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Above threshold s-wave resonances illustrated by the 1/2$^+$ states in $^9$Be and $^9$B

We solve the persistent problem of the structure of the lowest $1/2^+$ resonance in $^9$Be which is important to bridge the A=8 gap in nucleosynthesis in stars. We show that the state is a genuine three-body resonance even though it decays entirely into neutron-$^8$Be relative s-waves. The necessary barrier is created by "dynamical" evolution of the wave function as the short-distance $α$-$^5$He structure is changed into the large-distance n-$^8$Be structure. This decay mechanism leads to a width about two times smaller than table values. The previous interpretations as a virtual state or a two-body resonance are incorrect. The isobaric analog 1/2$^+$ state in $^9$B is found to have energy and width in the vicinity of 2.0 MeV and 1.5 MeV, respectively. We also predict another 1/2$^+$ resonance in $^9$B with similar energy and width.