A new statistical scission-point model fed with microscopic ingredients Sophie Heinrich CEA/DAM-Dif/DPTA/Service de Physique Nucléaire CEA/DAM-Dif/DPTA/Service de Physique Nucléaire CEA DAM/DPTA/SPN/MED/Sophie Heinrich ESNT Workshop May Workshop on the Theories of Fission and Related Phenomena ESNT Workshop May 9- 12, 2006 Workshop on the Theories of Fission and Related Phenomena ESNT Workshop May 9- 12, 2006

CEA DAM/DPTA/SPN/MED/Sophie Heinrich ESNT Workshop May A new statistical scission-point model Preamble Preamble Our goal: To reconsider the original Wilkins scission-point model (1976) in order to provide some fission fragments properties, sustaining it with microscopic ingredients, and avoiding ad hoc parameters. (Thesis work)

Observations: Wide amplitude process Dramatic importance of shell effects of the fission fragments.  Reorganization of the nucleus internal structure statistical equilibrium scission point  System’s “history” is simulated by a statistical equilibrium at the scission point. Static Approach CEA DAM/DPTA/SPN/MED/Sophie Heinrich ESNT Workshop May Fundamental Hypothesis

 Many reachable observables We have: Experimental data with new insight (exotic nuclei, super heavy nuclei) and wide energy range (SPIRAL, GSI, …) A need of predictions for nuclear data (used directly or as a guide for reaction models) Why a renewal of the static approach ? Why a renewal of the static approach ? CEA DAM/DPTA/SPN/MED/Sophie Heinrich ESNT Workshop May We should provide: Fission fragments distributions (mass, energy …) Fragments properties (deformation, isospin …) Without phenomenological ajustement.

CEA DAM/DPTA/SPN/MED/Sophie Heinrich ESNT Workshop May Huge increase in computer processing power (CCRT, Very good microscopic description for individual (deformed) energy levels New level densities Better comprehension of scission-point features  Possible improvements to scission-point model Why a renewal of the static approach ? Why a renewal of the static approach ?

Scission Point Fission fragments distributions are entirely determined at Scission Point by the energy available in the system of the complementary fragment pairs...  If scission point can be precisely characterized, there is no more ajustable parameter ! Heavy fragment Light fragment Tips distance HH LL CEA DAM/DPTA/SPN/MED/Sophie Heinrich ESNT Workshop May Scission-point Model Energy at the scission point = Individual microscopic energy (HF + Gogny force) Individual microscopic energy (HF + Gogny force) for each fragments +Nuclear interaction + Nuclear interaction between the 2 fragments +Coulombian interaction + Coulombian interaction between the 2 fragments Available Energy of the system = E( compound system before fission ) – E( scission )

Available energy:  Relative probability of a given fragment pair :  Phase space: Wilkins et al. CEA DAM/DPTA/SPN/MED/Sophie Heinrich ESNT Workshop May Basic equation

 If we can precisely evaluate D at the scission point, there is no more adjustable parameters. Heavy fragment Light fragment D Tips Distance D HH LL CEA DAM/DPTA/SPN/MED/Sophie Heinrich ESNT Workshop May Scission-point Model

Evolution of 228Th distributions D = 1fm to 10fm How to choose D ??? CEA DAM/DPTA/SPN/MED/Sophie Heinrich ESNT Workshop May Tips-Distance Effect

Fusion path Potential barrier S P Exit Point ~ D CEA DAM/DPTA/SPN/MED/Sophie Heinrich ESNT Workshop May Fission Path

Z Axis (fm) radius (fm) Q 20 Selection of the Exit Points : Strong modification of total binding energy Hexadecapolar moment drop Nucleon density at the neck < 0.01 nuc.fm -3 : CEA DAM/DPTA/SPN/MED/Sophie Heinrich ESNT Workshop May Correlation between Scission-point and Exit-point D ~ 4 to 6fm Fit on 2 ellipsoids

CEA DAM/DPTA/SPN/MED/Sophie Heinrich ESNT Workshop May Mass and charge distributions 228 Thorium D = 5fm Excitation energy of fissioning nucleus = 10MeV Direct access to mass and charge yields. Outline of involved deformations.

CEA DAM/DPTA/SPN/MED/Sophie Heinrich Journées de physique nucléaire >228 Thorium K-H. Schmidt et al. N=132 N=134 N=136 N=138 Competition between the symmetric and the asymmetric fission for isotopes from A=222 to A=228.

CEA DAM/DPTA/SPN/MED/Sophie Heinrich ESNT Workshop May Mean Values X

CEA DAM/DPTA/SPN/MED/Sophie Heinrich ESNT Workshop May Total Kinetic Energy : Total Kinetic Energy : 5U5U Z A A Average kinetic energy for one fragment

CEA DAM/DPTA/SPN/MED/Sophie Heinrich ESNT Workshop May Average TKE of a specific fragment pair We can pick a specific fragment pair … … and calculate the TKE of the system distribution.

CEA DAM/DPTA/SPN/MED/Sophie Heinrich ESNT Workshop May Average deformation and excitation energies A Z A Average deformation of one fragment Average excitation energy of one fragment with respect to the mass Saw-tooth curve

Spherical/deformed and proton/neutron shell effects are well reproduce (Gogny force works fine). Most probable configurations: reliable predictions for nuclear data with a parameter coming from microscopic calculation. Peak width too short: needs dynamical consideration. CEA DAM/DPTA/SPN/MED/Sophie Heinrich ESNT Workshop May What have we learned ? Many observables are available : mean TKE, mean excitation energy,... and can be used for further evaluations (number of emitted neutron, …) We still suffer from a lack of description about what happens before the scission-point (prescission energy, emission of particules,…).

Rethink the whole definition of scission point. Include temperature microscopic calculation (no more shell effect). CEA DAM/DPTA/SPN/MED/Sophie Heinrich ESNT Workshop May Still to be done : Try out microscopic level densities.

J.L. Sida (PhD Director) H. Goutte J.F. Berger M. Girod S. Hilaire P. Romain B. Morillon P.Morel M. Dupuis F. Chappert CEA DAM/DPTA/SPN/MED/Sophie Heinrich ESNT Workshop May Cast & Crew :

CEA DAM/DPTA/SPN/MED/Sophie Heinrich ESNT Workshop May Level Density : G S M Generalized Superfluid Model : Generalized Superfluid Model : Critical energy, critical temperature, …etc, corresponding to phase transition between normal and superfluid phase. Level Density : E > E crit : E < E crit :

First interpretation : liquid drop fission…  Equal mass fragments : Actually, we often observe a heavy and a light fragment…  We need to consider quantum effects CEA DAM/DPTA/SPN/MED/Sophie Heinrich ESNT Workshop May Experimental results

Multi-valley symmetric valley asymmetric valley Time dependant Potential Energy Surface Time dependant Potential Energy Surface Elongation Asymmetry Energy Exit Points Héloïse Goutte CEA/DAM Theoretical Nuclear Structure Lab. CEA DAM/DPTA/SPN/MED/Sophie Heinrich ESNT Workshop May Dynamical Calculations

CEA DAM/DPTA/SPN/MED/Sophie Heinrich ESNT Workshop May Microscopic Description of the Nucleus 1 Nucleus = N nucleons with strong interaction Force N-N ? No direct calculation from QCD N body physics Can be resolved up to N = For N >> 10 : approximation needed Shell Model Effective residual interaction Valence space Symmetry conservation Mean field Approach No core Separation between internal structure and collective excitation (mean field and beyond) Naked force Effective force Zero range Finite range Phenomenological Effective Force