The influence of the boundary conditions on characteristics of nuclear fission

Abstract: In this paper, using a quasi-classical statistical approach based on the Langevin equation, we simulate the fission dynamics of selected even-even $\rm U$, $\rm Pu$, $\rm Cm$, $\rm Cf$ and $\rm Fm$ actinide nuclei. As a preparatory part of the work, before solving the Langevin equations, the determination of transport parameters such as inertia and friction tensors within the hydrodynamic model is performed. Potential energy surfaces are calculated within a macroscopic-microscopic approach in a three-dimensional space of deformation parameters defined within the Fourier decomposition of the surface radius function in cylindrical coordinates. Using the Lublin-Strasbourg drop model, Strutinsky shell correction and BCS-like pairing energy model with the projection onto good particle number, we calculate the nuclear total potential energy surfaces (PES). The restoration of the particle number in the superfluid approach is realized within the Generator Coordinate Method (GCM) with the so called Gaussian Overlap Approximation (GOA). The final study is concerned with the effect of the starting point of the stochastic Langevin trajectory on its time evolution and, more importantly, the conditions for judging whether such a trajectory for a given time moment describes an already passed fission nucleus or not. Collecting a large number of such stochastic trajectories allows us to assess the resulting fragment mass distributions, which appear to be in good agreement with their experimental counterparts for light and intermediate actinides. More serious discrepancies are observed for single isotopes of californium and fermium.