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

An analytical expression for the energy spectrum of the ground and β bands was obtained through the JWKB approximation in the axially symmetric γ-rigid regime of the Bohr–Mottelson Hamiltonian with an oscillator potential and a sextic anharmonicity in the β shape variable. Due to the scaling property of the problem, the resulting energy depends up to an overall multiplicative constant on a single parameter. Studying the behavior of the energy spectrum as a function of the free parameter, one establishes the present model's place among other prolate γ-rigid models and in the more general extent of collective solutions. The agreement with experiment is achieved through model fits for few nuclei.