Abstract
The aim of the present work is to study some nuclear features of Erbium ( 98 166 68 Er ) such as energy levels E(J), energy transition Eγ, band crossing, and back bending phenomena in the mass region(A=166,and total number of bosons N=15)of the dynamical symmetry SU(3)-O(6) using interacting boson model version-1(IBM-1) and a variable moment of inertia model(VMI) In this study, we determined the most appropriate Hamiltonian that is needed for the present calculations of deformed understudy nucleus; these calculations have been estimated by best-fitting to the measured energies level. The IBM-1 results have been compared with the previous experimental and theoretical (VMImodel) data and it was observed that they are agreed in the most of the states. The predictions from the VMI model are more accurate than those of the IBM-1
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