The low-energy neutron−19C scattering in a neutron-neutron-core model is studied with large scattering lengths near the conditions for the appearance of an Efimov state. We show that the real part of the elastic s−wave phase-shift (δR 0) presents a zero, or a pole in k cot δR 0, when the system has an Efimov excited or virtual state. More precisely the pole scales with the energy of the Efimov state (bound or virtual). We perform calculations in the limit of large scattering lengths, disregarding the interaction range, within a renormalized zero-range approach using subtracted equations. It is also presented a brief discussion of these findings in the context of ultracold atom physics with tunable scattering lengths. PACS 03.65.Nk, 11.80.Jy, 03.65.Ge, 21.45.-v, 21.10.Dr Key words: Scattering theory, bound states, Faddeev equation, Few-body The experimental observation of an Efimov resonant state  in an ultracold gas of Cesium with tunable interactions, performed by the Innsbruck group , evidenced the universal properties of large three-body quantum states [3–6]. The observations of  gave support to several theoretical analysis on the possibility to identify Efimov states considering precise determinations of three-body recombination rates . They were also consistent with calculations of resonances for the atom-dimer channel  and for continuum triatomic Borromean configurations . In this situation, the properties o
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