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The scattering problem for two particles interacting via the Coulombpotential is examined for the case where the potential has a sharp cut-off atsome distance. The problem is solved for two complimentary situations, firstlywhen the interior part of the Coulomb potential is left in the Hamiltonian and,secondly, when the long range tail is considered as the potential. The partialwave results are summed up to obtain the wave function in three dimensions. Itis shown that in the domains where the wave function is expected to beproportional to the known solutions, the proportionality is given by anoperator acting on the angular part of the wave function. The explicitrepresentation for this operator is obtained in the basis of Legendrepolynomials. We proposed a driven Schr\"odinger equation including aninhomogeneous term of the finite range with purely outgoing asymptotics for itssolution in the case of the three dimensional scattering problem with longrange potentials.

The impact of sharp screening on the Coulomb scattering problem in three dimensions