  Based on the work of Nuttall and Cohen [Phys. Rev. {\bf 188} (1969) 1542] and
Resigno et al{} [Phys. Rev. A {\bf 55} (1997) 4253] we present a rigorous
formalism for solving the scattering problem for long-range interactions
without using exact asymptotic boundary conditions. The long-range interaction
may contain both Coulomb and short-range potentials. The exterior complex
scaling method, applied to a specially constructed inhomogeneous Schr\"odinger
equation, transforms the scattering problem into a boundary problem with zero
boundary conditions. The local and integral representations for the scattering
amplitudes have been derived. The formalism is illustrated with numerical
examples.
