Statistical Hauser-Feshbach theory with width-fluctuation correction including direct reaction channels for neutron-induced reactions at low energies

Abstract

A model to calculate particle-induced reaction cross sections with statistical Hauser-Feshbach theory including direct reactions is given. The energy average of scattering matrix from the coupledchannels optical model is diagonalized by the transformation proposed by Engelbrecht and Weidenmüller. The ensemble average of S-matrix elements in the diagonalized channel space is approximated by a model of Moldauer [Phys.Rev.C 12, 744 (1975)] using newly parametrized channel degree-of-freedom νa to better describe the Gaussian Orthogonal Ensemble (GOE) reference calculations. Moldauer approximation is confirmed by a Monte Carlo study using randomly generated S-matrix, as well as the GOE three-fold integration formula. The method proposed is applied to the 238 U(n,n') cross section calculation in the fast energy range, showing an enhancement in the inelastic scattering cross sections.

Evaluation of the neutron induced reactions on235U from 2.25 keV up to 30 MeV

“…The importance of considering the influence of direct reactions on calculated neutron inelastic scattering for well-deformed nuclei was recently highlighted [31,32]. This effect increases the neutron inelastic scattering cross section on coupled levels and decrease the elastic cross section, accordingly [32]. However, this effect is weaker for odd targets, due to the higher density of excited levels, and it was neglected in current calculations.…”

“…To account for the correlation between incident and exit channels in elastic scattering (i.e., the width fluctuation correction), the model proposed by Hofmann, Richert, Tepel and Weidenmüller (HRTW) [30] is used. The importance of considering the influence of direct reactions on calculated neutron inelastic scattering for well-deformed nuclei was recently highlighted [31,32]. This effect increases the neutron inelastic scattering cross section on coupled levels and decrease the elastic cross section, accordingly [32].…”

Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison

“…This reflects a general problem in analyzing compound-nuclear data. Unfortunately, we cannot exploit recent progress that has been made employing the K matrix [68,69], since it relies on the knowledge of the S-matrix elements. Instead, we put forward a seemingly new empirical method which is based on the observation that the peak exhibited by the cross-section distribution of compound-nuclear reactions at σ = 0 is shifted to a nonzero value by direct contributions.…”

Systematic and Statistical Uncertainties in Simulated r-Process Abundances due to Uncertain Nuclear Masses

“…The middle shaded region shows the additional influence of the neutron capture rate updates, similar to [6]. Here we calculate the neutron capture rates self-consistently with each mass table with version 3.3.3 of the Los Alamos Hauser-Feshbach code CoH [7]. The lightest shaded region includes updates to the β-decay properties as well.…”