Theory for matrix elements of one-body transition operators in the quantum chaotic domain of interacting particle systems

Demonstrating the equivalence between the recent theory of Flambaum and collaborators which is based on smoothed strength functions, with the much earlier formulation due to French and collaborators which is based on embedded random matrix ensembles and smoothed transition strength densities, we derive a theory for matrix elements of one-body transition operators in the quantum chaotic domain of isolated finite interacting particle systems with a mean-field and a chaos generating two-body interaction (V). The role of the bivariate correlation coefficient (zeta) arising out of the noncommutability of V and the transition operator (in the theory of Flambaum et al., zeta=0) is tested in numerical embedded ensemble calculations with a one- plus two-body Hamiltonian generating order-chaos transitions.