Low-EnergyΛ−pScattering and the Hypertriton Binding Energy with Sums of Separable Potentials

The ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}$ binding energy is calculated by finding the pole in the $\Lambda -d$ doublet $S$-wave scattering amplitude. This amplitude is obtained from a multiple-scattering formalism of the Faddeev type. Each of the two-body interactions was represented as a sum of an attractive and a repulsive $S$-wave nonlocal separable potential of the Yamaguchi form. The $\Lambda -N$ potentials were chosen to fit the scattering lengths and effective ranges obtained by Herndon, Tang, and Schmid (HTS) in a variation calculation. The $N-N$ potential was adjusted to fit the deuteron binding energy and the triplet scattering length. Calculations with several sets of values for the free parameters are carried out. By making the $\Lambda -N$ repulsive strengths infinite, fixing all three repulsive potential ranges at 0.2 F, and varying the range of the $N-N$ attractive potential, a value for the ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}$ binding energy that agrees with that of the HTS calculation is obtained.