano Panebianco - [SPY: a microscopic statistical scission point model]

SPY: a microscopic statistical scission-point model to predict fission fragment distributions

  • S. Panebianco1, N. Dubray2, H. Goutte1, S. Heinrich2*,
  • S. Hilaire2, J.-F. Lemaître, J.-L. Sida1

1CEA Centre de Saclay, Irfu, 91191 Gif-sur-Yvette, France 2CEA, DAM, DIF, 91297 Arpajon, France * Former member of the laboratory

WONDER 2012 Aix-en-Provence, 25-28 September 2012

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SLIDE 2

Stefano Panebianco - [SPY: a microscopic statistical scission point model]

SPY: a microscopic statistical scission-point model to predict fission fragment distributions

  • S. Panebianco1, N. Dubray2, H. Goutte1, S. Heinrich2*,
  • S. Hilaire2, J.-F. Lemaître, J.-L. Sida1

1CEA Centre de Saclay, Irfu, 91191 Gif-sur-Yvette, France 2CEA, DAM, DIF, 91297 Arpajon, France * Former member of the laboratory

WONDER 2012 Aix-en-Provence, 25-28 September 2012

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SLIDE 3

Stefano Panebianco - [SPY: a microscopic statistical scission point model]

The scission-point model

  • First proposed by Wilkins (Wilkins et al., Phys. Rev. C 14 (1976) 5)
  • Static approach:
  • Fission process is slow
  • A statistical «quasi»-equilibrium is reached at scission
  • The main fragment characteristics are freezed at this point
  • Dynamics is not explicitly treated
  • The scission configuration is defined by two ellipsoids with an inter-

surface distance d

d

ZL, AL, βL ZH, AH,βH

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SLIDE 4

Stefano Panebianco - [SPY: a microscopic statistical scission point model]

The scission-point model

  • First proposed by Wilkins (Wilkins et al, Phys. Rev. C 14 (1976) 5)
  • Static approach
  • Based on an energy balance at scission
  • Main limitations:
  • Collective and intrinsic temperature parameters (+ d!) fitted on data
  • Energy potentials are relative to the scission point
  • Only prolate deformations
  • Individual energies are not microscopic (liquid drop + Strutinski + pairing)

d

ZL, AL, βL,τint ZH, AH,βH,τint

Tcoll

V(Z1,2,N1,2,β1,2,d,τ1,2) = ΣVLD

1,2(Z1,2,N1,2,β1,2)+ΣVStr. 1,2(Z1,2,N1,2,β1,2,τ1,2)

+ Vcoul(Z1,2,N1,2,β1,2,d) +Vnucl(Z1,2,N1,2,β1,2,d)

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SLIDE 5

Stefano Panebianco - [SPY: a microscopic statistical scission point model]

The SPY model

  • A revised version of Wilkins model was developed by S. Heinrich

(PhD thesis, 2006) and J.-L. Sida

  • Main core of SPY (Scission Point model for fission fragment Yields)
  • Based on microscopic ingredients
  • Individual microscopic energies based on HFB calculation with the

Gogny D1S interaction (avail. @ Amedee database)

  • No dependence on intrinsic temperature
  • Available energy is calculated as:
  • Coulomb interaction based on Cohen Swiatecki formalism

Cohen and Swiatecki, Annals of Physics 19 (1962) 67

  • Nuclear interaction based on the Blocki proximity potential

Blocki et al, Annals of Physics 105 (1977) 427

Eavail = Etot – V V(Z1,2,N1,2,β1,2,d) = ΣVHFB

1,2(Z1,2,N1,2,β1,2)

+ Vcoul(Z1,2,N1,2,β1,2,d) +Vnucl(Z1,2,N1,2,β1,2,d)

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SLIDE 6

Stefano Panebianco - [SPY: a microscopic statistical scission point model]

SPY into the Hg fission debate…

Andreyev et al., PRL 105 (2011) 252502

β-delayed fission of 180Tl Surprising asymmetric yields of 180Hg fission fully attributed to the nuclear structure of the fissioning nucleus

Möller et al., PRC 85 (2012) 024306

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SLIDE 7

Stefano Panebianco - [SPY: a microscopic statistical scission point model]

SPY into the Hg fission debate…

Andreyev et al., PRL 105 (2011) 252502

β-delayed fission of 180Tl Surprising asymmetric yields of 180Hg fission fully attributed to the nuclear structure of the fissioning nucleus

Möller et al., PRC 85 (2012) 024306

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SLIDE 8

Stefano Panebianco - [SPY: a microscopic statistical scission point model]

Available energy at scission: symmetric fragmentation

90Zr 180Hg fission @ E*=10MeV

SPY

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SLIDE 9

Stefano Panebianco - [SPY: a microscopic statistical scission point model]

Available energy at scission: asymmetric fragmentation

76Se 104Pd 180Hg fission @ E*=10MeV

SPY

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SLIDE 10

Stefano Panebianco - [SPY: a microscopic statistical scission point model]

Available energy at scission

180Hg fission @ E*=10MeV

SPY

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SLIDE 11

Stefano Panebianco - [SPY: a microscopic statistical scission point model]

