Abstract
In this study, we determined the most appropriate limit using the IBM-2 model and the IVBM model that is needed for present calculations of isobars 〖Ra〗^((220-224)),〖Rn〗^((220-224)),and 〖Th〗^((220-224)). To determine the characteristics of each isotope inside the aforementioned isobars, we computed energy levels and compared the outcomes with the experimental data, and then the values of the ratio (E(I+2))/E_(2_1^+ ) , the E-GOS curve, and the ratio (r(I+2))/I were adopted. From these values it was possible to determine the dynamic symmetries of each isotope, since (〖Ra〗^222,〖Rn〗^224) were classified as having O(6) symmetry, while the isobars (〖Ra〗^224,〖Th〗^224) have X(5) symmetry, the isobars (〖Ra〗^220,〖Rn〗^220) and ( 〖Rn〗^222,〖Th〗^222) have E(5) symmetry, and the 〖Th〗^220 has U(5) symmetry. The phenomenon of back bending of these isobars, which was all unbinding, was studied. Analysis was done on the startling energy differential between the negative party band states and the ground state band.