Trinucleon system in a two-body model: Coulomb effect on bound and scattering states

Recently it has been suggested that as in the neutron deuteron problem the theoretically calculated spin-doublet S wave proton deuteron scattering length 2a/sub pd/ is correlated with 3He binding energy. This strongly suggests that 2a/sub pd/≅0. In this paper we study various properties of the low energy trinucleon system including this correlation among scattering length and binding energy for the spin-doublet neutron deuteron and the proton deuteron systems in an ad hoc two-body model. The two-body potential models we employ have a long range tail of r/sup -2/ type and have been parametrized to produce the correct binding energies of 3H and 3He and the correct s wave spin-doublet neutron deuteron scattering lengths 2a/sub nd/. The present study predicts the low energy nucleon deuteron phase shifts and predicts the proton deuteron scattering length to be 2a/sub pd/≅(0.15 +- 0.1) fm