bohr hamiltonian and interplay between γ-stable and γ-rigid collective motions with both harmonic oscillation and ring-shaped potentials for the γ-part

In the present work, the eigenvalue and eigenvector has been obtained by the bohr hamiltonian for even-even nuclei. the competition between γ-stable and γ-rigid collective motions has been created in the presence of the rigidity parameter. the β-part of the collective potential has been chosen to be equal to the generalized hulthen potential, while the γ-angular part of the problem is associated with ring-shaped potential around the γ = π/6 and the harmonic oscillation around the γ = 0. in both cases, the effect of rigidity and free parameters on energy spectrum of os-180, dy-162, gd-160, ru-100, pd114, and xe-124 nuclei have been investigated. also, the rates of b(e2) transition have been calculated and compared with experimental data. this model has an appropriate description of energy spectra for the mentioned nuclei.