Evolution of the phenomenologically determined collective potential along the chain of Zr isotopes

Background: The properties of the collective low-lying states of Zr isotopes which include excitation energies and E2 reduced transition probabilities indicate that some of these states are mainly spherical and the other are mainly deformed ones. A consideration of these data in the framework of the geometrical collective model with beta, gamma, and rotational degrees of freedom is necessary for Zr92-102. Purpose: To investigate the properties of the low-lying collective states of Zr92-102 based on the five-dimensional geometrical quadrupole collective model, to obtain the collective potentials for the chain of Zr isotopes and to investigate their evolution with increase of the number of neutrons. Method: The quadrupole-collective Bohr Hamiltonian depending on both beta and gamma shape variables with a potential having spherical and deformed minima is applied. The relative depth of two minima, height and width of the barrier, and rigidity of the potential near both minima are determined so as to achieve the best possible description of the observed properties of the low-lying collective quadrupole states of Zr92-102. Results: Satisfactory agreement with the experimental data on the excitation energies and the E2 reduced transition probabilities is obtained. The evolution of the collective potential with increase of A is described and the distributions of the wave functions of the collective states in beta-gamma plane are found. Conclusion: It is shown that the low-energy structure of Zr92-102 can be described in a satisfactory way within the geometrical collective model with the Bohr Hamiltonian. The beta dependence of the potential energy is fixed to describe the experimental data in a best possible way. The resulting potential evolves with A increase from having only one spherical minimum in Zr-92, through the potentials having both spherical and deformed minima, to the potential with one deformed minimum in Zr-102. A beta dependence of the wave functions is presented in a set of figures illustrating their distribution over beta.