Λ0Binding in Light Nuclei

In an attempt to study the forces by which the hyperon ${\Lambda }^0$ is bound in light hyperfragments, several assumptions are made: (1) perturbation theory is adequate; (2) vertices like $N\to {\Lambda }^0+{\theta }^0$ are dominant; (3) the spin of the $\theta$ is 0 or 1, and the spin of the $\Lambda$ is ½ or $\frac{3}{2}$; (4) there are no attractive contact potentials; (5) $\Lambda$—nucleon forces are much weaker than nucleon-nucleon forces. If these assumptions are granted, the trend of the binding energy of the $\Lambda$ as a function of the mass number can be predicted for each coupling type. Certain assignments of spin and parity [$(s_{\Lambda }, s_{\theta })=({\frac{1}{2}}^{+}, 0^{+}), ({\frac{1}{2}}^{-}, 1^{-}), \mathrm{and} ({\frac{3}{2}}^{-}, 1^{-})$] can be ruled out, because in these cases a $\Lambda$ cannot be bound by ${\mathrm{H}}^3$, ${\mathrm{He}}^3$, or heavier nuclei, contrary to experimental findings.