# Effective lambda-proton and lambda-neutron potentials from subthreshold inverse scattering

## TL;DR

This paper constructs lambda-nucleon interaction potentials from theoretical scattering data using inverse scattering theory, revealing features like short-range repulsion and charge symmetry breaking, with implications for hypernuclear physics.

## Contribution

The paper introduces a novel application of Gel'fand-Levitan-Marchenko inverse scattering to lambda-nucleon potentials using theoretical data, resulting in explicit, unique potentials with physical features.

## Key findings

- Lambda-nucleon potentials exhibit short-range repulsion and intermediate-range attraction.
- The lambda-nucleon force is stronger in the $^1S_0$ channel than in the $^3S_1$ channel.
- Charge symmetry breaking is preserved in the reconstructed potentials.

## Abstract

Potentials are constructed for the lambda-nucleon interaction in the $^1\text{S}_0$ and $^3\text{S}_1$ channels. These potentials are recovered from scattering phases below the inelastic threshold through Gel'fand-Levitan-Marchenko theory. Experimental data with good statistics is not available for lambda-nucleon scattering. This leaves theoretical scattering phases as the only option through which the rigorous theory of quantum inverse scattering can be used in probing the lambda-nucleon force. Using rational-function interpolations on the theoretical scattering data, the kernels of the Gel'fand-Levitan-Marchenko integral equation become degenerate, resulting in a closed-form solution. The new potentials restored, which are shown to be unique through the Levinson theorem, bear the expected features of short-range repulsion and intermediate-range attraction. Charge symmetry breaking, which is perceptible in the scattering phases, is preserved in the new potentials. The lambda-nucleon force in the $^1\text{S}_0$ channel is observed to be stronger than in the $^3\text{S}_1$ channel, as expected. In addition, the potentials bear certain distinctive features whose effects on hypernuclear systems can be explored through Schr\"{o}dinger calculations.