Study of the fission process of²⁰⁰Pb and¹⁹⁷Tl produced in fusion reactions with the modified statistical model and multidimensional dynamical model

Abstract

The fission probability, pre-scission neutron, proton and alpha multiplicities, anisotropy of fission fragment angular distribution and the fission time have been calculated for the compound nuclei 200Pb and 197Tl based on the modified statistical model and four-dimensional dynamical model. In dynamical calculations, dissipation was generated through the chaos weighted wall and window friction formula. The projection of the total spin of the compound nucleus to the symmetry axis, K, was considered as the fourth-dimension in Langevin dynamical calculations. In our dynamical calculations, we have used a constant dissipation coefficient of K, and a non-constant dissipation coefficient to reproduce the above-mentioned experimental data. Comparison of the theoretical results of the fission probability and pre-scission particle multiplicities with the experimental data showed that the difference between the results of both dynamical models is small whereas, for the anisotropy of fission fragment angular distribution, it is slightly large. Furthermore, comparison of the results of the modified statistical model with the above-mentioned experimental data showed that with choosing appropriate values of the temperature coefficient of the effective potential, and the scaling factor of the fission-barrier height, the experimental data were satisfactorily reproduced.

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

“…It should be mentioned that, in the dynamical calculations, the fission fragment angular distributions can be obtained by averaging equation (19) over an ensemble of Langevin trajectories as follows:…”

“…But the fission process cannot be accurately modeled as a function of the excitation energy by using a fixed value of a a f n and the spin dependence of the T 0 = fission barriers [16] (T is temperature). Furthermore, many authors used dynamical models based on multidimensional Langevin equations or the multidimensional Fokker-Plank equation to simulate the fission process of excited nuclei (see [17][18][19][20][21][22][23][24][25][26] and references therein). It should be mentioned that the multidimensional Fokker-Plank equation can only be solved by using approximate methods, while numerical solution of the multidimensional Langevin equations is almost possible without any approximations.…”

“…In the dynamical calculations, dissipation is generated through the chaos-weighted wall and window friction formula, which we described in a previous paper [19]. For small elongation before neck formation, the chaos-weighted wall formula is used to calculate the friction tensor and after neck formation we used the chaos-weighted wall and window friction formula [22,28,38].…”