Solution of the Bohr Hamiltonian for a periodic potential with minimum at γ=π/6

We present an analytic solvable γ-periodic potential of the form μ/sin²(3γ) in the Bohr–Mottelson collective model. The choice allows for a separation in both β, γ and θι if the γ-variable in the moments of inertia is approximated by its expectation value γ0=π/6. Energy spectra, E2 transition rates and subsequent collective bands with their properties are presented. We compare the approximation of γ=γ0=π/6 with a full diagonalisation of the rotational part. These results clearly point out that the approximative analytical treatment describes the full numerical results very well.