Full-Coupled Channel Approach to Doubly Strange $s$-Shell Hypernuclei

Abstract

We describe {\it ab initio} calculations of doubly strange, $S=-2$, $s$-shell hypernuclei ($^4_{ΛΛ}$H, $^5_{ΛΛ}$H, $^5_{ΛΛ}$He and $^6_{ΛΛ}$He) as a first attempt to explore the few-body problem of the {\it full}-coupled channel scheme for these systems. The wave function includes $ΛΛ$, $ΛΣ$, $NΞ$ and $ΣΣ$ channels. Minnesota $NN$, D2$^\prime$ $YN$, and simulated $YY$ potentials based on the Nijmegen hard-core model, are used. Bound state solutions of these systems are obtained. We find that a set of phenomenological $B_8B_8$ interactions among the octet baryons in $S=0, -1$ and -2 sectors, which is consistent with all of the available experimental binding energies of $S=0, -1$ and -2 $s$-shell (hyper-)nuclei, can predict a particle stable bound state of $^4_{ΛΛ}$H. For $^5_{ΛΛ}$H and $^5_{ΛΛ}$He, $ΛN-ΣN$ and $ΞN-ΛΣ$ potentials enhance the net $ΛΛ-NΞ$ coupling, and a large $Ξ$ probability is obtained even for a weaker $ΛΛ-NΞ$ potential.

4 pages, 1 figure