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.

我们将 Jacobi 无核壳模型 (J-NCSM) 推广到研究双奇异超核。奇异性\(S=-1,-2\)扇区中的所有粒子转换都被明确考虑在内。在二体空间中，这种转变可能导致相同粒子和非相同粒子的状态之间的耦合。因此，在确定连接多体势矩阵元素和自由空间二体势的组合因素时需要仔细考虑。使用二次量化，我们系统地推导出\(S=0,-1,-2\)扇区的组合因子。作为第一个应用程序，我们使用 J-NCSM 来调查\(\varLambda \varLambda \)基于超子-超子 (YY) 势的 s 壳超核，在手性有效场理论中以领先顺序 (LO) 和最高次领先顺序 (NLO) 得出。我们发现 LO 电位过度绑定\(^{\,\,\,{\,}6}_{\varLambda \varLambda }\text {He}\)而 NLO 相互作用的预测接近实验。这两种相互作用也产生了\(^{\text { }\text { }\text { } \text {}5}_{\varLambda \varLambda }\text {He}\)的绑定状态。的\（^ {\ {文本} \ {文本} \ {文本} \文本{} 4} _ {\ varLambda \ varLambda} \文本{H} \）系统被预测为未结合的。