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 9 - 12, 2006

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

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

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

Primary isobaric charge distribution parametriztion

Configuration at the scission point

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.

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

Excitation energy dependence

Calculated neutron multiplicities in the thermal induced fission

Calculated fragment kinetic energies in the thermal neutron induced fission

Superasymmetric modes in the thermal neutron induced fission

Comparison between theortical calculations and LOHENGRIN data

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

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.

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 .

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

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

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

Compompound nucleus mass and charge distributions before scission

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

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

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

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