Spontaneous fission of the superheavy nucleusFl286

Abstract

The decimal logarithm of spontaneous fission half-life of the superheavy nucleus $^{286}$Fl experimentally determined is $\log_{10} T_f^{exp} (s) = -0.632$. We present a method to calculate the half-life based on the cranking inertia and the deformation energy, functions of two independent surface coordinates, using the best asymmetric two center shell model. In the first stage we study the statics. At a given mass asymmetry up to about $\eta=0.5$ the potential barrier has a two hump shape, but for larger $\eta$ it has only one hump. The touching point deformation energy versus mass asymmetry shows the three minima, produced by shell effects, corresponding to three decay modes: spontaneous fission, cluster decay and $\alpha$~decay. The least action trajectory is determined in the plane $(R,\eta)$ where $R$ is the separation distance of the fission fragments and $\eta$ is the mass asymmetry. We may find a sequence of several trajectories one of which gives the least action. The parametrization with two deformation coordinates $(R,\eta)$ and the radius of the light fragment, $R_2$, exponentially decreasing with $R$ is compared with the simpler one, in which $R_2$~=constant. The latter is closer to the reality and reminds us about the alpha or cluster preformation at the nuclear surface.