Stability of the s- and p-shell α cluster hypernuclei with strangeness S = -2 to -4

The energies of the s- and p-shell hypernuclei in the α cluster model with strangeness content S = −1 to −4 are calculated in a variational Monte Carlo framework. Two types of Λα and Ξ0α potentials and a variety of three-range Gaussian YY potentials simulated from models of the Nijmegen group are used. The Woods–Saxon Ξ0α potential with central depths −24.0 and −14.0 MeV is considered. Unlike the earlier Faddeev–Yakubovsky results, the system He is as strongly bound for the Isle Ξ0α potential as for the Woods–Saxon shape. The hypernuclei of the 8Be core with strange baryons Ξ0 and ΛΛΞ0 are also found to be stable, but the latter one is overbound without dispersive Λαα force. The strong conversion makes S = −3 hypernucleus Be unstable and no definitive conclusion about the stability of He can be drawn. The attractive three-body ααα force is required to fit the ground-state energy and root-mean-square radius of 12C for a αα potential, similar to earlier works. The BΛ of 13ΛC is not consistent with the data without Λαα dispersive force. The system C has been found to be stable.