1. Microscopic studies of the fission process
People involved:
J.-F. Berger,
J.-P. Delaroche CEA Bruyères-le-Châtel
N. Dubray (soon in the ESNT)
H. Goutte
D. Gogny Livermore, USA
Dobrowolski Lublin, Poland
futur development
D. Lacroix GANIL
C. Simenel Saclay

2. Many applications of the fission process
Energy production
Ex: Thorium cycle, ADS
Production of exotic nuclei
Ex: SPIRAL 2
Role of fission in astrophysics
Fission is used and/or studied in new domains where no exp.
data exist (new nuclei,for a large range of incident energy).
 Accurate predictions are needed

3. Fission: many fundamental questions !!
Nuclear properties brought into play:
* nuclear configurations far from equilibrium
* large amplitude collective vibrations
* coupling between collective degrees of freedom
* couplings between collective and intrinsic degrees of freedom
Many open questions:
* Shell effects at large elongation
* Influence of the dynamics :
(ex: coupling between collective modes and intrinsic excitations)
* Effects of the temperature (excitation energy)
* Description of the initial state of the fissioning system
* Fission of odd nuclei
* Number of fission modes
(number of collective coordinates needed)
* Very asymmetric fission
* …

4. Fission: different approaches
– Dynamical description
Non treated but effects are simulated using statistical hypothesis
Statistical equilibrium at the scission point (Fong’s model )
Random breaking of the neck (Brosa’s model )
Scission point model (Wilkins-Steinberg )
Saddle point model (ABBLA)
Treated using a (semi-)classical approach :
Transport equations
Classical trajectories + viscosity
Classical trajectories + Langevin term
Microscopic treatment with no pairing correlations :
Time-Dependent Hartree-Fock
Microscopic treatment using adiabatic hypothesis :
Time-Dependent GCM + GOA

5. Fission dynamics results from a time evolution in a collective space
What we have done:
Our hypothesis
• fission dynamics is governed by the evolution of two collective parameters qi (elongation and asymmetry)
• Internal structure is at equilibrium at each step of the collective movement
• Adiabaticity
• no evaporation of pre-scission neutrons
Assumptions valid only for low-energy fission
( a few MeV above the barrier)
Fission dynamics results from a time evolution in a collective space
• Fission fragment properties are determined at scission,
and these properties do not change when fragments are well-separated.

6. What we have done: the formalism used
1- STATIC : constrained-Hartree-Fock-Bogoliubov method
with
Multipoles that are not constrained take on values that minimize the total energy.
Use of the D1S Gogny force: mean- field and pairing correlations are treated on the same footing

7. 2- DYNAMICS : Time-dependent Generator Coordinate Method
with the same than in HFB.
Using the Gaussian Overlap Approximation it leads to a
Schrödinger-like equation:
with
With this method the collective Hamiltonian is entirely derived by
microscopic ingredients and the Gogny D1S force

8. The way we proceed
1) Potential Energy Surface (q20,q30) from HFB calculations,
from spherical shape to large deformations
2) determination of the scission configurations in the (q20,q30) plane
3) calculation of the properties of the FF at scission
4) mass distributions from time-dependent calculations

9. Potential energy surfaces
226Th
256Fm
* SD minima in 226Th and 238U (and not in 256Fm)
SD minima washed out for N > 156 J.P. Delaroche et al., NPA 771 (2006) 103.
* Third minimum in 226Th
* Different topologies of the PES;
competitions between symmetric and asymmetric valleys

10. Definition of the scission line
No topological definition of scission points.
Different definitions:
* Enucl less than 1% of the Ecoul L.Bonneau et al., PRC (2007)
* density in the neck  < 0.01 fm-3
+ drop of the energy ( 15 MeV)
+ decrease of the hexadecapole moment ( 1/3)
J.-F. Berger et al., NPA428 23c (1984); H. Goutte et al., PRC (2005)

11. Prompt neutron emission: comparison with exp. data
J.E. Gindler PRC (1979)
Underestimation probably due to
the intrinsic excitation energy not
considered here.
But good qualitative agreement
N. Dubray, H. Goutte, J.-P. Delaroche, Phys. Rev. C77 (2008)

12. DYNAMICAL EFFECTS ON MASS DISTRIBUTION
Comparisons between 1D and « dynamical » distributions
• Same location of the maxima
Due to properties of the potential
energy surface (well-known shell effects)
• Spreading of the peak
Due to dynamical effects :
( interaction between the 2 collective
Modes via potential energy surface
and tensor of inertia)
• Good agreement with experiment
« 1D »
« DYNAMICAL »
WAHL
Yield
H. Goutte, J.-F. Berger, P. Casoli and D. Gogny, Phys. Rev. C71 (2005)

13. Experimental information needed
We need data on fission fragment properties;
Ex:
Kinetic Energy, Excitation energy,
Prompt  and n emission,
Polarisation,
Yields
… with an identification in mass and charge !!!
Support the (TKE …)
@GANIL (ex: program of F. Rejmund)

14. The future New features:
* To increase the number of collective coordinates (new fission modes)
* To study in more details the initial state
* To take into account the pre-scission energy
New developpements:
* to get rid of the adiabatic assumption:
role of the “dissipation” in the fission process
A PhD thesis is proposed
Work in collaboration with D. Lacroix and C. Simenel

15. This study is part of the program of the DANSER collaboration:
C. Simenel, D. Lacroix, H. Goutte
Dynamical Approaches for Nuclear Structure
and low –Energy Reactions
If someone is interested in joining us, welcome !!