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

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.

Comments: 24 pages, 14 figures. arXiv admin note: substantial text overlap with arXiv:1703.09067, arXiv:1606.08767