in the quadrupole mode.

Some results of this work, at different phases of advancement, have been reported at several Conferences or Schools [@bizzetirila; @bizzeticamerino; @bizzetipredeal; @bizzetivico].

For convenience of the reader, we report in the next Section \[S:2\] some evidence of the phase transitions in the Radium and Thorium isotopic chain, while the definition of variables introduced in I, and a few results relevant to the present work, are briefly summarized in the Section \[S:3a\]. In the following subsections, the model introduced in I is specialized to a form suitable for a critical potential in two dimensions. Finally, in the Section \[S:4\] the model results are reported and compared with the existing experimental evidence for $^{224,226}$Ra and $^{224}$Th. Previous models of quadrupole–octupole deformation are quoted in I. Since then, new relevant papers have appeared. A new “Analytic Quadrupole–Octupole axially symmetric model” (AQOA) has been proposed by D.Bonatsos [*et al.*]{} [@bonatsos05] to discuss the evolution of the quadrupole and octupole collectivity in Ra and Th isotopes. A parameter free model starting from a similar approach has been developed by Lenis and Bonatsos [@lenis06] and compared with the experimental results for $^{226}$Ra and $^{226}$Th. Moreover, a variant of the AQOA model, introducing 