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, ‎Pd-114‎, ‎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.