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

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...

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Bibliographic Details
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
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Summary: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.
ISSN:0556-2813
1089-490X
DOI:10.1103/PhysRevC.83.044321