Dynamic approach to description of entrance channel effects in angular distributions of fission fragments

Abstract

Background: It is well known that the anomalous behavior of angular anisotropies of fission fragments at sub- and near-barrier energies is associated with a memory of conditions in the entrance channel of the heavy-ion reactions, particularly, deformations and spins of colliding nuclei that determine the initial distributions for the components of the total angular momentum over the symmetry axis of the fissioning system and the beam axis.Purpose: We develop a new dynamic approach, which allows the description of the memory effects in the fission fragment angular distributions and provides new information on fusion and fission dynamics.Methods: The approach is based on the dynamic model of the fission fragment angular distributions which takes into account stochastic aspects of nuclear fission and thermal fluctuations for the tilting mode that is characterized by the projection of the total angular momentum onto the symmetry axis of the fissioning system. Another base of our approach is the quantum mechanical method to calculate the initial distributions over the components of the total angular momentum of the nuclear system immediately following complete fusion.Results: A method is suggested for calculating the initial distributions of the total angular momentum projection onto the symmetry axis for the nuclear systems formed in the reactions of complete fusion of deformed nuclei with spins. The angular distributions of fission fragments for the $^{16}\mathrm{O}+\phantom{\rule{0.16em}{0ex}}^{232}\mathrm{Th},^{12}\mathrm{C}+\phantom{\rule{0.16em}{0ex}}^{235,236,238}\mathrm{U}$, and $^{13}\mathrm{C}+\phantom{\rule{0.16em}{0ex}}^{235}\mathrm{U}$ reactions have been analyzed within the dynamic approach over a range of sub- and above-barrier energies. The analysis allowed us to determine the relaxation time for the tilting mode and the fraction of fission events occurring in times not larger than the relaxation time for the tilting mode.Conclusions: It is shown that the memory effects play an important role in the formation of the angular distributions of fission fragments for the reactions induced by heavy ions. The approach developed for analysis of the effects is a suitable tool to get insight into the complete fusion-fission dynamics, in particular, to investigate the mechanism of the complete fusion and fission time scale.