Nuclear Structure and Energy Levels of ¹⁵⁸Er, ¹⁶⁰Yb and ¹⁶²Hf Isotones

The properties of even-even¹⁵⁸Er, ¹⁶⁰Yb and ¹⁶²Hf isotones are studied and its energy states calculated. To identify the properties of each isotone, the values of the first excited states $E{2}_{1}^{+}$ and the ratio of the second to the first excited states ${R}_{4/2}=E{4}_{1}^{+}/E{2}_{1}^{+}$ were adopted. The phenomenon of back-bending, the E-GOS curve and the odd-even staggering were studied. Examining the algebraic structure of the Bohr model (BM) clarified the relationship with the interacting vector boson model (IVBM) and the interacting boson model (IBM) which it has related solvable limits and corresponding dynamical symmetries. BM, IVBM and IBM were used to calculate the energy states for each isotone and compared with the experimental data. The results showed that the BM and IVBM are more comfort than the calculation of IBM-1. The contour plots of the potential energy surface (PES) to the IBM Hamiltonian for Er–Hf with N = 90 have been obtained using the intrinsic coherent state and evolve from deformed shapes to γ- unstable with decreasing the boson number.