Shapes and α- and β-decays of superheavy nuclei

We review several theoretical models based on the introduction of a mean-field that have been applied systematically to superheavy nuclei. The models that are considered are the macroscopic-microscopic approach and self-consistent mean-field models, based either on non-relativistic or on relativistic energy density functionals. A few examples illustrate results of beyond mean-field methods that explicitly consider collective correlations related to the symmetry restoration and fluctuations in the collective coordinates. We discuss in detail the evolution of the ground state shape and of α-decay with N and Z as predicted by the different models and compare them with experimental data. Finally, we present a brief account of predictions concerning β-decay.