Extracting S-matrix poles for resonances from numerical scattering data: Type-II Padé reconstruction

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 Padé approximant from given physical values (Bessis et al. (1994) [42]; Vrinceanu et al. (2000) [24]; Sokolovski and Msezane (2004) [23]). 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) [45]) developed by D.H. Bailey wherever double precision calculations fail due to a large number of input partial waves (energies) involved. The code has been successfully tested on several models, as well as the F + 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.Program summaryProgram title: PADE IICatalogue identifier: AEHO_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHO_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 19 959No. of bytes in distributed program, including test data, etc.: 158 380Distribution format: tar.gzProgramming language: FORTRAN 77Computer: Any computer equipped with a FORTRAN 90 compilerOperating system: UNIX, LINUXRAM: 256 MbClassification: 16.8External routines: NAG Program Library (http://www.nag.co.uk/numeric/fl/FLdescription.asp)Nature of problem: The package extracts the positions and residues of resonance poles from numerical scattering data supplied by the user. The data can then be used for quantitative analysis of interference patterns observed in elastic, inelastic and reactive integral and differential cross sections.Solution method: The S-matrix element is analytically continued in the complex plane of either energy or angular momentum with the help of Padé approximation of type II. Resonance (complex energy or Regge) poles are identified and their residues evaluated.Unusual features: Use of multiple precision MPFUN package (Bailey (1993) [45]). (Distributed with the PADE II code.)Running time: From several seconds to several minutes depending on the precision level chosen and the number of iterations performed.