  The zero range potential is constructed for a system of two particles
interacting via the Coulomb potential. The singular part of the asymptote of
the wave function at the origin which is caused by the common effect of the
zero range potential singularity and of the Coulomb potential is explicitly
calculated by using the Lippmann-Schwinger type integral equation. The singular
pseudo potential is constructed from the requirement that it enforces the
solution to the Coulomb Schr\"odinger equation to possess the calculated
asymptotic behavior at the origin. This pseudo potential is then used for
constructing a model of the imaginary absorbing potential which allows to treat
the annihilation process in positron electron collisions on the basis of the
non relativistic Schr\"odinger equation. The functional form of the pseudo
potential constructed in this paper is analogous to the well known
Fermi-Breit-Huang pseudo potential. The generalization of the optical theorem
on the case of the imaginary absorbing potential in presence of the Coulomb
force is given in terms of the partial wave series.
