Shell-Model Structure of thep-Shell Hypernuclei

A systematic study of the effective two-body $\Lambda -N$ interaction is made in an exact manner from the binding-energy data of the $p$-shell hypernuclei within the framework of the intermediate-coupling shell model. The binding energy is expressed in terms of the five independent potential integrals of the two-body $\Lambda -N$ interaction, and the latter are determined by a least-squares fit to the experimental data. The energy levels and the $\gamma$ transitions are calculated, and the structures of the $p$-shell hypernuclei are discussed. The potential integrals are then analyzed in terms of phenomenological potentials. A large contribution to the binding energy by noncentral forces, especially the tensor forces, is found. The effect of the existence of a three-body $\Lambda \mathrm{NN}$ force is also discussed.