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Description
In this study, the sextic oscillator adapted to the Bohr Hamiltonian was employed to describe even isotopes of platinum (Pt) and osmium (Os) within specific mass number ranges. The primary objective was to investigate the transition of these isotopes from a "γ-unstable" state to a "spherical vibrator" state. The model utilized a potential that was independent of the γ shape variable, allowing for closed analytical solutions for physical properties like energy eigenvalues and B(E2) values. The study aligned experimental energy levels with theoretical predictions and considered electric quadrupole transition data for this purpose. Special focus was placed on transitions between specific excited nuclear states, particularly those that indicate changes in shape phases between spherical and deformed potential minima. The study determined the parameters of the Hamiltonian through a weighted least square fit procedure and analyzed trends in ground-state and excited state bands. Additionally, the study plotted trajectories in a two-dimensional phase space, finding that most nuclei exhibited a deformed potential minimum, except for the heaviest Pt isotope (198Pt), which transitioned to a spherical shape phase. While data for other isotopes (200Pt and 194Os) was less complete, there were indications that they also approached or fell within the domain of a spherical potential minimum.
