Three-body model calculation of the $2{}^{+}$ state in ${}^{26}\mathrm{O}$

We discuss the energy of the excited $2{}^{+}$ state in the unbound nucleus ${}^{26}\mathrm{O}$ using the three-body model of ${}^{24}\mathrm{O}+n+n$. This model fully takes into account the continuum effects, as well as the dineutron correlation of the valence neutrons. The present calculation yields the energy of 1.354 MeV, which is slightly smaller than the unperturbed energy, 1.54 MeV. The energy shifts for the ground and the $2{}^{+}$ states with respect to the unperturbed energy suggest that $0{}^{+}$ and the $2{}^{+}$ states in ${}^{26}\mathrm{O}$ show a typical spectrum well described by a short-range pairing interaction acting on two valence nucleons in the same orbit.

Figure 1

(Top) The decay energy spectrum for the two-neutron emission decay of ${}^{26}\mathrm{O}$. The dashed and the solid lines are for the $0{}^{+}$ and $2{}^{+}$ states, respectively. The dotted line shows the uncorrelated spectrum obtained by ignoring the interaction between the valence neutrons. (Bottom) The decay energy spectrum obtained by superposing the $I=0$ and $I=2$ components. The dashed line is the same as the one in the top panel, that is, the decay energy spectrum for the pure $I=0$ configuration. The experimental data, normalized to the unit area, are taken from Ref. [5].