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 varLambda varLambda 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} 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}. The ^{text {}text { }text { }text {}4}_{varLambda varLambda }text {H} system is predicted to be unbound.
Highlights
Ξ hypernuclei are an indispensable source of information that can provide valuable additional constraints for constructing YY interactions
The YN interaction derived within the chiral effective field theory (EFT) approach up to next-to-leading order (NLO) likewise leads to realistic results for (s- and p-shell) hypernuclei [27,28,38,39,40] and for nuclear matter [31,41]
For all calculations presented here, we employ BB interactions that are derived within chiral EFT [32]
Summary
Ξ hypernuclei are an indispensable source of information that can provide valuable additional constraints for constructing YY interactions. Filikhin and Gal have solved the Faddeev–Yakubovsky equations formulated for three- (ΛΛα), four-cluster (ΛΛαα) and ΛΛnp components [16,17,18] Their calculations are based on simulated potentials similar to those used in the works of Hiyama et al but the ΛΛ interactions were mainly restricted to the s-wave. The Jacobi NCSM has been successfully employed by us in studies of single-Λ hypernuclei up to A = 7 [27,28] In these investigations, the full complexity of the underlying nucleon-nucleon (NN) and YN interactions (tensor forces, channel coupling) could be incorporated. The YN interaction derived within the chiral EFT approach up to NLO likewise leads to realistic results for (s- and p-shell) hypernuclei [27,28,38,39,40] and for nuclear matter [31,41].
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