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

Abstract

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. We investigate the properties of the low-lying collective states of $^{92-102}$Zr and their evolution with increase of the number of neutrons based on the five-dimensional Geometrical Quadrupole Collective Model. The quadrupole-collective Bohr Hamiltonian with a potential having spherical and deformed minima, is applied. The relative depth of two minima, height and width of the barrier, 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 $^{92-102}$Zr. 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. The resulting potential evolves with $A$ increase from having only one spherical minimum in $^{92}$Zr, through the potentials having both spherical and deformed minima, to the potential with one deformed minimum in $^{102}$Zr.