Solution of the Bohr Hamiltonian for a periodic potential with minimum at

We present an analytic solvable γ -periodic potential of the form μ / sin 2 ( 3 γ ) in the Bohr–Mottelson collective model. The choice allows for a separation in both β , γ and θ ι if the γ -variable in the moments of inertia is approximated by its expectation value γ 0 = π / 6 . Energy spectra, E2 transition rates and subsequent collective bands with their properties are presented. We compare the approximation of γ = γ 0 = 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.