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

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

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 * …

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

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.

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

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

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

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

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)

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)

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) 024316

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

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

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