Nıkıforov-uvarov yöntemi kullanılarak e(5) modeli için bohr hamiltonyeninin davıdson potansiyeli ile analitik çözümü

The goal of this research is to find unique Bohr Hamiltonian solutions that will clearly show the atomic nuclei's nuclear structures in the phase transition area. In this context, the Davidson potential in the Bohr Hamiltonian was used to develop a new model for the E(5) critical point symmetry. E(5)-D is the name of the γ-solid Bohr Hamiltonian solution for 𝛾 = 0° that was derived using the Davidson potential. An analytical technique created by Nikiforov and Uvarov was used to determine the energy eigenvalues by using the PYTHON 3 Jupyter (data science) program. Fundamental level bands of the E(5)-D model; it aligns with the available experimental data for the nuclei 110Xe and 134Ba. The reason for this incompatibility is that this solution is a γ-fold solution. Up to the highest spin levels, the predictions of the E(5)-D model overlap with the experimental results of the nuclei 156Dy, 154Gd, 154Sm, 102Pd, 150Nd, and 74Ge.