Scattering amplitude without an explicit enforcement of boundary conditions

It has been known for some time that for short range potentials scattering observables can be calculated using complex coordinates. We will show that the standard uniform complex scaling can be applied to calculate the scattering amplitude even in the presence of a long range interaction. The main advantage of the application of the complex scaling to the scattering problem is that the direct imposition of the complicated scattering boundary condition can be avoided. As a result, the scattering problem can be solved using only square integrable functions. The method will be applied not only for potential scattering but for the coupled-channel reaction model. As an application we calculate the phase shifts of the charge exchange reaction {sup 3}H(p,n){sup 3}He.