ΛBinding in Hypernuclei by Nonlocal Interaction

The characteristics of the $\Lambda -N$ interaction at low energy have been obtained assuming that the $\Lambda -N$ potential is nonlocal but separable and similar to that suggested by Yamaguchi in the case of $N-N$ potential. The unknown parameters entering in the proposed potential are determined on the basis of the global symmetry hypothesis of the strongly interacting particles. Our model predicts, in agreement with Dalitz and Downs' phenomenological findings of the nature of the $\Lambda -N$ potential based on hyperfragment data, that there is no bound $\Lambda$-nucleon system and that the singlet $\Lambda -N$ potential is stronger than the triplet potential, both being attractive. Binding energies of the $\Lambda$ particle in light hypernuclei based on the present model are, however, much too high compared with the experimental data. It is further pointed out that although the global symmetry hypothesis ($g_{\Lambda \pi }=g_{\Sigma \pi }=g_{N\pi }$) supplemented by the Yamaguchi type nonlocal $\Lambda -N$ potential is incompatible with the presently existing data, the restricted symmetry ($g_{\Lambda \pi }=g_{\Sigma \pi }\ne g_{N\pi }$) model is certainly admissible.