Shadow poles in a coupled-channel problem calculated with Berggren basis

TL;DR

This paper demonstrates that all poles of the S-matrix, including shadow poles, can be accurately calculated in coupled-channel problems using a properly constructed Berggren basis, enhancing understanding of scattering phenomena.

Contribution

It introduces a method to compute all S-matrix poles, including shadow poles, in coupled-channel models using the Berggren basis, validated against an exactly solvable Cox potential.

Findings

All S-matrix poles, including shadow poles, can be determined with the Berggren basis.

The method accurately reproduces poles in the Cox potential model.

Shadow poles significantly influence physical observables in coupled-channel systems.

Abstract

In coupled-channel 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. The purpose of this paper is to show that in coupled-channel problem all poles of the S-matrix can be calculated with properly constructed complex-energy basis. The Berggren basis is used for expanding the coupled-channel solutions. The location of the poles of the S-matrix were calculated and compared with an exactly solvable coupled-channel problem: the one with the Cox potential. We show that with appropriately chosen Berggren basis poles of the S-matrix including the shadow ones can be determined.