Octupole deformation in the nuclear chart based on the 3D Skyrme Hartree-Fock plus BCS model

We have performed a systematic study of the ground state for even-even 1,002 nuclei in which 28 octupole-deformed nuclei are found. The interplay between the spatial deformation and the pairing correlation, plays important roles in nuclear structure. Our model is based on the Skyrme Hartree-Fock plus BCS model represented in the three-dimensional Cartesian coordinate space which can describe any kind of nuclear shape. The quadrupole and octupole deformed nuclei appear in the mass region with characteristic neutron and proton numbers which are consistent with previous studies. In our results, there appear only pear shape ($\beta_{30}$) in the octupole deformed nuclei. We investigate the potential energy surfaces as functions of the octupole deformations ($\beta_{3m}, m = 0, 1, 2, 3$), which tells us that. $^{220}$Rn has also local minima in the $\beta_{31}$ and $\beta_{32}$ potential energy surfaces.