The energy analysis in γ-unstable nuclei Bohr Hamiltonian for Morse potential with deformation-dependent mass term

Abstract

Solution of Bohr Hamiltonian for Morse potential in the case of γ-unstable nuclei which the mass is allowed to depend on the nuclear deformation β was obtained by using supersymmetric quantum mechanics (SUSY QM). The visualization of deformation function for the certainty isotope was inverse with the visual of Morse potential in the same value of deformation. The heavy isotope has larger value of β0, and it gives effect to reduce the maximum value of deformation function. By using SUSY QM, we obtained the energy equation, which depends on the β0 and the Morse potential constants. The numerical results of energy show that for the heavier isotopes, the energy value increase in the same value of Morse potential constants. While for the changing of Morse potential constants, it wasn’t causing effect in energy value. The energy value becomes greater in the increasing of Morse potential free parameter α. The value of free parameter affects the deformation function, which in the greater value of free parameter caused in decreasing the deformation function. It means that the deformation function is inversely proportional to the value of energy.