Extended Analytical Solutions of the Bohr Hamiltonian with the Sextic Oscillator: Pt-Os Isotopes

Abstract

The sextic oscillator adapted to the Bohr Hamiltonian has been used to describe even Pt and Os isotopes from A = 188 to 198 and A = 186 to 192, respectively. The purpose of this study was to investigate the possible transition from the γ-unstable to the spherical vibrator shape phases. In this setup the potential appearing in the Bohr Hamiltonian is independent from the γ shape variable, and the physical observables (energy eigenvalues, B(E2)) can be obtained in closed analytical form within the quasi-exactly solvable formalism for the model space containing 30 of the lowest-lying levels. Experimental energy levels have been associated with the theoretical ones. The available electric quadrupole transition data (B(E2), decay preferences) have been taken into account in matching the experimental and theoretical levels. Special attention has been paid to transitions from the first two excited 0+ levels to the 2 1 + and 2 2 + levels, as these indicate the change of shape phases with spherical and deformed potential minimum. The three parameters of the Hamiltonian have been determined by a weighted least square fit procedure. Trends in the location of states belonging to the ground-state, the K π = 2+ and two excited K π = 0+ bands have been analysed. The trajectory determined by the fitted parameters in the two-dimensional phase space has also been plotted, and it has been found that all the nuclei are characterized by a deformed potential minimum, except for the heaviest Pt isotope (198Pt), for which the transition to the spherical shape phase is realised. Although the spectroscopic information on the next isotopes of the chains (200Pt and 194Os) is far less complete, there are indications that these nuclei are also close to or fall within the domain of spherical potential minimum.