Hydrogenic- and Sturmian-Function Expansions in Three-Body Atomic Problems

Hydrogenic-function and Sturmian-function expansions are examined in both the Schr\"odinger and Faddeev formulations for three-body atomic problems. A detailed comparison of their convergence behavior is made. The difficulty of Sturmian-function expansion in accounting for the strong coupling between degenerate target states at excitation thresholds does not arise in the Faddeev formulation. The difficulty with the uncontrolled continuum contribution in the hydrogenic-function expansion, however, persists in both formulations. An estimation of the continuum contribution in the hydrogenic-function expansion is made for off-shell amplitudes which appear in the Faddeev formulation.