Evolution of the “βexcitation” in axially symmetric transitional nuclei

The evolution of first excited 0⁺ states in transitional nuclei of the N≈90 region is correlated with the structure of the ground band. Iachello's $X(5)$ solution for the Bohr-Hamiltonian for axially symmetric prolate nuclei is generalized to the transition path between $X(5)$ and the rigid-rotor limit using infinite square-well potentials in the quadrupole deformation parameter β with boundaries at βM>βₘ0. Analytical solutions in terms of Bessel functions of first and second kind are derived and describe well the evolutionary trajectory of the studied 0₂⁺ states in this mass region.