Faddeev Equations for Atomic Problems. IV. Convergence of the Separable-Expansion Method for Low-Energy Positron-Hydrogen Problems

The separable-expansion method for solving the Faddeev equations is applied to the positron-hydrogen system at energies below the positronium-formation threshold. The results for the scattering length and phase shift are compared with those obtained by other methods. The three-body bound state and resonance obtained using only the first few terms in the separable expansion are shown to disappear when more terms are included in the expansion. The problem of convergence of the separable-expansion method in the Sturmian-function representation is discussed.