X(5) critical point symmetry solution with Davidson potential

In this study, the structure of the atomic nucleus was discussed with the Interacting Boson Model (IBM) approach. A specific solution of point X(5), which is the critical point symmetry of the transition region between spherical nuclei U(5) and prolate nuclei SU(3), was obtained. By choosing the Davidson potential for the γ ≈ 0 solution of the Bohr Hamiltonian, energy eigenvalues and wave functions were obtained by the Nikiforov-Uvarov analytical method. This solution is called the X(5)-D model. Energy spectra of the X(5)-D model were calculated for gsb, β1 and β2 bands depending on the β0 variable. The obtained data were compared with the excitation energies of 156Dy, 154Gd, 152Sm, 150Nd nuclei. It was observed that the gsb data of the 156Dy core was more compatible with the X(5) model and at the β level it was more compatible with the X(5)-D model. The data of the 154Gd core is very compatible with the X(5)-D model in the gsb band, the highest agreement in the study is in this band. In the β bands, the X(5)-D model is more consistent than the X(5) model predictions. In the examination of the 152Sm core, it was seen that the X(5)-D model predictions were consistent in both the gsb band and the β bands. In the comparison of the 150Nd core, it was seen that the X(5)-D model was more successful than X(5) in the gsb band. The lack of experimental data on β bands made it difficult to make an interpretation between the two models.