 unperturbed Green’s function, $G_0$, is evaluated at $E=e_1+e_2$. Notice that a series of $-vG_0+vG_0vG_0-\cdots$ in Eq. (\[amplitude1\]) describes the multiple rescattering effect of the two neutrons during the emission due to the final state $nn$ interaction, which is included to the all orders in Eq. (\[amplitude2\]). In contrast to the case of decay energy spectra shown in Fig. 1, we take $\eta$ in Eq. (\[green0\]) to be an infinitesimal number in evaluating the unperturbed Green’s function and use the Gauss-Legendre integration technique for Eq. as described in Ref. [@EB92]. The energy spectrum is then computed as, $$\frac{d^2P}{de_1de_2}=\sum_{j,l}|M_{j,l,k_1,k_2}|^2\,\frac{dk_1}{de_1}
\frac{dk_2}{de_2},$$ where the factors $dk/de$ are due to the normalization of the continuum single-particle wave functions, for which we follow Ref. [@EB92].

Figure 2(a) shows the energy distribution obtained by switching off the final state $nn$ interaction. The energy distribution is dominated by the single-particle $d_{3/2}$ resonance state at 0.77 MeV. A ridge appears as in the energy distribution for dipole excitations of Borromean nuclei [@EB92; @HSNS09]. The energy distribution with the $nn$ final state interaction is shown in Fig. 2(b). The energy distribution is drastically changed, being highly concentrated along the line of $e_1+e_2\sim$ 0.14 MeV with an extremely small width. The variation with $e_1$ is weak along this line, although the maximum still appears at $e_1=e_2$. This is a clear manifestation of a three-body resonance, and is in marked contrast to the continuum dipole excitations, in which the final state $nn$ interaction does not affect much the shape of the energy distribution [@HSNS09].

![(Color online) The differential probability distribution with respect to the opening angle of the emitted two neutrons from $^{26}$O. The solid and the dotted lines show the correlated and uncorrelated results, respectively. The dot-dashed and the dashed lines denote the correlated results obtained by includi