We revisit statistical wave function 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 $F_k\left(E\right)$ 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 $S^{\mathrm{info}}$ 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 ${\lambda }_d\sim 1∕\sqrt{m}$ ($m$ is number of fermions) for the duality point $\lambda ={\lambda }_d$, where $F_k\left(E\right)$, ${\xi }_2$, and $S^{\mathrm{info}}$ in both the weak $\left(\lambda =0\right)$ and strong mixing $\left(\lambda =\infty \right)$ basis coincide. 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 $8$.

• Received 6 January 2004

DOI:https://doi.org/10.1103/PhysRevE.70.016209