Neutron-proton scattering and singular potentials

Abstract

We consider a Bargmann-type rational parametrization of the nucleon scattering phase shifts. Applying Marchenko's method of quantum inverse scattering we show that the scattering data suggest a singular repulsive core of the potential of the form $2/r^2$ and $6/r^2$ in natural units, for the ${}^3{S}_1$ and ${}^1{S}_0$ channels respectively. The simplest solution in the ${}^3{S}_1$ channel contains three parameters only but reproduces all features of the potential and bound state wave function within one percent error. We also consider the ${}^3{S}_1$-${}^3{D}_1$ coupled channel problem with the coupled channel Marchenko inversion method.

arXiv comment39 pages. Extended version. Title changed, presentation improved and a new appendix on the coupled channel problem added

References in corpus (14)

• An accurate nucleon-nucleon potential with charge-independence breaking
• The high-precision, charge-dependent Bonn nucleon-nucleon potential (CD-Bonn)
• Chiral effective field theory and nuclear forces
• Construction of high-quality Nucleon-Nucleon potential models
• Nuclear Force from Lattice QCD
• The deuteron: structure and form factors
• Phase equivalent chains of Darboux transformations in scattering theory
• Single- and coupled-channel radial inverse scattering with supersymmetric transformations
• Supersymmetric Transformations in Coupled-Channel Systems
• Phase shift effective range expansion from supersymmetric quantum mechanics
• Application of the operator product expansion to the short distance behavior of nuclear potentials
• 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
• Hadron Interactions from lattice QCD

Cited by in corpus (2)

• Displacement Memory Effect from Supersymmetry
• Marchenko method with incomplete data and singular nucleon scattering