Investigation of the second-order shape phase transtions in medium-heavy and heavy odd-even nuclei with the collective model

Due to depending to the change in the number of nucleons in the atomic nuclei, Observed in the basic case of the phase transitions of the nuclei are one of the most important issues of nuclear structure. One of the most successful models used in the study of phase transitions is the collective bohr hamiltonian. In this thesis, the properties of single-double cores exhibiting the critical point are examined. Since the single-double nuclei can be obtained from a pair of nucleons containing a single nucleon, the double-double cores were first investigated. The property of E (5) critical point with second-order phase transition is determined. E (5/4) and E (5/12) dynamic symmetry limits for single-double cores the double cores were obtained by doubling the single nucleon moving in single particle trajectories j = 3/2 and j = 1 /2, 3 /2, 5/ 2 respectively. At these critical points, energy eigenvalues and eigenfunctions of the system were found analytically. The potential used to obtain experimental data of nuclei around the critical point must be dependent on the free parameter. For this purpose, the potentials of Coulomb, Kratzer and Davidson were used in the Bohr Hamiltonian. In addition, two different forms of interaction with core and single nucleon are discussed for each potential. The energy eigenvalues and eigenfunctions of the potentials used were obtained in analytical form. The results were used to estimate the energy quadrants of excitation energy spectrum and excited states of electric quadrupole transition to the system identified.