Solution of the Bohr Hamiltonian for the kratzer potential around the X(5) critical point

Obtaining the properties of nuclei exhibiting structures around the critical point theoretically is one of the subjects that nuclear structure physicists have focused on in recent years. In this thesis, the excitation energy spectra of nuclei, which are located between the critical points of U(5) and SU(3) and displaying structures around the critical point where the first-order shape phase transition takes place, indicated by X(5), were investigated. Since these nuclei deform their structures, the Collective Bohr Hamiltonian written depending on the deformation parameters was used. The Schrödinger equation, which is obtained by assuming that the potential energy of the nucleus is in the form of Kratzer potential, is solved analytically using the Nikiforov- Uvarov method. It is experimentally known that nuclei with mass numbers greater than 150 exhibit a prolate-deformed structure. Therefore, Er isotopes with mass numbers between 160 and 170 were chosen to test the suitability of the Kratzer potential. Using the Mathematica program, potential free parameters were determined for each isotope that would give the best experimental data. By using these parameters, the entire excitation energy spectrum of the isotopes was created and compared with the experimental data. However, the existence of some situations that cannot be measured experimentally has been shown theoretically and a data set has been created for future experimental studies.