Nucleon-antinucleon resonance spectrum in a potential model

We investigate the spectrum of antinucleon-nucleon resonances, using an optical potential we derived recently. An effective method to compute the $S$-matrix poles is presented. The corresponding phase shifts do not behave as ordinary resonances in the Argand diagram. We show, however, that the poles can be located by extrapolating the phase shifts with the aid of polynomial fits. The annihilation part of our potential is state and energy dependent and of short range. It yields a richer spectrum than that given by a longer ranged annihilation model.