Influence of boundary conditions on the characteristics of nuclear fission

In this work, we carried out a detailed study of the factors affecting the fission dynamics of selected even-even actinide nuclei within a quasiclassical statistical approach based on the Langevin formalism. Essentially, the influence of initial conditions and geometrical criteria for spontaneous and induced fission of 236U as for the test case are worked out and then, using the knowledge thus acquired, we perform more extensive calculations for selected nuclei of U, Pu, Cm, Cf, and Fm isotopic chains. Potential energy surfaces (PES) are calculated within a macroscopic-microscopic approach in a three-dimensional space of the so-called Fourier deformation parameters representing the square of surface radius function in cylindrical coordinates. We also use the Lublin-Strasbourg Drop and folded-Yukawa mean-field models to estimate the full PES for these isotopes. The restoration of the particle number in the superfluid BCS-like approach is realized within the generator coordinate method with the Gaussian Overlap Approximation in the one-dimensional gauge-angle space. The tensors of inertia and friction, which play the role of transport coefficients, are given respectively within the hydrodynamic Werner-Wheeler approximation and what we usually call the "wall" formula. The main part of our research focuses on studying the conditions imposed on the solutions of the Langevin equations. In particular, we analyze the effect of the initial point distribution used to generate Langevin trajectories on resulting fragment mass and total kinetic energy distributions. Furthermore, we derive a way to optimize the size of the neck showing up on a nuclear surface in the final stage of its evolution to fission, taking into account the random and sudden natures of its rupture. Neck thicknesses generated with an appropriate normal distribution reproduce reasonably well the empirical fragment mass distributions in the lighter actinides along various excitation energies. However, for heavier actinides, such as Cf and Fm, the capability of our model to reproduce the final fragmentation seems to be limited.