Bivariate-t distribution for transition matrix elements in Breit-Wigner to Gaussian domains of interacting particle systems

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 Gaussian orthogonal ensemble 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 a theory for the matrix elements of one-body transition operators is available, as valid in the Gaussian domain, with lambda >lambda(F), in terms of orbital occupation numbers, level densities, and an integral involving a bivariate Gaussian in the initial and final energies. Here we show that, using a 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 6 spinless fermions in 12 single-particle states.