Is Axially Asymmetric Nucleus $\gamma$ Rigid or Unstable?

Abstract

One of the important consequences of the analyses in Chaps. 4 and 5 concerns the issue of the regularity in the level structure of non-axial (or $\gamma$-soft) nuclei. For the past decades, structure of the non-axial nuclei has been studied based on the two major geometrical pictures: the rigid-triaxial rotor model of Davydov and Filippov and the $\gamma$-unstable rotor model of Wilets and Jean. Since vast majority of the observed non-axial nuclei fall exactly in between the two geometrical models, the relation between the two has been of intriguing subject from the theoretical point of view. In the IBM framework, the non-axial nuclei have been described only by the O(6) dynamical symmetry, which is nothing but a realization of the $\gamma$-unstable rotor picture. Any IBM Hamiltonian with O(6) symmetry, provided it is composed of only up to two-body terms, can never reproduce the level structure of non-axially symmetric nuclei, mainly because the two-body Hamiltonian does not reproduce a stable triaxial minimum which is however seen in microscopic energy surface. We then propose to introduce an essential three-body boson term in the proton-neutron IBM so as to reflect the microscopic calculation. With such suitably chosen boson Hamiltonian, we demonstrate that the above-mentioned empirical feature of non-axial nuclei can be explained naturally and that the finding resulting from this study is independent of the type of the EDFs used.