Harmonic oscillator potential with a quartic anharmonicity in the prolate γ-rigid collective geometrical model

Abstract

Abstract. An analytical expression for the energy spectrum of the ground and β bands was obtained in the axially symmetric γ-rigid regime of the Bohr-Mottelson Hamiltonian with a general quartic anharmonic oscillator potential in the β shape variable. As the Schrodinger equation for such a potential is not exactly solvable, the energy formula is derived on the basis of the JWKB approximation. Due to the scaling property of the quartic oscillator problem, the resulting energy depends on a single parameter up to an overall multiplicative constant. The upper limit of the domain of values for the free parameter is established by comparing the ground state eigenvalues with the corresponding numerically calculated results. Studying the behavior of the potential and of the whole energy spectrum as function of the free parameter, one establishes the present model's place between other γ-rigid models. The agreement with experiment is achieved through model fits for few nearvibrational nuclei.