Few-body aspects of light hypernuclei

Three- and four-body structure calculations of single A hypernuclei such as _Λ⁷He, _Λ⁹Be and _Λ¹³C and double _ΛΛ⁴H, _ΛΛ ⁷He; _ΛΛ⁷He, _Lambda;Λ⁸Li,_{, ΛΛ} ⁹Li, _ΛΛ⁹Be, and _ΛΛ¹⁰Be are discussed. The energy levels of _ΛΛ⁷He whose core is a famous halo nucleus, _Λ⁶;He, are predicted based on _Λ⁵He+ 2N three-body model.In the microscopic 2α+Λ (3α+Λ) model _Λ⁹Be(_Λ¹³C), we predict the spin-orbit splittings of 5/2₁⁺-3/2 ₁⁺ in _Λ⁹:Be and 3/2₁^--1/2₁^- in _Λ¹³C to be 0.08-0.16 MeV and 0.39-0.78 MeV, respectively, with the use of OBE-model NSC97a ∼f. On the other hand quark-model AN spin-orbit force gives rise to half of the splittings of the smallest OBE-model prediction. The experimental data were reported to be 31.4_-3.6^+2.5keV for _Λ ⁹:Be and to be 152± 54Plusmn; 36 keV for _Λ¹³C. By performing four-body calculation of _ΛΛH with both NNΛΛ and NNNΞ channels, we show that the ΛΛ - ΞN coupling potential plays an important role in making _ΛΛ ⁴H bound. Energy levels of the double-Λ hypernuclei, _ΛΛ⁷He, _ΛΛ⁸Li, _ΛΛ ⁹Li, _ΛΛ⁹Li, _ΛΛ⁹Be and _ΛΛ¹⁰Be are predicted on the basis of an α + x Λ + Λ four-body model, where x = n, p, d, t, ³He and α, respectively.