A dynamical interpretation of fusion–fission reactions using four-dimensional Langevin equations

Abstract

Four-dimensional Langevin equations have been applied to calculate the neutron multiplicity and evaporation residue cross section for hot nuclei. The projection of the total spin of the compound nucleus to the symmetry axis, K, is the fourth dimension in Langevin dynamical calculations. The relaxation time of the K as a function of the dynamical parameters is investigated. Calculations were performed for the 18 O+ 192 Os and 19 F+ 169 Tm reactions with a non-constant dissipation coefficient for the K coordinate. The obtained results based on four-dimensional Langevin equations with a non-constant dissipation coefficient in comparison with calculations based on a constant dissipation coefficient (γ K = 0.077(MeVzs) −1/2 ) are in better agreement with the experimental data. The difference between the two models for the evaporation residue cross section is high, whereas for neutron multiplicity, the discrepancy is low.

Investigation of dissipation in the tilting degree of freedom from four-dimensional Langevin dynamics of heavy-ion-induced fission

“…Various dependencies of the γ K parameter on elongation q 1 . The thin solid line corresponds to γ K (1) = 0.077 (MeV zs) −1 2 ; the dashed and dotted curves correspond to the γ K (2) , given by ( 15) and obtained with γ K const = 0.2 (MeV zs) −1 2 and γ K const = 0.0077 (MeV zs) −1 2 ; the thick solid curve corresponds to the deformation-dependent γ K (3) parameter given by (16).…”

“…However, the dependence of the γ K coefficient on deformation of the nuclear shape featuring a well defined neck was obtained in [15]. The deformation-dependent γ K coefficient was considered also in 4D Langevin calculations [16,17], but the obtained deformation dependence of γ K is different from [15]. The angular momentum and deformation dependent relaxation time of the K coordinate was investigate in [18].…”

Investigation of fission fragments average spin based on four dimensional Langevin dynamical model

“…In this relation A 1 , A 2 are the mass numbers of two fission fragments and A is the mass number of the compound nucleus. In the stochastic approach, evaluation of the collective coordinates is considered as motion of Brownian particles which interact stochastically with a large number of internal degrees of freedom, constituting the surrounding heat bath [25,26]. Based on this approach, the Langevin equations can be used as…”

“…In the present work we applied the one-body dissipation using the scaled version of wall and window friction for investigation of the angular dependence of fission fragment average spin. The evolution of the orientation degree of freedom (K coordinate) is obtained from the solution of the Langevin equations [26,33]…”

“…where ξ is a random number from a normal distribution with unit variance, and γ K is a parameter which controls the coupling between the orientation degree of freedom and the heat bath. This parameter can be calculated as [26,33]…”