Exact Results for the Ericson Transition in Stochastic Quantum Scattering and Experimental Validation

Abstract

At lower energies, the resonances in scattering experiments are often isolated. The crucial parameter is the ratio of average resonance width and average mean level spacing. Towards larger energies, this parameter grows, because the resonances overlap. Eventually the cross-section becomes a random function and the scattering matrix elements follow a universal Gaussian distribution. For more than sixty years, this Ericson transition awaits a concise analytical treatment. We provide a complete solution within the Heidelberg approach which provides a full-fledged model of the scattering process. As a side result, we obtain explicit formulae for the moments of the distributions. We compare with microwave experiments.