$$\Lambda -\alpha $$ Potential by Folding $$\Lambda $$-Nucleon Interaction with Realistic $$\alpha $$ Wave Function

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 the \(\alpha \)-\(\Lambda \) potential and with this potential the binding energy of \(^5_\Lambda \)He is (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 (e.g. 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 \(\Lambda \)-\(\alpha \) folding potential results from these \(\Lambda \)-N potential give a large binding energy of \(^5_\Lambda \)He .