Microscopic studies of the fission process

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. Microscopic treatment with no pairing correlations: Time-Dependent Hartree-Fock • Microscopic treatment using adiabatic hypothesis: Time-Dependent GCM + GOA 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

5. 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-Bogoliubovmethod 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 238U 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., PRC75 064313 (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., PRC71 024316 (2005)

11. Prompt neutron emission: comparison with exp. data J.E. Gindler PRC19 1806 (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 themaxima • 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) 024316

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 experiments @ILL (TKE …) @GANIL (ex: program of F. Rejmund) elise@FAIR

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 !! Heloise.goutte@cea.fr