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 ( E 2)) 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 ( E 2), 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 ( 198 Pt), for which the transition to the spherical shape phase is realised. Although the spectroscopic information on the next isotopes of the chains ( 200 Pt and 194 Os) is far less complete, there are indications that these nuclei are also close to or fall within the domain of spherical potential minimum.