Neutron-proton scattering and singular potentials

TL;DR

This paper uses inverse scattering methods to analyze neutron-proton scattering data, revealing that the potential includes a singular repulsive core of the form 2/r^2 and 6/r^2 in specific channels, with a simple model accurately reproducing key features.

Contribution

It introduces a rational parametrization of scattering phase shifts and applies Marchenko's inverse scattering method to identify singular core potentials in nucleon interactions.

Findings

Potential has a 2/r^2 and 6/r^2 repulsive core in specific channels.

A simple three-parameter model reproduces the potential and wave functions within 1% accuracy.

Inverse scattering methods effectively characterize nucleon-nucleon interactions.

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 ${}^3S_1$ and ${}^1S_0$ channels respectively. The simplest solution in the ${}^3S_1$ 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 ${}^3S_1$-${}^3D_1$ coupled channel problem with the coupled channel Marchenko inversion method.