Cassini-oval description of the multidimensional potential energy surface for U236 : Role of octupole deformation and calculation of the most probable fission path

Abstract

Multidimensional potential energy surfaces (PES) are calculated using the microscopic-macroscopic approach. The nuclear shapes are described by Cassinian ovals generalized by the inclusion of ${\ensuremath{\alpha}}_{1}$, ${\ensuremath{\alpha}}_{3}$, and ${\ensuremath{\alpha}}_{4}$ shape parameters in addition to the main fission coordinate $\ensuremath{\alpha}$. The influence of the octupole deformation $({\ensuremath{\alpha}}_{3})$ on the PES is studied in the case of the nuclear fission of $^{236}\mathrm{U}$. It is found that ${\ensuremath{\alpha}}_{3}$ plays an important role in the last stage of the fission process; for instance, it lowers the third minimum and the third barrier. Two methods to calculate the static fission path are investigated. They are found to be consistent in the sense that they lead to the same fission barrier. In certain subspaces, the least energy paths from the ground state to scission present discontinuities around one of the saddles. They are caused by sharp changes in the nuclear shapes involved occurring without a change in energy. Such transitions are smoothed out by the principle of stationary action, which transforms a discontinuous path into a continuous one. Finally, various macroscopic models have been employed in order to study their influence on the energies and positions of the saddles and the minima.