Unbound states by analytic continuation in the coupling constant

The energies and widths of resonance states are determined by the analytic continuation of bound-state energies as functions of a potential strength parameter (“the coupling constant”). Various numerical examples show the applicability of the method to systems decaying to two- and three-body channels. The examples include unbound states of the nuclei ${}^5\mathrm{He},$ ${}^5\mathrm{Li},$ ${}^9\mathrm{Be},$ and ${}^9\mathrm{B},$ described in $\alpha +N$ and $\alpha +\alpha +N$ microscopic cluster models. Some states considered are controversial. Here they are well defined, and their questionable features are understood to arise from their proximity to the complex-energy region of unphysical resonances with negative energies and positive widths.