  We revisit statistical wavefunction properties of finite systems of
interacting fermions in the light of strength functions and their participation
ratio and information entropy. For weakly interacting fermions in a mean-field
with random two-body interactions of increasing strength $\lambda$, the
strength functions $F_k(E)$ are well known to change, in the regime where level
fluctuations follow Wigner's surmise, from Breit-Wigner to Gaussian form. We
propose an ansatz for the function describing this transition which we use to
investigate the participation ratio $\xi_2$ and the information entropy $S^{\rm
info}$ during this crossover, thereby extending the known behavior valid in the
Gaussian domain into much of the Breit-Wigner domain. Our method also allows us
to derive the scaling law for the duality point $\lambda = \lambda_d$, where
$F_k(E)$, $\xi_2$ and $S^{\rm info}$ in both the weak ($\lambda=0$) and strong
mixing ($\lambda = \infty$) basis coincide as $\lambda_d \sim 1/\sqrt{m}$,
where $m$ is the number of fermions. As an application, the ansatz function for
strength functions is used in describing the Breit-Wigner to Gaussian
transition seen in neutral atoms CeI to SmI with valence electrons changing
from 4 to 8.
