Supersymmetric inversion of effective-range expansions

Abstract

A complete and consistent inversion technique is proposed to derive an accurate interaction potential from an effective-range function for a given partial wave in the neutral case. First, the effective-range function is Taylor or Padé expanded, which allows high precision fitting of the experimental scattering phase shifts with a minimal number of parameters on a large energy range. Second, the corresponding poles of the scattering matrix are extracted in the complex wave-number plane. Third, the interaction potential is constructed with supersymmetric transformations of the radial Schrödinger equation. As an illustration, the method is applied to the experimental phase shifts of the neutron-proton elastic scattering in the ${}^1{S}_0$ and ${}^1{D}_2$ channels on the $[0-350]$ MeV laboratory energy interval.

References in corpus (8)

• The Three-Nucleon System Near the N-d Threshold
• Effective-range approximations for resonant scattering of cold atoms
• Phase equivalent chains of Darboux transformations in scattering theory
• Phase shift effective range expansion from supersymmetric quantum mechanics
• Single- and coupled-channel radial inverse scattering with supersymmetric transformations
• Reconstructing the nucleon-nucleon potential by a new coupled-channel inversion method
• Description of the two-nucleon system on the basis of the Bargmann representation of the S matrix
• Toward a Spin- and Parity-Independent Nucleon-Nucleon Potential

Cited by in corpus (4)

• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• Low-energy theorems for nucleon-nucleon scattering at unphysical pion masses
• Low-energy theorems for nucleon-nucleon scattering at $M_{\pi }=450$ MeV
• Effective-range function methods for charged particle collisions