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 p arameter (''the coupling constant''). Various numerical examples show the a pplicability of the method to systems decaying to two- and three-body chann els. The examples include unbound states of the nuclei He-5, Li-5, Be-9, an d B-9, described in alpha+N and alpha+alpha+N microscopic cluster models. S ome states considered are controversial. Here they are well defined, and th eir questionable features are understood to arise from their proximity to t he complex-energy region of unphysical resonances with negative energies an d positive widths. [S0556-2813(99)00103-X].