Stable bound states of $N$'s, $\Lambda$'s, and $\Xi$'s

TL;DR

This paper reviews the stability of strange few-body systems containing nucleons and hyperons, using advanced interaction models and solving bound-state equations, finding some systems are bound while others are not.

Contribution

It provides new insights into the binding properties of hypernuclear systems using updated potentials and numerical methods, identifying potential bound states involving Xi hyperons.

Findings

The hypertriton is bound by 144 keV.

The $ extLambda nn$ system is unbound.

Some $ extXi$ hyperon systems may be bound.

Abstract

We review our recent work about the stability of strange few-body systems containing $N$'s, $\Lambda$'s, and $\Xi$'s. We make use of local central Yukawa-type Malfliet-Tjon interactions reproducing the low-energy parameters and phase shifts of the nucleon-nucleon system and the latest updates of the hyperon-nucleon and hyperon-hyperon ESC08c Nijmegen potentials. We solve the three- and four-body bound-state problems by means of Faddeev equations and a generalized Gaussian variational method, respectively. The hypertriton, $\Lambda np$ $(I)J^P=(1/2)1/2^+$, is bound by 144 keV; the recently discussed $\Lambda nn$ $(I)J^P=(1/2)1/2^+$ system is unbound, as well as the $\Lambda\Lambda nn$ $(I)J^P=(1)0^+$system, being just above threshold. Our results indicate that the $\Xi NN$, $\Xi\Xi N$ and $\Xi\Xi NN$ systems with maximal isospin might be bound.