No abstract

No abstract

In this work, we propose an exactly solvable model which is constructed by considering energy-dependent Davidson potential in the β part of the generalized version of the collective quadrupole Bohr Hamiltonian within deformation-dependent mass formalism. Analytical expression of the energy spectra and corresponding wave functions are derived by means of the asymptotic iteration method. The combined effect of deformation-dependent mass and the energy dependence of the potential coupling constant is duly investigated. Also, the numerical calculations of the electric quadrupole transition ratios and energy spectrum of several nuclei undergoing a γ-unstable shape phase transition are performed and compared with experimental data as well as with other theoretical models. Besides, we investigate the correlation between both formalisms: energy-dependent potential (EDP) and deformation-dependent mass (DDM), through solutions of Bohr hamiltonian for transition nuclei in the limit E(5) with Davidson potential.

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 investigating the possible transition from the $\gamma$-unstable to the spherical vibrator shape phases. In this setup the potential appearing in the Bohr Hamiltonian is independent from the $\gamma$ shape variable, and the physical observables (energy eigenvalues, $B(E2)$) can be obtained in closed analytical form within the quasi-exactly solvable (QES) formalism for the model space containing 30 of the lowest-lying levels. Experimental energy levels have been associated to 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 $K^{\pi}=2^+$ and two excited $K^{\pi}=0^+$ 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.