Fission and Fusion at the End of the Periodic System

We calculate in a macroscopic-microscopic model fission potential-energy surfaces for neutron-rich actinides and fission-fusion potential-energy surfaces relevant to the analysis of heavy-ion reactions employed to form heavy-element evaporation residues. We study the latter multidimensional potential-energy surfaces both inside and outside the touching point. Inside the point of contact we define the potential on a multi-million-point grid in 5D deformation space where elongation, merging projectile and target spheroidal shapes, neck radius and projectile/target mass asymmetry are independent shape variables. The same deformation space and the corresponding potential-energy surface also describe the shape evolution from the nuclear ground-state to separating fragments in fission, and the fast-fission trajectories in incomplete fusion. For separated nuclei we study the macroscopic-microscopic potential energy, that is the "collision surface" between a spheroidally deformed target and a spheroidally deformed projectile as a function of three coordinates which are: the relative location of the projectile center-of-mass with respect to the target center-of-mass and the spheroidal deformations of the target and the projectile. We limit our study to the most favorable relative positions of target and projectile, namely that the symmetry axes of the target and projectile are collinear. We also calculate fission barriers for a long sequence of uranium isotopes. The aim is to understand another attempted production mechanism for superheavy elements, namely neutron-capture in thermonuclear explosions.