Background: Searching for $\alpha$ condensation around a core nucleus, a new class of nuclear clustering, is an interesting topic. Previous theoretical studies predicted ${}^{16}\mathrm{O}+2\alpha$ condensed states. However, in those studies, the strong mixing with nonresonant states made the identification of true resonant states nontrivial.

Purpose: To address this issue, we aim to provide a more robust theoretical verification of the ${}^{16}\mathrm{O}+2\alpha$ condensation. Our goal is to clearly identify the resonant states and predict their properties, such as decay widths.

Method: We employ the real-time evolution method (REM), which generates physically important basis states using the equation of motion, minimizing contamination from the continuum. The analytical continuation in the coupling constant (ACCC) was used to estimate the $\alpha$-decay widths.

Results: The present calculations show much better convergence of eigenstates, and the $0_3^{+}$ and $0_4^{+}$ states show remarkable isoscalar monopole transition strengths, which are in good agreement with the predictions of Ichikawa et al. The small $\alpha$-decay widths for these states suggest that experimental observation appears feasible.

Conclusion: The present results show the reasonable agreement with a previous work, firmly establishing the $0_3^{+}$ and $0_4^{+}$ states approximately 5 and 1 MeV below the ${}^{16}\mathrm{O}+2\alpha$ threshold as candidates for the $2\alpha$ condensation around the core nucleus ${}^{16}\mathrm{O}$. The REM proved effective in identifying these states.

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• Nuclear structure & decays