Three- and Four-Body Cluster Models of Hypernuclei Using theG-Matrix N Interaction: 9 Be, 13 C, 6 He and 10 Be

The structure calculations of 5ΛHe, 9ΛBe, 13ΛC, 10ΛΛBe and 6ΛΛHe are carried out with an accurate three- and four-body model method in which all rearrangement Jacobian coordinates and associated Gaussian basis functions are taken. The characteristic properties of the spin-independent parts of five kinds of YNG ΛN interactions are focused on. We propose to improve the strengths of the odd-state parts in a systematic way. The improved YNG interaction explains theBΛ(5ΛHe) andBΛ(9ΛBe) consistently without an additional three-body force. By employing the 3α+Λ four-body model together with the improved YNG interactions, the second 1/2+ state of 13ΛC is predicted as a bound state at approximately 1 MeV below the lowest threshold. The four-body model enables us to find that response to the addition of the Λ particle to the core nucleus 12C is very different for the ground and second 0+ states. With the improved YNG interaction and the OBE-simulating ΛΛ interaction, the observedBΛΛ(10ΛΛBe) is reproduced in the framework of the 2α+2Λ four-body model. A new theoretical prediction forBΛΛ(6ΛΛHe) is made with the α+2Λ three-body model.