Coulomb exchange and pairing contributions in nuclear Hartree-Fock-Bogoliubov calculations with the Gogny force

We present exact Hartree-Fock-Bogoliubov calculations with the finite range density dependent Gogny force using a triaxial basis. For the first time, all contributions to the Pairing and Fock Fields arising from the Gogny and Coulomb interactions as well as the two-body correction of the kinetic energy have been calculated in this basis. We analyze the relevance of these terms in different regions of the periodic table at zero and high angular momentum. The validity of commonly used approximations that neglect different terms in the variational equations is also checked. We find a decrease of the proton pairing energies mainly due to a Coulomb antipairing effect.