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 (${}_{\Lambda \Lambda }^4$H, ${}_{\Lambda \Lambda }^5$H, ${}_{\Lambda \Lambda }^5$He and ${}_{\Lambda \Lambda }^6$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 $\Lambda \Lambda$, $\Lambda \Sigma$, $N\Xi$ and $\Sigma \Sigma$ 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 $B_8{B}_8$ 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 ${}_{\Lambda \Lambda }^4$H. For ${}_{\Lambda \Lambda }^5$H and ${}_{\Lambda \Lambda }^5$He, $\Lambda N-\Sigma N$ and $\Xi N-\Lambda \Sigma$ potentials enhance the net $\Lambda \Lambda -N\Xi$ coupling, and a large $\Xi$ probability is obtained even for a weaker $\Lambda \Lambda -N\Xi$ potential.

4 pages, 1 figure