Time dependent GCM GOA method

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Time dependent GCMGOA method applied to the
fission process
H. Goutte, J.-F. Berger, D. Gogny CEA/DAM Ile de
France
ESNT janvier 2006
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Fission many open theoretical questions
Shell effects (proton/neutron,
spherical/deformed) What kind of
deformations ? Role of the dynamics
Couplings between collective modes Couplings
between collective and intrinsic excitations
Effects of the excitation energy Definition of
the initial state of the fissioning system
Definition of the barriers for reaction model
Fission fragment properties Fission of odd
nuclei Emission of particles These
properties are both static/dynamical and related
to both the fissioning system and the fragments
!!!
With the help of K.-H. Schmidt

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Fission our study
Shell effects (proton/neutron,
spherical/deformed) What kind of
deformations ? Role of the dynamics
Couplings between collective modes Couplings
between collective and intrinsic excitations
Effects of the excitation energy Definition of
the initial state of the fissioning system
Definition of the barriers for reaction model
Fission fragment properties Fission of odd
nuclei Emission of particles Results on
fission barriers and potential energy surfaces
kinetic energy distributions
fission fragment properties fragment
mass distributions
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FORMALISM

• Assumptions
• 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

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• A two-steps formalism
• STATIC calculations determination of
• Analysis of the nuclear properties as functions
  of the deformations
• Constrained- Hartree-Fock-Bogoliubov method using
  the D1S Gogny effective interaction
• DYNAMICAL calculations determination of f(qi,t)
• Time evolution in the fission channel
• Formalism based on the Time dependent Generator
  Coordinate Method (TDGCM)

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FORMALISM
Theoretical methods

• 1- STATIC constrained-Hartree-Fock-Bogoliubov
  method
• 
  
• with

• 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

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STATIC RESULTS

• Potential energy surface

Exit Points

• Multi valleys
• asymmetric valley
• symmetric valley

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STATIC RESULTS

• Definition of the scission line
• The set of exit points defined for all q30
  represent the scission line.
• The scission line is defined by 3 criteria
  density in the neck ? lt 0.01 fm3
• drop of the energy (? 15 MeV) decrease of
  the hexadecapole moment (? 1/3)
• Along the scission line we determine
• ? masses and charges of the fragments,
• ? distance between the fragments
• ? deformations of the fragments,
• ? . . .
• We can derive
• ? kinetic energy distributions
• ?  1D static mass and charge distributions,
• ? fragment deformation energy,
• ? polarisation of the fragments,
• ? . . .

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STATIC RESULTS

• Total kinetic energy distribution
• The dip at AH AL and peak at
• AH? 134 are well reproduced
• Overestimation of the structure
• (up to 6 for the most probable
• fragmentation)

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STATIC RESULTS
Fission fragment properties Polaris
ation Quadrupole Deformation ?q20A-5/3
Spherical most heavy fragment
ZUCD(Z/A)238UA
Fragment Mass
H. Goutte, J.-F. Berger, and D. Gogny, proceeding
Fission 2005 Cadarache, AIP
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STATIC RESULTS

• FRAGMENT MASS DISTRIBUTION
• FROM 1D MODEL
• Vibrations along the scission line

POTENTIAL ENERGY
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STATIC RESULTS

• FRAGMENT MASS DISTRIBUTION
• FROM 1D MODEL
• Maxima are well located
• Widths are 2 times smaller

THEORY WAHL
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(No Transcript)
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DYNAMICAL RESULTS

• CONSTRUCTION OF THE INITIAL STATE
• We consider the quasi-stationary states of the
  modified 2D first well.
• They are eigenstates of the parity with a 1 or
  1 parity.
• Peak-to-valley ratio much sensitive
• to the parity of the initial state
• The parity content of the initial state controls
  the symmetric
• fragmentation yield.

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DYNAMICAL RESULTS
INITIAL STATES FOR THE 237U (n,f)
REACTION(1) Percentages of positive and
negative parity states in the initial state in
the fission channel with E the energy and
P ? (-1)I the parity of the compound nucleus
(CN) where ?CN is the formation
cross-section and Pf is the fission probability
of the CN that are described by the Hauser
Feschbach theory and the statistical model.
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DYNAMICAL RESULTS
INITIAL STATES FOR THE 237U (n,f) REACTION
Percentage of positive and negative parity
levels in the initial state as functions of the
excess of energy above the first
barrier W. Younes and H.C. Britt, Phys.
Rev C67 (2003) 024610. LARGE VARIATIONS AS
FUNCTION OF THE ENERGY Low energy structure
effects High energy same contribution of
positive and negative levels
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EFFECTS OF THE INITIAL STATES

E 2.4 MeV P 54 P- 46
E 1.1 MeV P 77 P- 23
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DYNAMICAL RESULTS

• 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
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CONCLUSIONS First microscopic
quantum-dynamical study of fission fragment mass
distributions based on a time-evolution
formalism. Application to 238U good
agreement with experimental data. Most
probable fragmentation due to potential energy
surface properties Dynamical effects on the
widths of the mass distributions, and
influence of the initial condition on the
symmetric fission yield have been
highlighted.