The 12C + 13C scattering is investigated microscopically in the framework of the generator-coordinate model. The microscopic phase shifts are employed to adjust simple local potentials. Significant parity and spin-orbit dependences are displayed by these potentials. They arise from the combined effect of antisymmetrization and of the conservation of parity and angular momentum, respectively. The sign of the parity effect agrees with a general rule derived from a simplified microscopic model. The spin-orbit interaction does not vanish when the nucleon-nucleon spin-orbit interaction is turned off and does not depend much on its strength. The spin-orbit interaction also exhibits a strong parity dependence because of the small nucleon number difference between the colliding nuclei.