Extracting resonance poles from numerical scattering data: type-II Pad\`e reconstruction

TL;DR

This paper introduces a FORTRAN code that uses type-II Padé approximants for analytically continuing scattering matrices to extract resonance poles and residues from numerical data, with noise handling and high-precision options.

Contribution

The paper presents a novel FORTRAN implementation for resonance pole extraction using type-II Padé approximants, including noise robustness and multiple-precision support.

Findings

Successfully tested on multiple physical models

Able to handle noisy data for pole stability analysis

Provides accurate resonance parameters extraction

Abstract

We present a FORTRAN 77 code for evaluation of resonance pole positions and residues of a numerical scattering matrix element in the complex energy (CE) as well as in the complex angular momentum (CAM) planes. Analytical continuation of the S-matrix element is performed by constructing a type-II Pad\'e approximant from given physical values [Bessis et al (1994); Vrinceanu et al (2000); Sokolovski and Msezane (2004)] . The algorithm involves iterative "preconditioning" of the numerical data by extracting its rapidly oscillating potential phase component. The code has the capability of adding non-analytical noise to the numerical data in order to select "true" physical poles, investigate their stability and evaluate the accuracy of the reconstruction. It has an option of employing multiple-precision (MPFUN) package [Bailey (1993)] developed by D. H. Bailey wherever double precision calculations fail due to a large number of input partial wave (energies) involved. The package has been successfully tested on several models, as well as theF+H2->HF+H,F+HD->HF +D,Cl+HCl->ClH+Cl and H+D2->HD+D reactions. Some detailed examples are given in the text. PACS:34.50.Lf,34.50.Pi