Research of the possibility of freezing some degrees of freedom of the system in the calculation of the collision process of atomic nuclei

Background and Objectives: A large number of theoretical and experimental papers have been devoted to the study of the fusionfission reaction of heavy ions. This is primarily due to the fact that these reactions allow us to obtain superheavy nuclei or exotic isotopes that lie far from the beta-stability line. To describe these reactions, you must be able to describe the collision process of the initial nuclei. Moreover, the accuracy of the entrance channel description affects the quality of all subsequent modeling results. Recently, a number of works have appeared that seek to take into account all possible deformations and orientations when calculating the interaction of colliding atomic nuclei. At the same time, increasing the number of system shape parameters taken into account (increasing the dimension of the space of collective coordinates of the system) increases the complexity of performing dynamic calculations. So, the purpose of this work is to find an approximation that takes into account the main physical processes that occur when two atomic nuclei collide, but does not lead to serious complication of calculations. Materials and Methods: In this paper, we consider the collision of atomic nuclei in the hot fusion reactions $^{36}$S + $^{23}$8U and $^{64}$Ni + $^{23}$8U. To model this process, a dynamic stochastic model is used. It takes into account the shell structure of colliding cores and their mutual orientation in space. Four deformation parameters are used to describe the shape of the system under consideration. The dynamic evolution of these parameters is described in the framework of the Langevin equations. Results: The paper discusses the possibility of freezing some of the degrees of freedom of the system. It is shown that a relatively heavy target nucleus, deformed in the ground state, weakly changes its deformation and orientation in space during the evolution of the system up to the transition through the Coulomb barrier. The numerical results are compared with the experimental data. Conclusion: The prohibition of the evolution of the target nucleus deformation and orientation degrees of freedom does not significantly affect the simulation results, namely, the probability of the system passing through the Coulomb barrier and the distance between the centers of mass of colliding nuclei at the moment of the penetration through the Coulomb barrier. The choice of the reactions under consideration allows us to judge the effect of the mass of the projectile nucleus on the results of calculations, and also allows us to generalize the results obtained in the present work to a wide range of reactions with the mass ratio of colliding nuclei lying in the range from 0.15 to 0.27. Most of the reactions currently used for the synthesis of superheavy elements are in this range.