Statistical properties of neutron-induced reaction cross sections using a random-matrix approach

We investigate the statistical properties of neutron-induced nuclear reactions on $^{238}\mathrm{U}$ using the GOE-$S$-matrix model, in which the Gaussian orthogonal ensemble (GOE) is embedded into the scattering ($S$) matrix. The GOE-$S$-matrix model does not require any experimental values of the average level spacing $D$ and average decay width $\ensuremath{\langle}\mathrm{\ensuremath{\Gamma}}\ensuremath{\rangle}$ with their statistical distributions, but the model is fully characterized by the channel transmission coefficients used in the Hauser-Feshbach theory. We demonstrate that the obtained compound-nucleus decay-width distribution resembles the $\ensuremath{\chi}$-squared distribution with the degree of freedom greater than unity. This approach enables us to generate fluctuating cross sections while preserving requisite unitarity and accounting for interference between resonances. By comparing the calculated cross-section distribution with that from $R$-matrix theory, we demonstrate a smooth transition from the resolved resonance region to the continuum region.