Collective motion in γ-unstable nuclei within energy-dependent Davidson potential and deformation dependent mass formalisms

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 (BH) within deformation-dependent mass (DDM) formalism. Analytical expression of the energy spectra and corresponding wave functions are derived by means of the asymptotic iteration method. The combined effect of DDM 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 and DDM, through solutions of BH for transition nuclei in the limit E(5) with Davidson potential.