To consider the dynamic octupole correlations in odd-mass nuclei, an angular-momentum-dependent octupole-vibration core is incorporated into the octupole core-quasiparticle coupling model, and the structure of ${}^{233}\mathrm{Th}$ is studied as a representative example. The calculated positive- and negative-parity bands for both ${}^{233}\mathrm{Th}$ and its core ${}^{232}\mathrm{Th}$ are in good agreement with experimental data, revealing a transition from octupole vibration to static octupole deformation, and confirming the necessity of including the octupole vibration. The electromagnetic transition and probability distributions of spherical single-particle orbitals and core states further elucidate the evolution characteristics of the configuration. This work establishes an effective theoretical approach for studying octupole vibration in odd-mass nuclei.

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• Collective levels
• High spin states
• Nuclear structure & decays
• A ≥ 220
• Collective models