Evolution of the “βexcitation” in axially symmetric transitional nuclei

Abstract

The evolution of first excited ${0}^{+}$ states in transitional nuclei of the $N\ensuremath{\approx}90$ 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 $\ensuremath{\beta}$ with boundaries at ${\ensuremath{\beta}}_{M}>{\ensuremath{\beta}}_{m}\ensuremath{\geqslant}0$. 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.