abstract

The structure of the even-even Erbium (158-172Er) isotopes has been studied using the Interacting Boson Model. Energy states, reduced transition probabilities B(E2), electric quadrupole moment for 21+ state, and potential energy surface were calculated. The result were compared with the recent experimental data and it were observed that they are in agreement. The structure of the 158-172Er nuclei or shape changes correspond to the system moving between O(6) and SU(3) limits. The 158,160Er isotopes have been considered in O(6)-SU(3) transitional region, 162-170Er nuclei perturb SU(3) limit with the pairing term, while 172Er isotope lies under pure SU(3). The 162-172Er isotopes have a prolate deformed shape, where it was found that the 162Er isotope lying in the beginning of the deformed nuclei in Erbium series and represents a link between deformed and transition nuclei.

The consistent – Q formalism was applied for even-even 164-168Er isotopes. Energy levels, B(E2) values and electric quadrupole moment for 21+ state were calculated, and the results of CQF are comparable in the energy level with normal IBM-1, while for both B(E2) and Q21+ the CQF gives better results than IBM-1.

Some levels were not definitely assigned of spins and parities or do not have any spins and parities in the experimental,. In the current study, these levels were confirmed and determined the spins and parities for others.