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

Abstract

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 $\Lambda \Lambda$ 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 ${}_{\Lambda \Lambda }^6\text{He}$ while the prediction of the NLO interaction is close to experiment. Both interactions also yield a bound state for ${}_{\Lambda \Lambda }^5\text{He}$. The ${}_{\Lambda \Lambda }^4\text{H}$ system is predicted to be unbound.

Comments: 23 pages, 3 figures