data concerning $^{226,228}$Th were compared with the model predictions [@bizzeti04]. The former appears to be close to the critical point, while the latter can be interpreted as an example of harmonic oscillations in the axial octupole mode.

In the present paper, we extend the investigation to the cases where the quadrupole deformation is not steady but performs oscillations under the effect of a proper potential, and in particular for situations close to the quadrupole critical point described by the X(5) symmetry, in the Radium and Thorium isotopic chain.

As we shall see, the properties of the already mentioned nuclei $^{224}$Th and $^{224}$Ra result to be reasonably described by our model with a “critical” (flat) potential well, extending both in the $\beta_2$ and $\beta_3$ directions. Moreover, we observe that, as far as the level scheme is concerned, also the next isotope $^{226}$Ra can be accounted for with a proper critical–point potential, in spite of the fact that the positive–parity part of the ground–state band does not follow the X(5) predictions. As in the case of Thorium, heavier isotopes of Radium have a permanent quadrupole deformation and octupole excitations of vibrational character, while the lighter ones are either non collective or vibrational 