The apparent U(5) to near O(6) shape evolution in even-even 152→162Dy inside the symmetry triangle

In this article, we showed that even-even $A=152⟶162$ Dysprosium isotopic chain follows a specific trajectory of evolution that appear to be from U(5) to near O(6) vertex inside the symmetry triangle. The analysis was done using the Extended Consistent Q formalism (ECQF) of the interacting boson model, and catastrophe theory. We determined the Hamiltonian parameters using the method of orthogonal crossing contours for key observables. The Potential Energy Surfaces (PES's) for each isotope was also obtained using the intrinsic coherent state formalism. The path of evolution for the chain showed the same trend-line in both the symmetry triangle and the separatrix plane of catastrophe theory. We also showed that despite being located near the O(6) limit in the symmetry triangle, neutron-rich Dy isotopes still exhibit the behaviour of good axially symmetric rotors but with a reduced gamma rigidity, and this apparent location is due to the non linearity of scales for observables inside the symmetry triangle.