Shell structure of superheavy nuclei in self-consistent mean-field models

We study the extrapolation of nuclear shell structure to the region of superheavy nuclei in self-consistent mean-field models-the Skyrme-Hartree-Fock approach and the relativistic mean-held model-using a large number of parametrizations which give similar results for stable nuclei but differ in detail. Results obtained with the folded-Yukawa potential which is widely used in macroscopic-macroscopic models are shown for comparison. We focus on differences in the isospin dependence of the spin-orbit interaction and the effective mass between the models and their influence on single-particle spectra. The predictive power of the mean-held models concerning single-particle spectra is discussed for the examples of Pb-208 and the spin-orbit splittings of selected neutron and proton levels in O-16, Sn-132, and Pb-208. While all relativistic models give a reasonable description of spin-orbit splittings, all Skyrme interactions shaw a wrong trend with mass number. The spinorbit splitting of heavy nuclei might be overestimated by 40%-80%, which exposes a fundamental deficiency of the current nonrelativistic models. In most cases the occurrence of spherical shell closures is found to be nucleon-number dependent. Spherical doubly magic superheavy nuclei are found at (298)(184)114, (292)(172)120, .or (310)(184)126 depending on the parametrization. The Z = 114 proton shell closure, which is related to a large spin-orbit splitting of proton 2f states, is predicted only by forces which by far overestimate the proton spin-orbit splitting in Pb-208. The Z = 120 and N = 172 shell closures predicted by the relativistic models and some Skyrme interactions are found to be related to a central depression of the nuclear density distribution. This effect cannot appear in macroscopic-microscopic models or semiclassical approaches like the extended Thomas-Fermi-Strutinski integral approach which have a limited freedom for the density distribution only. In summary, our findings give a strong argument for (292)(172)120 to be the next spherical doubly magic superheavy nucleus. [S0556-2813(99)02708-9].