Unitary pole expansion applied to the trinucleon problem

The unitary pole expansion of a central local potential effective in ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ two-nucleon states is applied to the calculation of the trinucleon bound state and the nucleon-deuteron doublet and quartet scattering lengths. An iteration method is used to solve the Faddeev equations in both cases and Padé techniques used to find the scattering lengths. The convergence rate of the Padé approximants is found to be good in both the doublet and quartet channels and a three-term unitary pole expansion is found to give fair agreement with the exact results for the trinucleon binding energy and the scattering lengths.