The structure of $^{26}$O is currently being investigated on both theoretical and experimental fronts. It is well established that it is unbound and the resonance parameters are fairly well-known. The theoretical analysis may involved two- and three-body interactions, as well as correlations with the continuum spectrum of energy. In order to properly assess the structure of the ground and excited states, it is imperative to include a large single particle representation with the right asymptotic behavior. The purpose of this work is to provide details of the single particle continuum configurations of the ground and excited $0^+$ states. We use a large complex energy single particle basis, formed by resonances and complex energy scattering states, the so called Berggren basis, and a separable interaction, which is convenient to solve in a large model space. Three $0^+$ states were found in the complex energy plane. Changes of the resonant parameters, i.e. energy and width, were analyzed as a function of strength of the residual interaction. It is shown how a subtle difference in the interaction could change the unbound character of $^{26}$O into a Borromean nucleus. Only one of the two excited states can be considered as a candidate for a physical meaningful resonance. The calculated occupation probabilities are in agreement with other theoretical approaches although the calculated half live is three-order of magnitude smaller than the experimental one.
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