  The study of scattering processes in few body systems is a difficult problem
especially if long range interactions are involved. In order to solve such
problems, we develop here a potential-splitting approach for three body
systems. This approach is based on splitting the reaction potential into a
finite range core part and a long range tail part. The solution to the
Schr\"odinger equation for the long range tail Hamiltonian is found
analytically, and used as an incoming wave in the three body scattering
problem. This reformulation of the scattering problem makes it suitable for
treatment by the exterior complex scaling technique in the sense that the
problem after the complex dilation is reduced to a boundary value problem with
zero boundary conditions. We illustrate the method with calculations on the
electron scattering off the hydrogen atom and the positive helium ion in the
frame of the Temkin-Poet model.
