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

TL;DR

This paper extends the Jacobi no-core shell model to study double-strangeness hypernuclei, explicitly including particle conversions, and applies it to $ ext{Lambda} ext{-} ext{Lambda}$ hypernuclei using chiral EFT potentials, finding results consistent with experimental data.

Contribution

It introduces a systematic derivation of combinatorial factors for hypernuclei in the J-NCSM and applies this framework to $ ext{Lambda} ext{-} ext{Lambda}$ hypernuclei with chiral EFT potentials, providing new insights into their binding energies.

Findings

LO potential overbinds $^{6}_{ ext{Lambda} ext{-} ext{Lambda}} ext{He}$

NLO potential predicts results close to experiment

Both potentials predict a bound state for $^{5}_{ ext{Lambda} ext{-} ext{Lambda}} ext{He}$

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