Pade approximation of the S-matrix as a way of locating quantum resonances and bound states

TL;DR

This paper introduces a universal method using Pade approximation of the S-matrix along the real energy axis to locate quantum resonances and bound states without complex energy calculations.

Contribution

It presents a novel rational parametrization approach that simplifies spectral analysis by relying solely on real-axis S-matrix data, applicable to various potential types.

Findings

Effective in locating spectral points using real-axis data

Applicable to local, non-local, and discontinuous potentials

Compatible with experimental scattering data

Abstract

It is shown that the spectral points (bound states and resonances) generated by a central potential of a single-channel problem, can be found using rational parametrization of the S-matrix. To achieve this, one only needs values of the S-matrix along the real positive energy axis. No calculations of the S-matrix at complex energies or a complex rotation are necessary. The proposed method is therefore universal in that it is applicable to any potential (local, non-local, discontinuous, etc.) provided that there is a way of obtaining the S-matrix (or scattering phase-shifts) at real collision energies. Besides this, combined with any method that extracts the phase-shifts from the scattering data, the proposed rational parametrization technique would be able to do the spectral analysis using the experimental data.