Adiabatic and configuration-fixed constrained triaxial relativistic mean field (RMF) approaches are developed for the first time. A new phenomenon, the existence of multiple chiral doublets (MχD), i.e., more than one pair of chiral doublet bands in one single nucleus, is suggested for ${}^{106}\mathrm{Rh}$ based on the triaxial deformations and their corresponding proton and neutron configurations.

Magnetic rotation and antimagnetic rotation are exotic rotational phenomena observed in weakly deformed or near-spherical nuclei, which are respectively interpreted in terms of the shears mechanism and two shearslike mechanism. Since their observations, magnetic rotation and antimagnetic rotation phenomena have been mainly investigated in the framework of tilted axis cranking based on the pairing plus quadrupole model. For the last decades, the covariant density functional theory and its extension have been proved to be successful in describing series of nuclear ground-states and excited states properties, including the binding energies, radii, single-particle spectra, resonance states, halo phenomena, magnetic moments, magnetic rotation, low-lying excitations, shape phase transitions, collective rotation and vibrations, etc. This review will mainly focus on the tilted axis cranking covariant density functional theory and its application for the magnetic rotation and antimagnetic rotation phenomena.

The properties of even-even O, Ca, Ni, Zr, Sn, and Pb isotopes from the $\beta$-stability line to the neutron drip line are studied with the relativistic continuum Hartree-Bogoliubov theory, where both the spin-orbit interaction and continuum are properly taken into account. The available experimental binding energies $E_b$ and two-neutron separation energies $S_{2n}$ are reproduced very well. The predicted neutron drip-line nuclei are, respectively, ${}^{74}\mathrm{Ca},$ ${}^{100}\mathrm{Ni},$ ${}^{140}\mathrm{Zr},$ ${}^{176}\mathrm{Sn},$ and ${}^{268}\mathrm{Pb}.$ Based on the analysis of two-neutron separation energies, single-particle energy levels, the orbital occupation, the contribution of continuum and nucleon density distribution, giant halo phenomena due to pairing, correlation and the contribution from the continuum are suggested to appear in Ca isotopes with $A>\mathrm{}60\mathrm{}$ apart from Zr isotopes predicted earlier.

The self-consistent tilted axis cranking relativistic mean-field theory based on a point-coupling interaction has been established and applied to investigate systematically the newly observed shears bands in 60Ni. The tilted angles, deformation parameters, energy spectra, and reduced M1 and E2 transition probabilities have been studied in a fully microscopic and self-consistent way for various configurations and rotational frequencies. It is found the competition between the configurations and the transitions from the magnetic to the electric rotations have to be considered in order to reproduce the energy spectra as well as the band crossing phenomena. The tendency of the experimental electromagnetic transition ratios B(M1)/B(E2) is in a good agreement with the data, in particular, the B(M1) values decrease with increasing spin as expected for the shears mechanism, whose characteristics are discussed in detail by investigating the various contributions to the total angular momentum as well. © 2011 Elsevier B.V.Articl