1. Department of Physics, University of Jyväskylä, Finland
Frozen quantal fluctuation approach for modelling fission fragment charge distribution
V.A. Rubchenya
Department of Physics, University of Jyväskylä, Finland
ESNT Workshop, May , 2006

2. Y(A,Z), W(ΘF,Ekin), Mn(En,Θn), Mγ(Eγ,Θγ)p n d γ
Pre-compound stage
5·10-22
Pre-saddle evaporation
10-19
Saddle point
Descent from saddle
1.1·10-19
Charge distribution formation
Scission
Post-scission evaporation
10-8
Fission products
Y(A,Z), W(ΘF,Ekin), Mn(En,Θn), Mγ(Eγ,Θγ)
Time/ s

3. The main dynamical effects
Pre-compound particle emission: Mnpre-eq, Mppre-eq, Epre-eqelapsed
Role of the nuclear friction in the fission:
delay time for formation of fission degree of freedom
modification of the fission width
overdamped collective motion on the descent from saddle
Mnpre-sc, Mppre-sc, Eelapsedpre-sc
Charge polarization during the descent from saddle to scission: charge distribution for isobaric chains: Y(Z/A)
Competion between different fission modes as function of composition and exitation energy of compound nuclei: Y(A, E*comp)
Distribution of excitation energy between fragments: Mn(A, Z, E*comp)
Shell structure for very deformed nuclei: shell corrections, fission barriers, mass parameters, fission modes, level density

4. Frozen quantal fluctuatuations in the charge equlibration mode
Time evolution of isobaric width in the harmonic approximation

5. Primary isobaric charge distribution parametriztion

6. Configuration at the scission point

7. Δtip p p n n
AL, ZL, {εL} AH, ZH, {εH}
Strutinsky’s shell correction method was applied using single particle spectra in deformed Woods-Saxon potential.

15. The approximation of the liquid drop charge distribution parameters
Deviation from uniform distribution:
The reverse stiffness parameter:

16. Excitation energy dependence

19. Calculated neutron multiplicities in the thermal induced fission

20. Calculated fragment kinetic energies in the thermal neutron induced fission

22. Superasymmetric modes in the thermal neutron induced fission

23. Comparison between theortical calculations and LOHENGRIN data

27. A=78 Y=0.089% for the 242Pu(p,f) Ep=55 MeV
Y=0.016% for the 242Am(nth, f)

28. The code can be used for calculation folloiwing output in the proton and neutron induced reactions at energy up to 100 MeV:
Evaporation residues cross sections.
Pre-compound neutron and proton emission spectra.
Pre-compound proton and neutron multiplicity.
Pre-scission light charged particles (p, d, α) emission multiplicities.
Pre-scission neutron spectrum.
Post-scission light charged particle multiplicities.
Post-scission neutron spectrum.
Fragment kinetic energies.
Pre-neutron emission fragment mass yields.
Fission product mass yields.
Fission product yields for isobaric chains.
Fission product yields for elemental chains.

29. The two-component exciton model was used for our objectives: an adequate description of the initial excitation energy distribution and composition of the compound nuclei in the neutron and proton induced fission. For description of exciton evolution process the folloing transitions are taken into account: - proton particle-hole pair creation; - neutron particle-hole pair creation; - conversion of a proton particle-hole pair into a neutron particle-hole pair; - conversion of a neutron particle-hole pair into a proton particle-hole pair; - the proton emission; - the neutron emission; -after particle emission the exciton evolution process may develop further until reaching the criteria for transition to the compound stage of the reaction; The exciton transition cascade is ruptured at reaching one of conditions: 1. exciton number reaches limited value n ≥ nmax; ;2. total life time of the exciton stage exceeds limiting value Texc ≥ Tmax which corresponds to statistical width decay; 3. the number of emitted particles exceeds the lemited value Mn ≥ Mnmax or Mn ≥ Mnmax .

30. We use the two-component exciton model for our objective:
Pre-compound stage
We use the two-component exciton model for our objective:
an adequate description of the initial excitation energy distribution and composition
of the compound nuclei in the neutron and proton induced fission at the incident
energy from 10 to 100 MeV.
The lifetime of exciton state
The proton pre-compound single spectra from given exciton state
The neutron pre-compound single spectra from given exciton state

31. Nuclear friction at pre-sadlle stage and transition through fission barrier.
Modification of the statistical Bohr-Wheeler fission width
are collective frequences at equilibrium and saddle shapes
and
β denotes the reduced dissipation coefficient
Competition between particle evaporation and fission channels defines the fission chances

32. Neutron and proton multiplicities as function of neutron energy in 238U(n, f)

33. Compompound nucleus mass and charge distributions before scission

34. Comparison with mass spectrometer experimental data in 238U(p, f)

35. Comparison with mass spectrometer experimental data in 238U(p, f)

36. Comparison with IGISOL-TRAP data in 238U(p, f) at Ep=25 MeV

37. Saddle-to-scission descent stage
saddle-to-scission time is altered by the nuclear dissipation
Saddle and bifurcation points and valleys on the potential-energy surface of
fissioning nucleus determine the properties of fission modes