From the resonance theory to the statistical model
When a fast-energy neutron (in the keV to MeV region) interacts with a nucleus, the reaction cross section no longer shows a distinct resonating shape because the compound states are strongly overlapped. Under this circumstance, each of the resonances cannot be resolved anymore, and the energy-average cross section is only meaningful. The average cross section can be related to statistical properties of resolved resonances, namely the average resonance spacing and decay widths. In this talk, theories for the neutron resonance are first summarized, paying a special attention to a nuclear-technology viewpoint. Then the statistical properties of the resonances are discussed by applying the Gaussian Orthogonal Ensemble (GOE) implemented in the S and K matrices. Although this is an old problem, our recent development on the GOE Monte Carlo technique sheds a new light on some compound nuclear reaction problems.