  We present nucleon elastic scattering calculation based on Green's function
formalism in the Random-Phase Approximation. For the first time, the Gogny
effective interaction is used consistently throughout the whole calculation to
account for the complex, non-local and energy-dependent optical potential.
Effects of intermediate single-particle resonances are included and found to
play a crucial role in the account for measured reaction cross section. Double
counting of the particle-hole second-order contribution is carefully addressed.
The resulting integro-differential Schr\"odinger equation for the scattering
process is solved without localization procedures. The method is applied to
neutron and proton elastic scattering from $^{40}$Ca. A successful account for
differential and integral cross sections, including analyzing powers, is
obtained for incident energies up to 30 MeV. Discrepancies at higher energies
are related to much too high volume integral of the real potential for large
partial waves. Moreover, this works opens the way for future effective
interactions suitable simultaneously for both nuclear structure and reaction.
