Superheavy nuclei in self-consistent mean-field models

The extrapolation of self-consistent nuclear mean-field models to the region of superheavy elements is discussed within the framework of Skyrme-Hartree-Fock and relativistic mean-field models. We present results for spherical and deformed shell closures for a large number of current parameterizations and potential energy surfaces of a few selected nuclei. We find conflicting predictions for the next major shell closures which are related to the effective mass and spin-orbit interaction. A critical examination of the performance of the various models with respect to the key features important for superheavy nuclei prefers Z = 120, N = 172 to be the doubly-magic superheavy nucleus.