Fission of transactinide elements described in terms of generalized Cassinian ovals: Fragment mass and total kinetic energy distributions

The total deformation energy at scission for Z=100Z=100, 102, 104 and 106 isotopes is calculated using the Strutinsky's procedure and nuclear shapes described in terms of Cassinian ovals generalized by the inclusion of three additional shape parameters: α1α1, α4α4 and α6α6. The corresponding fragment-mass distributions are estimated supposing they are due to thermal fluctuations in the mass asymmetry degree of freedom. For these four series of isotopes the experimentally observed transition from asymmetric to symmetric fission, that happens with increasing mass number A, is qualitatively reproduced. In lighter isotopes (e.g. 254Fm and 254Rf) two mass-asymmetric fission modes are predicted to occur with comparable yields: one having relatively compact and the other relatively elongated scission configurations. On the other hand, in heavier isotopes (e.g. 264Fm and 264Rf) the fragment-mass distributions are predicted to be narrow single-peaked around A/2A/2 corresponding to essentially one mass-symmetric fission mode. The mass distributions are estimated separately for each fission mode, in the case of Fm and Rf isotopes, in order to display their inversion when A increases. Finally the distributions of the total kinetic energy of the fragments are calculated, for the same isotopes, in the point-charge approximation. Non-Gaussian shapes are obtained. With increasing mass number A, a transition from a distribution tailing towards higher energies to a distribution tailing towards lower energies and an increase of the difference in the peak positions of the two modes were observed; again in qualitative agreement with experimental data.