  We present an extended application of the analytic quadrupole octupole
axially symmetric model, originally employed to study the octupole deformation
and vibrations in light actinides using an infinite well potential (IW). In
this work, we extend the model's applicability to a broader range of nuclei
exhibiting octupole deformation by incorporating a sextic potential instead of
the Davidson potential.Similarly to conventional models, such as AQOA-IW (for
infinite square potential) and AQOA-D (for the Davidson potential), our
proposed model is referred to as AQOA-S. By employing the sextic potential,
phenomenologically represented as $v(\tilde\beta) = a_1\tilde \beta^2+a_2\tilde
\beta^4+a_3\tilde \beta^6$, we can derive analytical expressions for the energy
spectra and transition rates (B(E1), B(E2), B(E3)). The energy spectra of the
model are essentially governed by two critical parameters: $\phi_0$, indicating
the balance between octupole and quadrupole strain, and $\alpha$, a key factor
in adjusting the shape and behavior of the spectra through the sextic
potential. In terms of applications, the study encompasses five isotopes,
namely $^{222-226}$Ra and $^{224,226}$Th. Significantly, our model demonstrates
remarkable agreement with the corresponding experimental data, particularly for
the recently determined B(EL) transition rates of $^{224}$Ra, surpassing the
performance of the model that employs the Davidson potential. The stability of
the octupole deformation in $^{224}$Ra adds particular significance to these
findings.
