Abstract
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 $\ensuremath{\alpha}+N$ and $\ensuremath{\alpha}+\ensuremath{\alpha}+N$ 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.
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