  Fidelity decay is studied for quantum many-body systems with a dominant
independent particle Hamiltonian resulting e.g. from a mean field theory with a
weak two-body interaction. The diagonal terms of the interaction are included
in the unperturbed Hamiltonian, while the off-diagonal terms constitute the
perturbation that distorts the echo. We give the linear response solution for
this problem in a random matrix framework. While the ensemble average shows no
surprising behavior, we find that the typical ensemble member as represented by
the median displays a very slow fidelity decay known as ``freeze''. Numerical
calculations confirm this result and show, that the ground state even on
average displays the freeze. This may contribute to explanation of the
``unreasonable'' success of mean field theories.
