S-shell $\varLambda \varLambda$ hypernuclei based on chiral interactions

We generalize the Jacobi no-core shell model (J-NCSM) to study double-strangeness hypernuclei. All particle conversions in the strangeness S=−1,−2 sectors are explicitly taken into account. In two-body space, such transitions may lead to the coupling between states of identical particles and of non-identical ones. Therefore, a careful consideration is required when determining the combinatorial factors that connect the many-body potential matrix elements and the free-space two-body potentials. Using second quantization, we systematically derive the combinatorial factors in question for S=0,−1,−2 sectors. As a first application, we use the J-NCSM to investigate ΛΛ s-shell hypernuclei based on hyperon-hyperon (YY) potentials derived within chiral effective field theory at leading order (LO) and up to next-to-leading order (NLO). We find that the LO potential overbinds 6ΛΛHe while the prediction of the NLO interaction is close to experiment. Both interactions also yield a bound state for 5ΛΛHe. The 4ΛΛH system is predicted to be unbound