Various aspects of the Deformation Dependent Mass model of nuclear structure

Recently, a variant of the Bohr Hamiltonian was proposed where the mass term is allowed to depend on the beta variable of nuclear deformation. Analytic solutions of this modified Hamiltonian have been obtained using the Davidson and the Kratzer potentials, by employing techniques from supersymmetric quantum mechanics. Apart from the new set of analytic solutions, the newly introduced Deformation-Dependent Mass (DDM) model offered a remedy to the problematic behaviour of the moment of inertia in the Bohr Hamiltonian, where it appears to increase proportionally to the square of beta. In the DDM model the moments of inertia increase at a much lower rate, in agreement with experimental data. The current work presents an application of the DDM-model suitable for the description of nuclei at the point of shape/phase transitions between vibrational and gamma-unstable or prolate deformed nuclei and is based on a method that was successfully applied before in the context of critical point symmetries.