Continuum excitations of ${}^{26}\mathrm{O}$ in a three-body model: $0^{+}$ and $2^{+}$ states

The structure and decay dynamics for $0^{+}$ and $2^{+}$ continuum excitations of ${}^{26}\mathrm{O}$ are investigated in a three-body ${}^{24}\mathrm{O}+n+n$ model. The validity of a simple approximation for the cross section profile for long-lived $2n$ emission is demonstrated. A sequence of three $0^{+}$ monopole (“breathing mode” type) excited states is predicted. These states could probably be interpreted as analogs of Efimov states pushed in the continuum due to insufficient binding. The calculated energies of the $2^{+}$ states are related to the excitation spectrum of ${}^{25}\mathrm{O}$. We discuss the correlation between the predicted ${}^{26}\mathrm{O}$ spectrum and experimental observations.

Figure 1

Experimentally observed energy levels of ${}^{26}\mathrm{O}$ [3, 4, 5] and ${}^{25}\mathrm{O}$. For theory results the level scheme predicted for ${}^{26}\mathrm{O}$ is shown which is based on the one assumed for ${}^{25}\mathrm{O}$.

Figure 2

The $0^{+}$ excitation spectrum of ${}^{26}\mathrm{O}$ calculated by the three-body model for proton knockout from ${}^{27}\mathrm{F}$. Weights, $W_i$, of the peaks are shown in percent.

Figure 3

Cross section profiles for the very narrow ${}^{26}\mathrm{O}$ g.s. calculated by the three-body model and obtained by the $R$-matrix–type approximation are shown on two different scales in (a) and (b).

Figure 4

Spectroscopic factor ${\theta }^2$ Eq. (7) as a function of channel radius ${\rho }_{\text{ch}}$. The dotted curve shows the dependence of the “internal normalization” $I$ on ${\rho }_{\text{ch}}$.

Figure 5

WF densities for the ${}^{26}\mathrm{O}$ ground state and two excited $0^{+}$ states. All WFs are normalized to unity maximum value. Arrows indicate the humps connected with monopole excitations.

Figure 6

Width estimates for the $0^{+}$ and $2^{+}$ states of ${}^{26}\mathrm{O}$ in the $R$-matrix–type approach of Eq. (8) for different ${\left[j_1{j}_2\right]}_J$ configurations. Vertical dashed lines indicate the predicted positions of the $0^{+}$ states.

Figure 7

The ${}^{26}\mathrm{O}$ WF correlation density $W(\rho ,{\theta }_{\rho })$ in the “Y” Jacobi system for the ground state (a) and two excited $0^{+}$ states (b) and (c). Notice the change of $\rho$ scale.

Figure 8

The systematics of the $0^{+}$ and $2^{+}$ states of ${}^{26}\mathrm{O}$ as a function of the $ls$ interaction intensity $V_{ls}$ in the $d$-wave ${}^{24}\mathrm{O}-n$ channel under the condition that the ${}^{25}\mathrm{O}{d}_{3/2}$ g.s. position remains fixed. The result for $V_{ls}=-5$ MeV (indicated by vertical dots) is provided in Fig. 1 as our main result. The predictions of Ref. [6] are indicated by arrows in the left part of the plot.