  The rapid transition between spherical and $\gamma$-soft shapes in Ba and Xe
nuclei in the mass region $A \geq 130$ is analyzed using excitation spectra and
collective wave functions obtained by diagonalization of a five-dimensional
Hamiltonian for quadrupole vibrational and rotational degrees of freedom, with
parameters determined by constrained self-consistent relativistic mean-field
calculations for triaxial shapes. The results reproduce the characteristic
evolution of excitation spectra and E2 transition probabilities and, in
general, a good agreement with available data is obtained. The calculated
spectra display fingerprints of a second-order shape phase transition that can
approximately be described by analytic solutions corresponding to the E(5)
dynamical symmetry.

Nuclear Theory