Algebraic reduction and approximate intertwining relation in the strong approximation of Moller wave operators approach

Nonrelativistic quantum scattering processes can be calculated from strong approximations of Moller wave operators, based on finite rank approximations of the full and asymptotic Hamiltonians. Firstly, similarly to Faddeev-type integral equations, we show that this approach also reduces a three-body system with separable two-body interactions to an effective two-body system. In the simplest case of an s-wave interaction without tensor forces, it reduces to a one-dimensional equation after partial wave decomposition. Secondly, we show that the intertwining relation is approximately valid in this approach and holds in the limit where the approximation parameters tend to infinity. We give a proof for the two-body system with short range interactions and for the long range Coulomb interaction. Implications for practical calculations are discussed