Theoretical study of different features of the fission process of excited nuclei in the framework of the modified statistical model and four-dimensional dynamical model

Abstract

Evaporation residue cross section, fission probability, anisotropy of fission fragment angular distribution, mass and energy distributions of fission fragments and the pre-scission neutron multiplicity for the excited compound nuclei and produced in fusion reactions have been calculated in the framework of the modified statistical model and multidimensional dynamical model. In the dynamical calculations, the dynamics of fission of excited nuclei has been studied by solving three- and four-dimensional Langevin equations with dissipation generated through the chaos-weighted wall and window friction formula. Three collective shape coordinates plus the projection of total spin of the compound nucleus to the symmetry axis, were considered in the four-dimensional dynamical model. A non-constant dissipation coefficient of was applied in the four-dimensional dynamical calculations. A comparison of the results of the three- and four-dimensional dynamical models with the experimental data showed that the results of the four-dimensional dynamical model for the evaporation residue cross section, fission probability, anisotropy of fission fragment angular distribution, mass and energy distributions of fission fragments and the pre-scission neutron multiplicity are in better agreement with the experimental data. It was also shown that the modified statistical model can reproduce the above-mentioned experimental data by choosing appropriate values of the temperature coefficient of the effective potential, and the scaling factor of the fission-barrier height, .

Analysis of the total kinetic energy of fission fragments with the Langevin equation

“…In the linear response approach to the nuclear collective motion [16] the nuclear many-body HamiltonianĤ is represented as the sum of the deformed (time dependent) mean field HamiltonianĤ mf (q(t)) and the residual interactionV (2) res which is assumed to be deformation independent,Ĥ =Ĥ mf +V (2) res . In this case the derivative of HamiltonianĤ with respect to deformation q…”

“…In the above expressions for friction and mass tensors the infinitely small quantity ǫ was replaced by the average of the collisional widths Γ k and Γ j of k and j states, Γ kj = (Γ k + Γ j )/2. In this way one can take into account the effect of residual interactionV (2) res , which is absent in the mean-field Hamiltonian. The calculation of Γ k is discussed in detail in [15].…”

Correlated transitions in TKE and mass distributions of fission fragments described by 4-D Langevin equation

“…The study of fission by Langevin equation in recent years has had some considerable success [1][2][3][4][5][6][7][8][9][10] , especially in unraveling the physics involved in the fission process. Recently, we have introduced the microscopic mass and friction tensors to improve the calculations of 3-D Langevin equation 7 instead of the usual macroscopic mass and friction tensors [11][12][13] .…”

Four-dimensional Langevin approach to low-energy nuclear fission of U236

“…The model can also determine the fission time scale, which is not the case for the Random-walk method [3]. At present there are several groups which use the Langevin approach for the description of the fission process [5,[7][8][9][10][11]. Due to the difficulty of the calculation of the multi-dimensional transport coefficients used in the Langevin equations, and due to the lack of sufficient resources for numerical calculations the number of shape parameters in most cases is restricted to 2 or 3 collective variables.…”