The cranked relativistic Hartree+Bogoliubov theory has been applied for a systematic study of the nuclei around 254No, the heaviest elements for which detailed spectroscopic data are available. The deformation, rotational response, pairing correlations, quasi-particle and other properties of these nuclei have been studied with different parametrizations for the effective mean-field Lagrangian. Pairing correlations are taken into account by a finite range two-body force of Gogny type. While the deformation properties are well reproduced, the calculations reveal some deficiencies of the effective forces both in the particle-hole and particle-particle channels. For the first time, the quasi-particle spectra of odd deformed nuclei have been calculated in a fully self-consistent way within the framework of the relativistic mean field (RMF) theory. The energies of the spherical subshells, from which active deformed states of these nuclei emerge, are described with an accuracy better than 0.5 MeV for most of the subshells with the NL1 and NL3 parametrizations. However, for a few subshells the discrepancies reach 0.7-1.0 MeV. In very heavy systems, where the level density is high, this level of accuracy is not sufficient for reliable predictions of the location of relatively small deformed shell gaps. The calculated moments of inertia reveal only small sensitivity to the RMF parametrization and, thus, to differences in the single-particle structure. However, in contrast to lighter systems, it is necessary to decrease the strength of the D1S Gogny force in the pairing channel in order to reproduce the moments of inertia.
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