The fluctuations exhibited by the cross sections generated in a compound-nucleus reaction or, more generally, in a quantum-chaotic scattering process, when varying the excitation energy or another external parameter, are characterized by the width ${\mathrm{\Gamma }}_{\mathrm{corr}}$ of the cross-section correlation function. Brink and Stephen [Phys. Lett. 5, 77 (1963)] proposed a method for its determination by simply counting the number of maxima featured by the cross sections as a function of the parameter under consideration. They stated that the product of the average number of maxima per unit energy range and ${\mathrm{\Gamma }}_{\mathrm{corr}}$ is constant in the Ercison region of strongly overlapping resonances. We use the analogy between the scattering formalism for compound-nucleus reactions and for microwave resonators to test this method experimentally with unprecedented accuracy using large data sets and propose an analytical description for the regions of isolated and overlapping resonances.

• Received 26 March 2015

DOI:https://doi.org/10.1103/PhysRevE.92.022904