Evolution of the “βexcitation” in axially symmetric transitional nuclei

Abstract

The evolution of first excited $0^{+}$ states in transitional nuclei of the $N\approx 90$ region is correlated with the structure of the ground band. Iachello’s $X\left(5\right)$ solution for the Bohr-Hamiltonian for axially symmetric prolate nuclei is generalized to the transition path between $X\left(5\right)$ and the rigid-rotor limit using infinite square-well potentials in the quadrupole deformation parameter $\beta$ with boundaries at ${\beta }_M>{\beta }_m⩾0$. Analytical solutions in terms of Bessel functions of first and second kind are derived and describe well the evolutionary trajectory of the studied $0_2^{+}$ states in this mass region.