Nuclear shape transition between the limiting symmetries U(5) and SU(3) of interacting boson model applied to double even Hafnium isotopic chain

Abstract

The shape structure of even-even Hafnium isotopic chain 160–180Hf is investigated within the framework of sd-version of interacting boson model (IBM1) using coherent state formalism, the Hamiltonian operator of the model contains Casimir operators of the dynamical symmetries U(5) and SU(3) of the IBM1 besides the Casimir operator of the subgroup O(3). The potential energy surfaces (PES's) are calculated by diagonalizing the Hamiltonian between the coherent states. The PES's are analyzed in terms of the shape variables β, γ and the essential parameters r1, r2 and the locus of the critical points are identified. The model parameters for each nucleus are adjusted so as to reproduce some selected low lying energy levels and reduced electric quadrupole transition probabilities B(E2) with corresponding experimental data.For each nucleus the calculations are performed using the computer codes PHINT, BEFM besides a simulated fitting search program to give best fit between IBM and experimental values. The characteristic of energy ratios and B(E2) values are studied and analyzed with respect to increasing of the total number of bosons.It is concluded that the Hf isotopes lies in shape transition U(5) – SU(3) region of the IBM1 such that lighter isotopes comes very close to spherical vibrator limit U(5), while the heavier isotopes tends to be near the deformed rotator limit SU(3).