Exact method for locating potential resonances and Regge trajectories

We propose an exact method for locating the zeros of the Jost function for analytic potentials in the complex momentum--plane. We further extend the method to the complex angular--momentum plane to provide the Regge trajectories. It is shown, by using several examples, that highly accurate results for extremely wide as well as for extremely narrow resonances with or without the presence of the Coulomb interaction can be obtained.