  We prove decay with respect to some Lebesgue norms for a class of
Schr\"odinger equations with non-local nonlinearities by showing new Morawetz
inequalities and estimates. As a byproduct, we obtain large-data scattering in
the energy space for the solutions to the systems of $N$ defocusing
Schr\"odinger-Choquard equations with mass-energy intercritical nonlinearities
in any space dimension and of defocusing Hartree-Fock equations, for any
dimension $d\geq3$.
