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

Abstract

AbstractWe generalize the Jacobi no-core shell model (J-NCSM) to study double-strangeness hypernuclei. All particle conversions in the strangeness $$S=-1,-2$$ 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 $$S=0,-1,-2$$ S = 0 , - 1 , - 2 sectors. As a first application, we use the J-NCSM to investigate $$\varLambda \varLambda $$ Λ Λ 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 $$^{\,\,\,{\,}6}_{\varLambda \varLambda }\text {He}$$ Λ Λ 6 He while the prediction of the NLO interaction is close to experiment. Both interactions also yield a bound state for $$^{\text { }\text { }\text { } \text {}5}_{\varLambda \varLambda }\text {He}$$ Λ Λ 5 He . The $$^{\text {}\text { }\text { }\text {}4}_{\varLambda \varLambda }\text {H}$$ Λ Λ 4 H system is predicted to be unbound.