In this paper, the ${}^{18}\mathrm{O}$ nucleus is studied by means of a three-body model consisting of an inert ${}^{16}\mathrm{O}$ core and two neutrons. For the three-body system, the Faddeev equations are solved directly in momentum space using the partial-wave decomposition. The momentum-space formulation usually requires the momentum representation $\tilde{V}\left(\right|\mathbf{p}-{\mathbf{p}}^{\prime }\left|\right)$ of the two-body interaction $V\left(r\right)$ used. However, our method allows us to deal directly with any $V\left(r\right)$ in its original form in coordinate space, while avoiding the use of its representation in momentum space. In this way, we can then easily introduce the coordinate-space techniques, such as the supersymmetric transformation, to deal with the possible Pauli-blocking problem for the core-$n$ subsystem. For ${}^{18}\mathrm{O}$, the partial spectrum, including the ground state and several positive-parity low-lying excited states, is obtained, and the distribution of energy levels is consistent with previous work. For each state, the root-mean-square radius is calculated, and the structure is discussed in terms of partial-wave components. In addition, we performed some calculations on the ${}^{22}\mathrm{C}$ nucleus for further application. The results obtained are close to the most recent experimental values. Our momentum-space method can also be used to calculate the properties of other nuclei suitable for the three-body model.

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• Energy levels
• Few-body systems
• Nuclear forces
• Nuclear radii
• 6 ≤ A ≤ 19