we see that its effect on $\psi_a(i)$ is
$$\label{eq:uhf} u_{HF}(i) \psi_a(i) =\left[ \sum_b^{occ} \int \psi_b(j) \frac{e^{2}}{4\pi\epsilon_{0}} \frac{1}{r_{ij}} \psi_b(j) dV_j \right] \psi_a(i) - \left[ \sum_b^{occ} \int \psi_b(j) \frac{e^{2}}{4\pi\epsilon_{0}} \frac{1}{r_{ij}} \psi_a(j) dV_j \right] \psi_b(i).$$%%                                                  %   9
Due to the presence of the last term, the {\em exchange potential}, the
potential is non-local.