Remarcs on the shape transition from spherical to deformed gamma   unstable nuclei
  Energies and transition probabilities for low lying states in $^{134}$Ba and $^{104$Ru were calculated within a hybrid model.The ground and the first $2^+$ states are described alternatively as a harmonic and anharmonic vibrator states while the remaining states as states with E(5) symmetry. One concludes that a gradual setting of the 'critical' potential yields a better agreement with the experimental data. Very good agreement with the data is obtained for $^{104}$Ru. Comparing the present results with those of E(5) symmetry, it is conspicuous that the present formalism add corrections to the E(5) formalism by bringing the predictions closer to the experimental data. Analytical relationship between the states with U(5) symmetry and those given by the E(5) description is established. 
A. A. Raduta, A.C. Gheorghe and Amand Faessler