Zhou, SG (reprint author), Chinese Acad Sci, Inst Theoret Phys, Key Lab Theoret Phys, Beijing 100190, Peoples R China.
The intrinsic nuclear shapes deviating from a sphere not only manifest themselves in nuclear collective states but also play important roles in determining nuclear potential energy surfaces (PES's) and fission barriers. In order to describe microscopically and self-consistently nuclear shapes and PES's with as many shape degrees of freedom as possible included, we developed multidimensionally constrained covariant density functional theories (MDC-CDFTs). In MDC-CDFTs, the axial symmetry and the reflection symmetry are both broken and all deformations characterized by beta(lambda mu) with even mu are considered. We have used the MDC-CDFTs to study PES's and fission barriers of actinides, the non-axial octupole Y-32 correlations in N = 150 isotones and shapes of hypernuclei. In this Review we will give briefly the formalism of MDC-CDFTs and present the applications to normal nuclei.