Pre-scission model predictions of fission fragment mass distributions for super-heavy elements

The total deformation energy just before the moment of neck rupture for the heaviest nuclei for which spontaneous fission has been detected (Ds279-281, Rg281 and Cn282-284) is calculated. The Strutinsky's prescription is used and nuclear shapes just before scission are described in terms of Cassinian ovals defined for the fixed value of elongation parameter α=0.98 and generalized by the inclusion of four additional shape parameters: α1, α3, α4, and α6. Supposing that the probability of each point in the deformation space is given by Boltzmann factor, the distribution of the fission-fragment masses is estimated. The octupole deformation α3 at scission is found to play a decisive role in determining the main feature of the mass distribution: symmetric or asymmetric. Only the inclusion of α3 leads to an asymmetric division. Finally, the calculations are extended to an unexplored region of super-heavy nuclei: the even-even Fl (Z=114), Lv (Z=116), Og (Z=118) and (Z=126) isotopes. For these nuclei, the most probable mass of the light fragment has an almost constant value (≈136) like in the case of the most probable mass of the heavy fragment in the actinide region. It is the neutron shell at 82 that makes this light fragment so stable. Naturally, for very neutron-deficient isotopes, the mass division becomes symmetric when N=2×82.