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

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 V-4 and all shape degrees of freedom beta(gamma mu) with even mu 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 Zr-110 is predicted to be tetrahedral with both functionals and so is that of Zr-112 with the functional DD-PC1. The tetrahedral ground states are caused by large energy gaps around Z = 40 and N = 70 when beta(32) deformation is included. Although the inclusion of the beta(30) deformation can also reduce the energy around beta(20) = 0 and lead to minima with pear-like shapes for nuclei around Zr-110, these minima are unstable due to their shallowness.