We employ the three-body model to the ${}^{12}\mathrm{Be}$ nucleus by solving the Faddeev equations in momentum space using the partial-wave decomposition method. Four sets of interactions between the ${}^{10}\mathrm{Be}$ core and the neutron, $V_{cn}$, are constructed in different ways to test the validity of the three-body model. The spectra of ${}^{12}\mathrm{Be}$ are obtained, including the $0_1^{+}, 2^{+}, 1^{-}, 0^{-}$, and $0_3^{+}$ states, together with the rms radii, $R_m$. Our results are consistent with previous three-body computations of ${}^{12}\mathrm{Be}$ in coordinate space and the most recent ab initio calculations. For the $0_1^{+}$ ground state, the energies and radii of four sets of $V_{cn}$ are close to the experimental data. In particular, when $V_{cn}$ is constructed close to the realistic core-neutron interaction, the resulting probabilities of the $p$-wave configurations are similar to those obtained from earlier shell-model calculations. Additionally, we predict two excited states, $0^{-}$ and $0_3^{+}$, together with their two-neutron separation energies. For the first excited $2^{+}$ state, our calculations suggest that, if the $d_{3/2}$ and $d_{5/2}$ orbitals share the 1.28 MeV resonance state in ${}^{11}\mathrm{Be}$, then the three-body model could produce results that align with the experimental data.

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• Few-body systems
• Nuclear structure & decays
• 6 ≤ A ≤ 19