Application and extrapolation of mean-field models in the heavy and superheavy regions

Mean-field models have been quite successful in the description of bulk nuclear properties and the shell structure, so that they provide an attractive basis for the extrapolation of nuclear structure to the boundaries of the periodic system. We have investigated the performance of both Skyrme-force and relativistic mean-field models for a larger sample of experimentally well known nuclei by comparing the predictions of various parameter sets corresponding to different versions of the models or simply distinguished by the data used for their fitting. This allows a critical evaluation of the uncertainty of extrapolation. The calculations show that while all parametrizations produce acceptable results in known nuclei, even the major magic shells predicted for the superheavy region depend on the choice of parameter set. The exact formulation and strength of the spin-orbit force appear to be the decisive factor. In addition a new formulation and parametrization of the relativistic point-coupling model with derivative and nonlinear terms is also discussed. (author)