Convergence of a separable expansion method in three-nucleon calculations

The efficiency of a separable expansion method proposed by Ernst, Shakin, and Thaler is examined in three-nucleon calculations. Separable approximations with increasing accuracy are constructed for the ${}_{}{}^1{}_{}{}^{}\mathrm{S}_0^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{S}_1^{}{}_{}{}^{}$ ${\mathrm{-}}^3$ ${\mathrm{D}}_1$ partial waves of the Paris potential. With these models we compute the three-body bound state and observables of the nucleon-deuteron scattering. The stability of the three-nucleon results is investigated as a function of the number of terms in the separable representation. Convergence is observed already for a few terms retained.