Conclusions

In this work we have used three different EDF approaches, each for two different parameter sets, so as to gain some insight into the degree of systematic uncertainties that are related to applying these approaches to spectroscopic properties of heavy nuclei at the gateway to superheavy region. On the one hand, we concluded that the overall coarse description of several spectroscopic properties of nuclei in this region is, in general, correct. On the other hand, we identified numerous smaller or larger differences between the results obtained within these different EDFs. In particular, none of the studied global EDF parameterisations precisely describes variations of the shell structure seen in experiment. This can be associated with small deficiencies of the obtained deformed shell properties.

On the scale of very precise spectroscopic experimental data, differences between various EDF approaches are large. They are of the same order as the degree of differences with experiment. This points to still fairly large systematic uncertainties inherent to the models currently in use. Moreover, none of the studied models could at present be identified as the one that systematically performs significantly better than another one. However, it is interesting that on the average the accuracy of the description of the excitation energies of deformed one-quasiparticle states in the nobelium region is substantially better than the accuracy of the description of the energies of dominant single-particle states at spherical shape in odd-mass nuclei neighbouring to doubly magic $^{208}$Pb (even as compared with the calculations which include particle-vibration coupling [13,82].

The obtained results suggest that further work on improving the performance of the EDF methods is very much required. First, one can hope that within the existing forms of EDFs, one can still find better global parametrizations. For Skyrme EDFs, this route has already been explored and a negative conclusion was reached [27], but for covariant and Gogny EDFs similar work has not yet been performed. Second, one can hope that various beyond-mean-field corrections, not included in the present analysis, may have strong impact on the results, and thus modify the current conclusions. At least that happens in the covariant framework, where accounting for the (quasi)particle-vibration coupling improves substantially the accuracy of the description of predominantly single-particle states in spherical medium and heavy nuclei [54,15]. In addition, there is still a possibility of building new functionals, with beyond-mean-field effects incorporated from the very beginning. Again, for the Skyrme EDFs, employed together with odd-particle polarization effects included, a negative conclusion has recently been reached [82]. However, so far in the covariant and Gogny EDF approaches no such studies have been performed, and such route has to be explored. Third, one can also attempt building new classes of EDFs, where systematic expansions within different schemes are used. Only very recently this route was started to be explored in non-relativistic EDFs, see, Refs. [83,84,85,86,87,88,89,90,91], so its eventual impact on the physics discussed here is not yet known.