  The three-body scattering problem in Coulombic systems is widespread, however
yet unresolved problem by the mathematically rigorous methods. In this work
this long term challenge has been undertaken by combining distorted waves and
Faddeev-Merkuriev equation formalisms in conjunction with the complex scaling
technique to overcome difficulties related with the boundary conditions. Unlike
the common belief, it is demonstrated that the smooth complex scaling method
can be applied to solve three-body Coulomb scattering problem in a wide energy
region, including fully elastic domain and extending to the energies well
beyond atom ionization threshold.
  Newly developed method is used to study electron scattering on ground states
of Hydrogen and Positronium atoms as well as a $e^+$+H(n=1) $\rightleftarrows$
p+Ps(n=1) reaction. Where available, obtained results are compared with the
experimental data and theoretical predictions, proving accuracy and efficiency
of the newly developed method.
