The Ericson Transition in Time-Reversal Invariant Systems: Symplectically Invariant Hamiltonians

We investigate the distributions of off-diagonal scattering matrix elements and cross-sections in the Ericson regime for time-reversal invariant systems with odd spin. Within the universal Heidelberg approach we prove that Gaussian and exponential behavior is found as the leading-order term of an asymptotic expansion of the aforementioned distributions. Furthermore, the subleading-order term is derived and compared with numerical simulations.