From resonances to fluctuations: A microscopic analysis of the cross-section for inelastic neutron scattering to a definite state

Abstract

Thomas' approximation to the general R-matrix theory of Wigner and Eisenbud is used to study the development of fluctuations in the cross-section for inelastic neutron scattering, to a definite state, in the transition from the resonance region to the continuum. In standard analyses of Ericson fluctuations, averaging of all resonance parameters is carried out from the beginning. Here, no averaging is performed; it is therefore possible to study, in detail, the effects of variations in both the random distributions of the phases of interfering amplitudes associated with elastic and inelastic scattering and the statistical distributions of parameters of the underlying resonances. The present microscopic model is not limited to the study of nuclear reactions; studies of inelastic scattering associated with quantum dots in semiconductors at low temperature and electron–atom interactions that involve many overlapping resonances, require analyses of the kind reported.