Two reference cases

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

198Hg fission @ E*=10 MeV

SPY

236U fission @ E*=8 MeV

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SLIDE 12

Stefano Panebianco - [SPY: a microscopic statistical scission point model]

On the scission point definition

  • 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

Elongation Asymmetry

Energy

Exit Points

  • H. Goutte

z (fm) r (fm)

Nucleon density at the neck ρ < 0.01 fm3 Total binding energy drop (≈ 15 MeV) Hexadecupolar moment drop (≈ 1/3) d=5fm

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SLIDE 13

Stefano Panebianco - [SPY: a microscopic statistical scission point model]

On the choice of the scission distance

Self-consistent HFB of 180Hg: most probable configuration (q20=256.12b ; q30=33.28b3/2) d = 5.7 fm

  • N. Dubray

SPY

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SLIDE 14

Stefano Panebianco - [SPY: a microscopic statistical scission point model]

The statistical treatment

  • The probability of a given fragmentation is linked 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 level/state density

  • The energy partition at scission is supposed to be equiprobable

between each state available to the system (microcanonical system)

  • Therefore the phase space is defined as:
  • The relative probability of a given fragment pair is:

ε ε β ρ ε β ρ β β π

ε ε

d A h h l l A h l h Z l Z h N l N

A

) , ( ) , ( ) , , , , , , ( − = ∫

= =

h l h l h l h l

d d A Z Z N N P β β β β π

β β

∫ ∫

=

max max

) , , (..., ) , , , (

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SLIDE 15

Stefano Panebianco - [SPY: a microscopic statistical scission point model]

The level density ingredient

  • Very delicate point of the model…
  • In this approach the level densities are a natural counterbalance to a

stronger stabilization of spherical deformations and even-even nuclei, which leads to unphysical fragment mass distributions

  • For the time being, a Fermi gas approach has been tested
  • The CTM effective level density is parameterized as:

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

with , and

  • A microscopic calculation of level densities has been recently

performed (at zero temperature) in the framework of HFB formalism

  • Very time consuming since the we need the energy evolution at each

deformation for some 1500 nuclei

4 / 5 4 / 1 2

12 2 1 ) ( E a E

e

aE F

π σ π ρ =

3 / 2

A A a β α + = 282769 . , 0692559 . = = β α a E a I / = σ

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SLIDE 16

Stefano Panebianco - [SPY: a microscopic statistical scission point model]

From the available energy to the yield

Amin Yields Mass yields

180Hg fission @ E*=10MeV

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Stefano Panebianco - [SPY: a microscopic statistical scission point model]

Conclusions and perspectives

  • SPY: a scission-point model fully based on microscopic

ingredients (beyond Wilkins)

  • Work in progress but first results are rather encouraging
  • Able to explain the mass asymmetry observed in 180Hg fission

(paper just submitted for publication…)

  • The lack of dynamics is visible (width of yields distributions… see
  • B. Jurado talk!) and expected
  • Ongoing and future developments (PhD thesis starting):
  • Take into account pre-scission energy into the balance (this can wash
  • ut the dependence on d)
  • Integration of the new D1M Gogny interaction
  • Integration of HFB calculation at finite temperature (E* ≈ T2)
  • Microscopic level densities from HFB (intrinsic + collective)
  • Integration of full spin populations
  • Integration in THALYS
  • …
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SLIDE 18

Stefano Panebianco - [SPY: a microscopic statistical scission point model]

Backup slides

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SLIDE 19

Stefano Panebianco - [SPY: a microscopic statistical scission point model]

From the available energy to the yield

nth + 235U

Amin Yields Mass yields

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SLIDE 20

Stefano Panebianco - [SPY: a microscopic statistical scission point model]

Observables: mass and charge yields

nth + 235U

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SLIDE 21

Stefano Panebianco - [SPY: a microscopic statistical scission point model]

Systematics: mass yields for n-induced fission

nth + 229Th nth + 233U nth + 235U nth + 239Pu nth + 245Cm nth + 249Cf nth + 254Es

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Stefano Panebianco - [SPY: a microscopic statistical scission point model]

Systematics: mass yields for spontaneous fission

246Cm(sf) 248Cm(sf) 250Cf(sf) 252Cf(sf) 254Cf(sf) 256Fm(sf)

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SLIDE 23

Stefano Panebianco - [SPY: a microscopic statistical scission point model]

Systematics: mean TKE

We miss around 10 MeV: prescission energy (d dependence), Coulomb?

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SLIDE 24

Stefano Panebianco - [SPY: a microscopic statistical scission point model]

Systematics: mean deformation energy

The deformation energy is somehow related to the number of emitted particles

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SLIDE 25

Stefano Panebianco - [SPY: a microscopic statistical scission point model]

Available energy at scission: asymmetric fragmentation

132Sn 104Mo

nth + 235U Driven by the double shell effect

  • f spherical 132Sn
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SLIDE 26

Stefano Panebianco - [SPY: a microscopic statistical scission point model]

Available energy at scission: symmetric fragmentation

Quite large deformations available for soft nuclei nth + 235U

118Pd