Microscopic Calculation of $\Lambda-\alpha$ Folding Potential

TL;DR

This paper develops a microscopic folding potential for the alpha-Lambda system, comparing phenomenological and realistic interactions, and finds that realistic potentials tend to overbind due to missing repulsive features.

Contribution

It introduces a method to construct alpha-Lambda potentials from underlying interactions and highlights the overbinding issue with realistic potentials in this framework.

Findings

Phenomenological potentials reproduce experimental binding energy.

Realistic potentials tend to overbind due to missing repulsive components.

Separable approximations can match scattering data but may lack necessary repulsion.

Abstract

We construct a folding potential between the $\alpha$ and $\Lambda$ particles based on underlying nucleon-nucleon and hyperon-nucleon interactions. Starting from a phenomenological $\Lambda$-N potential and a Gaussian form of the $\alpha$-particle wave function we obtain for the built $\alpha$-$\Lambda$ interaction a bound $^5_\Lambda$He state with the binding energy (3.10 MeV), which is consistent with recent experimental data $3.12 \pm 0.02$ MeV. When in turn an exact solution of the four-body Faddeev-Yakubovsky equation for the $\alpha$-particle calculated with the CDBonn, Nijmegen or Argonne V18 realistic nucleon-nucleon potential is used and the phenomenological Gaussian $\Lambda$-N potential is replaced by the realistic (Nijmegen NSC97f) potential approximated by a rank-1 separable form, then $^5_\Lambda$He is overbound. In particular, its binding energy given by the folding potential generated with the $\alpha$ particle wave function based on the CDBonn potential is 7.47 MeV. Although the rank-1 separable $\Lambda$-N potential reproduces the exact scattering length and the effective range of the original $\Lambda$-N potential, the overbinding results from the lack of the required repulsive properties in the assumed separable form.