Search

Cranked relativistic Hartree–Bogoliubov theory without and with approximate particle number projection by means of the Lipkin–Nogami method is presented in detail as an extension of relativistic mean field theory with pairing correlations to the rotating frame. Pairing correlations are taken into account by a finite range two-body force of Gogny type. The applicability of this theory to the description of rotating nuclei is studied in detail on the example of superdeformed bands in even–even nuclei of the A∼190 mass region. Different aspects such as the importance of pairing and particle number projection, the dependence of the results on the parametrization of the RMF Lagrangian and Gogny force, etc., are investigated in detail. It is shown that without any adjustment of new parameters the best description of experimental data is obtained by using the well established parameter sets NL1 for the Lagrangian and D1S for the pairing force. Contrary to previous studies at spin zero it is found that the increase of the strength of the Gogny force is not necessary in the framework of relativistic Hartree–Bogoliubov theory provided that particle number projection is performed.

Yrast levels for a chain of Dy isotopes are investigated at low and intermediate angular momenta. Different versions of the cranking model are used for the description of the spectra. It turns out that variation after number projection yields good qualitative, and sometimes even quantitative, agreement with the experimental data. In addition to the energy levels, we calculate electromagnetic properties such as B(E2) values and gyromagnetic factors. A systematic analysis for the existence of diabolical points in this region of the periodic table is presented.

A three-dimensional angular momentum projection is carried out for cranking model wave functions. The projected matrix elements of electromagnetic operators are evaluated using a method originally developed by Kamlah for the case of projected energy, which is valid for large deformations and weakly triaxial nuclei. The calculated spectroscopic quadrupole moments deviate substantially from the predictions of a rigid rotor model with axial symmetry. For E2 transitions the deviations are small. Projected values of the magnetic moments are almost identical with those of a semiclassical calculation. Cranking model wave functions are decomposed into its components having good angular momentum.