The rotational spectroscopic properties and the evolution of the octupole deformation with spin in ${}^{224}\mathrm{Ra}$ are investigated by using the cranking relativistic density functional theory on a three-dimensional lattice space together with the shell-model-like approach to introduce the pairing correlations. The available experimental data, including the $I\text{−}\omega$ relation and the electric transition probabilities $B\left(E2\right)$ and $B\left(E3\right)$, are well reproduced after introducing the pairing correlations. The average value of the calculated octupole deformation with (without) pairing correlations for the observed spin region ($I\le 28\hslash$) is approximately 0.124 (0.129), indicating the robustness of the octupole collectivity with the nuclear rotation in ${}^{224}\mathrm{Ra}$. It is found that the pairing correlations effect induces a more rigid octupole shape for ${}^{224}\mathrm{Ra}$ at the ground state $(\hslash \omega =0.00 \mathrm{MeV})$, while it becomes less pronounced with the increase of the rotational frequency.

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• Collective levels
• Electromagnetic transitions
• Nuclear structure & decays
• Nucleon distribution
• A ≥ 220
• Nuclear density functional theory