Transcript The SPY model: how the microscopic - FUSTIPEN

THE SPY MODEL: HOW A
MICROSCOPIC DESCRIPTION OF THE
NUCLEUS CAN SHED SOME LIGHT
ON FISSION
S. Panebianco, N. Dubray, S. Hilaire, J-F. Lemaître, J-L. Sida
CEA - Irfu/SPhN, Saclay, France
CEA – DIF, Arpajon, France
FUSTIPEN topical meeting
October 13th 2014
GANIL, Caen (FR)
www.cea.fr
www.cea.fr
| PAGE 1
INTRODUCTION
Why a scission-point model?
Non-adiabatic dynamics
N-body problem
Shell effects
Nuclear structure
Intrinsic vs collective DoF
Deformations
Viscosity and friction
High spin exotic nuclei
Event-odd effects
Fission is the ideal nuclear physics laboratory and is still a challenge for theory and experiments
INTRODUCTION
Why a scission-point model?
Non-adiabatic dynamics
N-body problem
Shell effects
Nuclear structure
Intrinsic vs collective DoF
Deformations
Viscosity and friction
High spin exotic nuclei
Event-odd effects
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?
Non-adiabatic dynamics
N-body problem
Shell effects
Nuclear structure
Intrinsic vs collective DoF
Deformations
Viscosity and friction
High spin exotic nuclei
Event-odd effects
Fission is the ideal nuclear physics laboratory and is still a challenge for theory and experiments
Scission-point model
B. 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?
Non-adiabatic dynamics
N-body problem
Shell effects
Nuclear structure
Intrinsic vs collective DoF
Deformations
Viscosity and friction
High spin exotic nuclei
Event-odd effects
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
Microscopic data
Scission-point model
• Strong hypothesis are needed:
• Static
• CN formation neglected
• All fragment properties are freezed
• Very low computing cost
•
•
•
•
Precise treatement of nuclear structure
No parameters needed
Only way to explore unkown regions
Microscopic data are tabulated (fast!)
THE SCISSION-POINT DEFINITION
THE SCISSION-POINT DEFINITION
- Thermodynamic equilibrium at scission is assumed
→ statistical equilibrium among system degrees of freedom
- Isolated fragments
→ microcanonical statistical description
 all states at scission are equiprobable
THE SCISSION-POINT DEFINITION
The system configuration is defined by the two fragments DoF :
- proton and neutron numbers (Z1, N1, Z2, N2)
- quadrupolar deformations ( b1 , b2)
- intrinsic excitation energy (E1* , E2*)
Two quantities are needed to calculate average observables :
- available energy for each configuration : Eavail
- state density of the two fragments: r1 , r2
THE ENERGY BALANCE AT SCISSION
- Available energy calculation for each fragmentation (500-1000)
236U*

132Sn
+ 104Mo
→ fragments individual energy
from 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) 427
S. Cohen et al., Annals of Physics 19 (1962) 67
Eavail =
EHFB1 (Z N β ) +EHFB2 (Z N β )
+ Ecoul (d ,Z N β Z N β )+Enucl (d ,Z N β Z N β )
- ECN
if E <0 : fragmentation is allowed
1,
1,
1,
1,
1
2,
1,
2,
2,
2,
2
2
1,
avail
1,
1,
2,
2,
2
WHAT THE MICROSCOPY BRINGS
- Available energy calculation for each fragmentation (500-1000)
E avail = E HFB1 + E HFB2 + E coul + E nucl - E CN
THE STATISTICS AT SCISSION
• 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:
π Z1 , N1 , Z 2 , N 2 , β1 , β2 , x  = ρ1 xE avail ρ2 1  x E avail δE 2
with x the fraction of energy available to excite fragment 1
• Hence, the probability of a fragmentation is easily calculated:
1
Π Z1 , N1 , Z 2 , N 2 , β1 , β2  =  π Z1 , N1 , Z 2 , N 2 , β1 , β2 , x dx
0
PZ1 , N1 , Z 2 , N 2  =
1.3 1.3
  Π Z , N , Z , N
1
 0.6  0.6
1
2
2
, β1 , β2 dβ1dβ2
THE STATISTICS AT SCISSION
For the time being, a Fermi gas level density is used (CT model)
2 aU
1
 e
r F (U ) 
1/ 4 5 / 4
2  12 a U
a  A  bA2 / 3
  0.0692559, b  0.282769
  I0a U / a
A. 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
180Hg
fission @ E*=10MeV
SPY
90Zr
BACKUP
AVAILABLE ENERGY AT SCISSION: ASYMMETRIC FRAGMENTATION
180Hg
fission @ E*=10MeV
SPY
104Pd
76Se
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 180Hg
SPY results for 180Hg fission @ E*=10MeV
SPY
SPY
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
BACKUP
TWO REFERENCE CASES
198Hg
236U
fission @ E*=10 MeV
Itkis et al., Yad. Fiz. 53 (1991) 1225
SPY
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
132Sn
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
132Sn
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
SOME UNEXPECTED RESULTS
Impact of SPY prediction on stellar nucleosynthesis (collab. with S. Goriely)
White : Solar r-abundance distribution
Red : fission yields from SPY
Blue : fission yields from empirical formula
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
BACKUP
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
Nucleon density at the neck r < 0.01 fm3
Total binding energy drop ( 15 MeV)
Hexadecupolar moment drop ( 1/3)
Exit Points
d=5fm
H. Goutte
z (fm)
BACKUP
Wilkins VS SPY
Wilkins model
SPY model
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
Relative : Epot
Absolute : Eavail = Epot – ECN
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
Canonical
Microcanonical
Individual energy
Energy balance
Statistics
(if < 0 ; fragmentation is allowed)
Epot = E1ind +E2ind +Ecoul +E nucl
BACKUP
On the mean deformation energy
The deformation energy is directly
related to the number of emitted particles