Solution of the Bohr Hamiltonian for the Davidson potential in the ɣ~unstable region

In this study, we investigated the behavior of gamma-unstable nuclei through the application of the Collective Bohr Hamiltonian with the Davidson potential. To solve the Hamiltonian, we employed the Nikiforov-Uvarov method, which enabled us to obtain the energy eigenvalue equation in a closed form. The derived energy equation was then subjected to rigorous testing by predicting the excitation energy spectra of a range of Cd isotopes (106-120Cd). Our comprehensive analysis and comparison of the obtained results with experimental data revealed a remarkable agreement between theory and observation. This strong alignment between theoretical predictions and experimental findings substantiates the validity and accuracy of the proposed model. Consequently, our study represents a significant step forward in understanding the behavior of gamma-unstable nuclei and contributes to the advancement of collective models employed in nuclear structure studies. The outcomes of this research have broad implications for nuclear physics and may serve as a valuable foundation for future investigations in the field. By shedding light on the intricate interplay between nuclear structure and the Collective Bohr Hamiltonian with the Davidson potential