Woods-saxon potansiyeli içeren bohr hamiltoniyeninin özel çözümleri

The recent influential studies on the nuclear structure have focused on the quantum shape phase transitions of atomic nuclei within the frame of the Collective Model, which have enabled many researchers to test the reliability of the models used. As the special solutions of the Bohr Hamiltonian dealing with collective behaviour of the nucleus in terms of collective variables beta and gama in five-dimension, E(5) and X(5) are the most important critical point symmetries, which describe the shape phase transition between vibrational and gama-unstable/axially symmetric prolate rotor, respectively. Hence, for the first time in the related literature, considering both E(5) and X(5) critical point symmetries, the Bohr Hamiltonian with the well-known Woods-Saxon potential involving the repulsive angular momentum barrier in the non-relativistic domain is solved analytically. We observe that the corresponding new solution well reproduces energy spacing within the ground state and gama bands for more than 100 even-even deformed nuclei, and gives an insight to the physically acceptable parameters that is required for reliable and accurate calculations.