Three-body continuum of ${}^{26}\mathrm{O}$

We investigate the ${}^{26}\mathrm{O}$ unbound nucleus in a ${}^{24}\mathrm{O}+n+n$ three-body model. We use the hyperspherical formalism, which relies only on ${}^{24}\mathrm{O}+n$ and $n+n$ interactions. As ${}^{26}\mathrm{O}$ is unbound, even in its ground state, the long-range behavior of the wave functions is crucial. We adapt the $R$-matrix technique to derive the wave functions and the associated phase shifts. We start from a ${}^{24}\mathrm{O}+n$ potential which nicely reproduces the known ${}^{25}\mathrm{O}$ properties. Using a weakly repulsive three-body potential, we find the ${}^{26}\mathrm{O}$ ground state at 0.08 MeV, i.e., just above the threshold, in agreement with the latest experimental value. An analysis of the wave function suggests a dominant dineutron configuration. We extend the model to $J=1^{-}$ and $J=2^{+}$. For $J=2^{+}$, we find a relatively narrow resonance near $E_R=1.3$ MeV ($\mathrm{\Gamma }\approx 0.4$ MeV), which is supported by recent experimental data. Broad structures are seen in the $0^{+}$ and $1^{-}$ phase shifts but cannot be associated with physical resonances.

Figure 1

${}^{24}\mathrm{O}+n+n$ three-body eigenphases for $J=0^{+}$, and for different $K_{\max }$ values (two eigenphases are displayed).

Figure 2

Application of the box method to the ${}^{26}\mathrm{O}$ ground state. (a) Eigenvalues of the system (10) as a function of the box radius, for $K_{\max }=24$. The labels represent the eigenvalue index. (b) Energy of the ground state for increasing $K_{\max }$ values.

Figure 3

${}^{26}\mathrm{O}$ probabilities (16) for the dominant $S=0$ component. The coordinates are defined in the text.

Figure 4

${}^{24}\mathrm{O}+n+n$ three-body eigenphases for $J=1^{-}$, and for different $K_{\max }$ values.

Figure 5

Same as Fig. 4, but for $J=2^{+}$.