  Recent experiments on quantum dots in the Coulomb Blockade regime have shown
how adding successive electrons into a dot modifies the energy spectrum and the
wave functions of the electrons already present in the dot. Using a microscopic
model, we study the importance of electron-electron interaction on these
``scrambling'' effects. We compute the Hartree-Fock single particle properties
as function of the number $p$ of added electrons. We define parametric
correlation functions that characterize the scrambling properties of the
Hartree-Fock wave functions and energy spectra. We find that each of these
correlation functions exhibit a universal behavior in terms of the ratio
$p/p^{\ast}$ where $p^{\ast}$ is a characteristic number that decreases with
increasing either the interaction strength, the disorder strength or the system
size
