We extend the recently developed Jacobi no-core shell model to hypernuclei. Based on the coefficients of fractional parentage for ordinary nuclei, we define a basis where the hyperon is the spectator particle. We then formulate transition coefficients to states that single out a hyperon–nucleon pair which allow us to implement a hypernuclear many-baryon Hamiltonian for p-shell hypernuclei. As a first application, we use the basis states and the transition coefficients to calculate the ground states of $$^{4}_{\varLambda }\hbox {He}$$ Λ 4 He , $$^{4}_{\varLambda }\hbox {H}$$ Λ 4 H , $$^{5}_{\varLambda }\hbox {He}$$ Λ 5 He , $$^{6}_{\varLambda }\hbox {He}$$ Λ 6 He , $$^{6}_{\varLambda }\hbox {Li}$$ Λ 6 Li , and $$^{7}_{\varLambda }\hbox {Li}$$ Λ 7 Li and, additionally, the first excited states of $$^{4}_{\varLambda }\hbox {He}$$ Λ 4 He , $$^{4}_{\varLambda }\hbox {H}$$ Λ 4 H , and $$^{7}_{\varLambda }\hbox {Li}$$ Λ 7 Li . In order to obtain converged results, we employ the similarity renormalization group (SRG) to soften the nucleon–nucleon and hyperon-nucleon interactions. Although the dependence on this evolution of the Hamiltonian is significant, we show that a strong correlation of the results can be used to identify preferred SRG parameters. This allows for meaningful predictions of hypernuclear binding and excitation energies. The transition coefficients will be made publicly available as HDF5 data files.

We 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.

Stimulated by recent indications that the binding energy of the hypertriton could be significantly larger than so far assumed, requirements of a more strongly bound 3 Λ H state for the hyperon-nucleon interaction and consequences for the binding energies of A = 4, 5 and 7 hypernuclei are investigated. As basis a Y N potential derived at next-to-leading order in chiral effective field theory is employed, Faddeev and Yakubovsky equations are solved to obtain the corresponding 3-and 4-body binding energies, respectively, and the Jacobi no-core shell model is used for 5 Λ He and 7 Λ Li. It is found that the spin-singlet Λp interaction would have to be much more attractive which can be, however, accommodated within the bounds set by the available Λp scattering data. The binding energies of the 4 Λ He hypernucleus are predicted to be closer to the empirical values than for Y N interactions that produce a more weakly bound 3 Λ H. The quality of the description of the separation energy and excitation spectrum for 7 Λ Li remains essentially unchanged.PACS. 13.75.Ev Hyperon-nucleon interactions -21.80.+a Hypernuclei -21.30.Fe Forces in hadronic systems and effective interactions arXiv:1909.02882v1 [nucl-th]

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