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An approach based on splitting the reaction potential into a finite rangepart and a long range tail part to describe few-body scattering in the case ofa Coulombic interaction is proposed. The solution to the Schr\"odinger equationfor the long range tail of the reaction potential is used as an incoming wave.This reformulation of the scattering problem into an inhomogeneousSchr\"odinger equation with asymptotic outgoing waves makes it suitable forsolving with the exterior complex scaling technique. The validity of theapproach is analyzed from a formal point of view and demonstrated numerically,where the calculations are performed with the finite element method. The methodof splitting the potential in this way is illustrated with calculations of theelectron scattering on the hydrogen atom and the positive helium ion in energyregions where resonances appear.

Potential splitting approach to e-H and e-He${}^+$ scattering with zero total angular momentum