Identical bands in doubly even nuclei in framework of variable moment of inertia (VMI) and interacting boson models

Abstract

The variable moment of inertia (VMI) model and the interacting boson model (IBM) are applied to study the identical bands (IB's) for doubly even normally deformed nuclei in rare earth mass region 158 ≤ A ≤ 170. The VMI used to calculate the energy levels of the positive parity state bands before the band crossing. One important feature of the IBM is its ability to describe the nuclear shapes by using the consistent Q-formalism and intrinsic coherent state, which allow generating the potential energy surface (PES). The PES′s, which describe all deformation effects, are systematically analyzed. For most of our considered nuclei the plot of PES against the deformation parameter shows two wells, one on the prolate and one on the oblate side, which indicate that the considered nuclei are deformed and have rotational character.The IB's parameters are extracted it is observed that the nuclei having similar NpN/nΔ values exhibit identical excitation energies where, Np and Nn are the valence proton and neutron numbers and Δ is the average-pairing gap. Pairs of conjugate nuclei with the same F-spin and ±F0 projections have identical NpNn value. The nuclear kinematic and dynamic moments of inertia for the ground state bands for our proposed nuclei are calculated and systematically analyzed. For each nucleus, the best parameters for both VMI and IBM models are obtained by using a fitting procedure of the theoretical results with experimental data for the positive parity excitation energies by using the computer code PHINT and a simulated search program.