AN EIGENFUNCTION APPROXIMATION FOR 2-BODY T-MATRIX

We present an eigenfunction analysis of the off-shell partial wave two-body t-matrix. The intention is to construct a general finite rank separable approximation for the two-body t-matrix that is suitable for use in numerical solutions of Faddeev's equation. We do this by extending the single term separable approximation suggested by Kowalski and Noyes. It is proved that if the potential satisfies the conditions stated by Faddeev then the kernel in the Kowalski-Noyes equation, Λ(s), is compact and has an eigenfunction representation. Our extension of the Kowalski-Noyes approximation is to add additional separable terms composed of the eigenfunctions of Λ(s). Finally, we are able to show that the non-physical poles which occur in the single term separable approximation are cancelled by these additional separable terms. © 1969.