Tetrahedral shapes of neutron-rich Zr isotopes from multidimensionally-constrained relativistic Hartree-Bogoliubov model

摘要: We develop a multidimensionally constrained relativistic Hartree-Bogoliubov (MDC-RHB) model in which the pairing correlations are taken into account by making the Bogoliubov transformation. In this model, the nuclear shape is assumed to be invariant under the reversion of x and y axes; i.e., the intrinsic symmetry group is V4 and all shape degrees of freedom βλμ with even μ are included self-consistently. The RHB equation is solved in an axially deformed harmonic oscillator basis. A separable pairing force of finite range is adopted in the MDC-RHB model. The potential energy curves of neutron-rich even-even Zr isotopes are calculated with relativistic functionals DD-PC1 and PC-PK1 and possible tetrahedral shapes in the ground and isomeric states are investigated. The ground state shape of 110Zr is predicted to be tetrahedral with both functionals and so is that of 112Zr with the functional DD-PC1. The tetrahedral ground states are caused by large energy gaps around Z = 40 and N = 70 when β32 deformation is included. Although the inclusion of the β30 deformation can also reduce the energy around β20 = 0 and lead to minima with pear-like shapes for nuclei around 110Zr, these minima are unstable due to their shallowness.