Bohr Hamiltonian with deformation-dependent mass term for the Kratzer potential

Abstract

The Deformation Dependent Mass (DDM) Kratzer model is constructed by considering the Kratzer potential in a Bohr Hamiltonian, in which the mass is allowed to depend on the nuclear deformation, and solving it by using techniques of supersymmetric quantum mechanics (SUSYQM), involving a deformed shape invariance condition. Analytical expressions for spectra and wave functions are derived for separable potentials in the cases of gamma-unstable nuclei, axially symmetric prolate deformed nuclei, and triaxial nuclei, implementing the usual approximations in each case. 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, moderates the increase of the moment of inertia with deformation, removing a main drawback of the model.

27 pages, 6 figures, 8 tables. arXiv admin note: text overlap with arXiv:1103.5935

References in corpus (8)

• Solutions of the Bohr hamiltonian, a compendium
• Bohr Hamiltonian with deformation-dependent mass term for the Davidson potential
• Exactly separable version of the Bohr Hamiltonian with the Davidson potential
• Analytical solutions of the Bohr Hamiltonian with the Morse potential
• Bohr Hamiltonian with Davidson potential for triaxial nuclei
• Solution of the Bohr hamiltonian for soft triaxial nuclei
• Phonon and multi-phonon excitations in rotational nuclei by exact diagonalization of the Bohr Hamiltonian
• Spectrum generating algebras for position-dependent mass oscillator Schrodinger equations

Cited by in corpus (25)

• Vibrational and rotational excited states within Bohr Hamiltonian with deformation-dependent mass formalism
• On γ-rigid regime of the Bohr-Mottelson Hamiltonian in the presence of a minimal length
• Energy states of the Hulthen plus Coulomb-like potential with position-dependent mass function in external magnetic fields
• Closed analytical solutions of Bohr Hamiltonian with Manning-Rosen potential model
• Approximate energy states and thermal properties of a particle with position-dependent mass in external magnetic fields
• Electric quadrupole transitions of the Bohr Hamiltonian with Manning-Rosen potential
• Bohr Hamiltonian with an energy dependent $\gamma$-unstable Coulomb-like potential
• Nuclear shape phase transition within a conjonction of γ-rigid and γ-stable collective behaviours in deformation dependent mass formalism
• Davydov-Chaban Hamiltonian with deformation-dependent mass term for γ = 30°
• Bohr Hamiltonian with a deformation-dependent mass term: physical meaning of the free parameter
• Conjunction of $\gamma$-rigid and $\gamma$-stable collective motion in the critical point of the phase transition from spherical to deformed nuclear shapes
• Competing $\gamma$-rigid and $\gamma$-stable vibrations in neutron rich Gd and Dy isotopes
• Collective motion in prolate γ-rigid nuclei within minimal length concept via a quantum perturbation method
• Shape vibrations and quasiparticle excitations in the lowest 0+ excited state of the Erbium isotopes
• Calculations of the Decay Transitions of the Modified Poschl-Teller Potential Model via Bohr Hamiltonian Technique
• Description of the low-lying collective states of ${}^{96}$Zr based on the quadrupole-collective Bohr Hamiltonian
• Excited states of odd-mass nuclei with different deformation-dependent mass coefficients
• Bohr Hamiltonian with Hulthen plus ring-shaped potential for triaxial nuclei with deformation-dependent mass term
• Excited collective states of nuclei within Bohr Hamiltonian with Tietz-Hua potential
• Application of the triaxial quadrupole-octupole rotor to the ground and negative-parity levels of actinide nuclei
• Bohr Hamiltonian with Pöschl Teller potential in γ unstable and γ stable pictures
• General formalism of collective motion for any deformed system
• Coriolis contribution to excited states of odd-mass nuclei with different deformation-dependent mass coeffcients
• Kinetic energy in the collective quadrupole Hamiltonian from the experimental data
• Approximate Solution of Bohr-Mottelson Hamiltonian with Minimal Length Effect for Hulthen Potential Using Asymptotic Iteration Method