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Structure and three-body decay of $^9$Be resonances

The complex-rotated hyperspherical adiabatic method is used to study the decay of low-lying $^9$Be resonances into one neutron and two $α$-particles. We investigate the six resonances above the break-up threshold and below 6 MeV: $1/2^\pm$, $3/2^\pm$ and $5/2^\pm$. The short-distance properties of each resonance are studied, and the different angular momentum and parity configurations of the $^8$Be and $^5$He two-body substructures are determined. We compute the branching ratio for sequential decay via the $^8$Be ground state which qualitatively is consistent with measurements. We extract the momentum distributions after decay directly into the three-body continuum from the large-distance asymptotic structures. The kinematically complete results are presented as Dalitz plots as well as projections on given neutron and $α$-energy. The distributions are discussed and in most cases found to agree with available experimental data.