Analytical solution of bohr hamiltonian with kratzer potantial for X(3) and X(5) model by using Nikiforov-Uvarov method

The purpose of the study is to obtain special Bohr Hamiltonian solutions that will accuratelly represent the nuclear structures of the atomic nuclei in the phase transition region. In this context, two new models were created by using Kratzer potential in the Bohr Hamiltonian for X(3) and X(5) critical point symmetries. It is possible to separate the study into two parts. In the first part; a solution of γ-rigid Bohr Hamiltonian for γ=0^° is obtained from Kratzer potential. This solution was called X(3)-Kratzer. Energy eigenvalues and wave functions are obtained by using an analytic method developed by Nikiforov and Uvarov. The ground state band of the X(3)-K model are consistent with the experimental data available for the 112Cd, 142Sm and 156Gd nuclei. However, this consistency has not been observed in the β_1-band. The inconsistency results from that this solution ia a γ-rigid solution. In the second part; an approximate solution of Bohr Hamiltonian for γ≃0^° was obtained from Kratzer potential. This solution was called X(5)-Kratzer. Energy eigenvalues and wave functions were obtained. It was observed that the X(5)-K model predictions are consistent with the experimentel data of 150Nd, 152Sm, 154Gd, 156Dy and 176-178Os nuclei upper spin levels.