Bohr Hamiltonian with a deformation-dependent mass term for the Davidson potential

• Published in: Physical review. C, Nuclear physics Nuclear physics, 2011-04, Vol.83 (4), Article 044321
• Main Authors: Bonatsos, Dennis, Georgoudis, P. E., Lenis, D., Minkov, N., Quesne, C.
• Format: Article
• Language: English
• Subjects: APPROXIMATIONS; AXIAL SYMMETRY; CALCULATION METHODS; DEFORMATION; DEFORMED NUCLEI; E2-TRANSITIONS; ENERGY-LEVEL TRANSITIONS; FUNCTIONS; HAMILTONIANS; MASS; MATHEMATICAL OPERATORS; MATHEMATICAL SOLUTIONS; MECHANICS; MOMENT OF INERTIA; MULTIPOLE TRANSITIONS; NUCLEAR DEFORMATION; NUCLEAR PHYSICS AND RADIATION PHYSICS; NUCLEI; QUANTUM MECHANICS; QUANTUM OPERATORS; SPECTRA; SUPERSYMMETRY; SYMMETRY; WAVE FUNCTIONS
• ISSN: 0556-2813; 1089-490X
• DOI: 10.1103/PhysRevC.83.044321

Analytical expressions for spectra and wave functions are derived for a Bohr Hamiltonian, describing the collective motion of deformed nuclei, in which the mass is allowed to depend on the nuclear deformation. Solutions are obtained for separable potentials consisting of a Davidson potential in the {beta} variable, in the cases of {gamma}-unstable nuclei, axially symmetric prolate deformed nuclei, and triaxial nuclei, implementing the usual approximations in each case. The solution, called the deformation-dependent mass (DDM) Davidson model, is achieved by using techniques of supersymmetric quantum mechanics (SUSYQM), involving a deformed shape invariance condition. Spectra and B(E2) transition rates are compared to experimental data. The dependence of the mass on the deformation, dictated by SUSYQM for the potential used, reduces the rate of increase of the moment of inertia with deformation, removing a main drawback of the model.