  In this note we establish the existence of ground states for atoms within
several restricted Hartree-Fock theories. It is shown, for example, that there
exists a ground state for closed shell atoms with $N$ electrons and nuclear
charge $Z \geq N-1$. This has to be compared with the general Hartree-Fock
theory where the existence of a minimizer is known for $Z>N-1$ only.
