Two-particle Coulomb Green's function in the momentum space with explicity separated singularities

The problem of the Coulomb scattering of two charged particles with initial and final momenta off the energy shell is considered. For the case of positive energy a new analytic expression is obtained for the two-particle Coulomb Green's function in which all singularities with respect to the momentum transfer and the singularities in the neighborhood of the energy shell are explicitly separated.