Shadow poles in coupled-channel problems calculated with the Berggren basis

Abstract

Background: In coupled-channels models the poles of the scattering S matrix are located on different Riemann sheets. Physical observables are affected mainly by poles closest to the physical region but sometimes shadow poles have considerable effect too. Purpose: The purpose of this paper is to show that in coupled-channels problems all poles of the S matrix can be located by an expansion in terms of a properly constructed complex-energy basis. Method: The Berggren basis is used for expanding the coupled-channels solutions. Results: The locations of the poles of the S matrix for the Cox potential, constructed for coupled-channels problems, were numerically calculated and compared with the exact ones. In a nuclear physics application the Jπ=3/2+ resonant poles of He5 were calculated in a phenomenological two-channel model. The properties of both the normal and shadow resonances agree with previous findings. Conclusions: We have shown that, with an appropriately chosen Berggren basis, all poles of the S matrix including the shadow poles can be determined. We have found that the shadow pole of He5 migrates between Riemann sheets if the coupling strength is varied.