  The distribution $P_1$ of the first many-body excitation energy of a weakly
and moderately interacting electron gas in a finite conductor (in the diffusive
regime) is calculated. As the interaction is increased, $P_1$ crosses over from
Wigner-Dyson to Poisson. We characterize this transition through the inverse
participation ratio in Hilbert space, and examine its manifestation in a
projected 2-dimensional space.
