Unbound states by analytic continuation in the coupling constant

Nuclei have a large number of discrete unbound states (viz. resonances and virtual states). Such unbound states may be put on the same footing as bound states by the concept of the S-matrix pole. The unbound-state poles may be located by an analytic continuation in the 'coupling constant', i.e. in a strength parameter of the potential. In this way the solution of the unbound-state problem is substituted by solutions of a number of bound-state problems, and the pole position is determined by extrapolation. In the present work the objective was to study controversial unbound states of the most typical two-cluster and three-cluster nuclei. In this way the applicability of the analytic continuation method was broadened and the nature of the states considered are explored. The general results are the following. First, with a slight generalization, the method performs well for l = 0 states as well, where the pole trajectory passes through the virtual-state region. Second, the three-body resonances of systems that interact via purely attractive forces behave like two-body resonances within a potential barrier. In this way the appearance of an effective three-body barrier is confirmed. Third, the analytic continuation is reliable even if the two-body thresholds, as functions of the coupling constant, cross the three-body threshold. (K.A.)