Λ-Nucleon Interaction from Analysis ofS-Shell Hypernuclei

From the binding-energy data of the $S$-shell hypernuclei, the triplet and singlet depth of a central $\Lambda$-nucleon potential, which has a hard core of radius 0.4 F and an attractive well of exponential shape with a range suggested by the mechanism of two-pion exchange, are determined. The results show that the singlet interaction is stronger than the triplet interaction. The well-depth parameters are equal to 0.865 and 0.675, indicating that the strength of the $\Lambda$-nucleon potential is not sufficient to bind a hyperdeuteron, although it is sufficient to allow the existence of a bound excited state in the hypernuclei ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^4{}_{}{}^{}$ and ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{He}_{}^4{}_{}{}^{}$ with a binding energy $B_{\Lambda }$ in the neighborhood of 0.35 MeV. Using the $\Lambda$-nucleon interaction found in this analysis, the binding energy of a $\Lambda$ particle in nuclear matter and the $\Lambda$-nucleon scattering cross sections have also been computed. In both these cases, fair agreement with experimental results has been obtained.