  Interacting many-particle systems with a mean-field one body part plus a
chaos generating random two-body interaction having strength $\lambda$, exhibit
Poisson to GOE and Breit-Wigner (BW) to Gaussian transitions in level
fluctuations and strength functions with transition points marked by
$\lambda=\lambda_c$ and $\lambda=\lambda_F$, respectively; $\lambda_F >>
\lambda_c$. For these systems theory for matrix elements of one-body transition
operators is available, as valid in the Gaussian domain, with $\lambda >
\lambda_F$, in terms of orbitals occupation numbers, level densities and an
integral involving a bivariate Gaussian in the initial and final energies. Here
we show that, using bivariate $t$-distribution, the theory extends below from
the Gaussian regime to the BW regime up to $\lambda=\lambda_c$. This is well
tested in numerical calculations for six spinless fermions in twelve single
particle states.
