The zero range potential is constructed for a system of two particlesinteracting via the Coulomb potential. The singular part of the asymptote ofthe wave function at the origin which is caused by the common effect of thezero range potential singularity and of the Coulomb potential is explicitlycalculated by using the Lippmann-Schwinger type integral equation. The singularpseudo potential is constructed from the requirement that it enforces thesolution to the Coulomb Schr\"odinger equation to possess the calculatedasymptotic behavior at the origin. This pseudo potential is then used forconstructing a model of the imaginary absorbing potential which allows to treatthe annihilation process in positron electron collisions on the basis of thenon relativistic Schr\"odinger equation. The functional form of the pseudopotential constructed in this paper is analogous to the well knownFermi-Breit-Huang pseudo potential. The generalization of the optical theoremon the case of the imaginary absorbing potential in presence of the Coulombforce is given in terms of the partial wave series.
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