Reconstructing the nucleon-nucleon potential by a new coupled-channel inversion method

TL;DR

This paper introduces a new coupled-channel inversion method using supersymmetric transformations to reconstruct nucleon-nucleon potentials, enabling precise fitting of realistic scattering parameters and providing an exactly-solvable model for neutron-proton interactions.

Contribution

It presents a novel second-order supersymmetric transformation technique for the two-channel Schrödinger equation that accurately fits scattering data without altering phase shifts.

Findings

Adds Breit-Wigner term to mixing parameter

Allows precise fit of scattering parameters via Pade expansion

Constructs an exactly-solvable neutron-proton potential

Abstract

A second-order supersymmetric transformation is presented, for the two-channel Schr\"odinger equation with equal thresholds. It adds a Breit-Wigner term to the mixing parameter, without modifying the eigenphase shifts, and modifies the potential matrix analytically. The iteration of a few such transformations allows a precise fit of realistic mixing parameters in terms of a Pade expansion of both the scattering matrix and the effective-range function. The method is applied to build an exactly-solvable potential for the neutron-proton $^3S_1$-$^3D_1$ case.