Low-EnergyΛ−dScattering and the Hypertriton with Separable Potentials

The $\Lambda -d$ scattering and ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}$ binding-energy problems are solved exactly using nonlocal separable $S$-wave potentials and a multiple-scattering formalism of the Faddeev type. $\Lambda -d$ scattering cross sections are presented for laboratory momenta in the range 100-250 MeV/c. No strong dependence of the $\Lambda -d$ scattering cross sections upon the low-energy $\Lambda -N$ scattering parameters is found. It is shown that the $\Lambda -N$ scattering data and the ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}$ binding energy cannot both be adequately fitted with purely attractive two-body potentials of the form used. Results are presented which illustrate the energy dependence of the $S$ matrix and the nonconvergence of the multiple-scattering series for the low-energy scattering amplitude when a three-body bound state is present.