# Faddeev calculations on lambda hypertriton with potentials from Gel'fand-Levitan-Marchenko theory

## TL;DR

This paper uses Gel'fand-Levitan-Marchenko theory to derive lambda-nucleon potentials and applies three-body Faddeev calculations to predict the lambda hypertriton's binding energy and radius.

## Contribution

It introduces a novel approach of restoring hyperon-nucleon potentials from scattering phases and applies it to hypertriton calculations.

## Key findings

- Binding energy of -2.462 MeV for lambda hypertriton
- Root-mean-square radius of 7.00 fm
- Potentials show satisfactory convergence

## Abstract

Effective lambda-proton and lambda-neutron potentials, restored from theoretical scattering phases through Gel'fand-Levitan-Marchenko theory, are tested on a lambda hypertriton through three-body calculations. The lambda hypertriton is treated as a three-body system consisting of lambda-proton, lambda-neutron and proton-neutron subsystems. Binding energy and root-mean-square radius are computed for the ground state of lambda hypertriton ($J^{\pi}=1/2^+$). In coordinate space, the dynamics of the system is described using a set of coupled hyperradial equations obtained from the Differential Faddeev Equations. By solving the eigenvalue problem derived from this set of coupled hyperradial equations, the binding energy and root-mean-square matter radius computed are found to be -2.462 MeV and 7.00 fm, respectively. The potentials are also shown to display a satisfactory convergence behaviour.