The simplest strange three-body halo

Abstract

The recently developed method to solve the Faddeev equations in coordinate space is used to study the weakly bound halo nucleus . The long distances are treated carefully to achieve convergence and high accuracy. We use several sets of two-body interactions which reproduce the deuteron properties and provide the low-energy - nucleon scattering data close to that of two of Nijmegen potentials. We show that the details of the potentials are unimportant unless the accuracy of the hypertriton binding energy is required to be better than 50 keV. We find that the most significant parameter of the - nucleon interaction, the singlet s-wave scattering length, must be within 10% of 1.85 fm, when the -separation energy from the deuteron is about 130 keV. Other details of the - nucleon interaction are less important for the hypertriton structure. The scattering length and effective range are computed for scattering of a -particle on a deuteron. The folding model reducing the three-body problem to a two-body problem is investigated in this context and found to be inadequate.