Description of nuclear octupole and quadrupole deformation close to axial symmetry: Critical-point behavior of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">Ra</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>224</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">Th</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>224</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>

The model, introduced in a previous paper, for the description of the octupole and quadrupole degrees of freedom in conditions close to axial symmetry, is applied to situations of shape phase transitions where the quadrupole amplitude can reach zero. The transitional nuclei $^{224,226}\mathrm{Ra}$ and $^{224}\mathrm{Th}$ are discussed in the frame of this model. Their level schemes can be reasonably accounted for by assuming a square-well potential in two dimensions. Electromagnetic transition amplitudes are also evaluated and compared with existing experimental data.

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