  Localization results for a class of random Schr\"odinger operators within the
Hartree-Fock approximation are proved in two regimes: large disorder and weak
disorder/extreme energies. A large disorder threshold $\lambda_{\mathrm{HF}}$
analogous to the threshold $\lambda_{\mathrm{And}}$ obtained by Schenker in
\cite{Schenkl} is provided. We also show certain stability results for this
large disorder threshold by giving examples of distributions for which
$\lambda_{\mathrm{HF}}$ converges to $\lambda_{\mathrm{And}}$, or to a number
arbitrarily close to it, as the interaction strength tends to zero.
