Marchenko method with incomplete data and singular nucleon scattering

TL;DR

This paper extends the Marchenko quantum inverse scattering method to handle incomplete data, enabling the analysis of nucleon scattering with fractional singularity strengths, and compares results to a known phenomenological potential.

Contribution

It introduces an analytical approach based on the incomplete data method to study nucleon scattering with fractional singularity strengths, expanding the applicability of the Marchenko method.

Findings

Estimated the singularity strength parameter in various channels.

Demonstrated the method's ability to handle fractional singularities.

Compared results with the Reid93 potential.

Abstract

We apply the Marchenko method of quantum inverse scattering to study nucleon scattering problems. Assuming a $\beta/r^2$ type repulsive core and comparing our results to the Reid93 phenomenological potential we estimate the constant $\beta$, determining the singularity strength, in various spin/isospin channels. Instead of using Bargmann type S-matrices which allows only integer singularity strength, here we consider an analytical approach based on the incomplete data method, which is suitable for fractional singularity strengths as well.