Study of the nuclear structure of the even-even isotopes 158 -160 Er

In this work, the energy levels of the ground state band (GSB), β-band and -bands for 158-160Er isotopes were calculated using the Interacting Boson Model(IBM-1), the Semi-Empirical Formula (SEF) and the New Empirical Equation (NEE). All three models were developed by IBM. In order to complete this study, the above-mentioned models and equations were applied. The results of the GSB, β-band and -bands showed that IBM-1, SEF, NEE, and the available experimental data are all in agreement with certain variations this was shown by the results of the GSB. The NEE calculations have a higher level of compatibility with the experimental data when compared to both the IBM-1 calculations and the SEF calculations. According to the findings of this research, the SEF and NEE equations are both capable of describing the energy spectra of Er isotopes in comparison to IBM-1. The electric quadrupole transition probabilities B(E2) transitions which obtained through IBM-1 for the above isotopes were calculated and found to be in agreement with the available experimental data, On the other hand, Isotopes of Er exhibit behavior that is consistent with a rotational SU(3) transition.