Fission barriers and probabilities of spontaneous fission for elements with Z ≥ 100

This paper briefly reviews recent progress in theoretical studies on fission barriers and fission half-lives of even-even superheavy nuclei. We compare and discuss results obtained in the semi-classical macroscopic-microscopic approach, the self-consistent mean-field models with the Skyrme and Gogny energy density functionals and in the relativistic mean-field theory. A short part of the paper is devoted to the calculation of the mass parameters and nuclear fission dynamics. We also discuss the predictive power of Skyrme energy density functionals applied to key properties of the fission path of 266Hs. Standard techniques of error estimates in the framework of a χ2 analysis are applied.