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

TL;DR

This paper develops an advanced statistical model incorporating direct reaction channels into the Hauser-Feshbach theory, improving neutron-induced reaction cross section calculations at low energies, with applications to uranium-238.

Contribution

It introduces a new method combining coupled-channels optical model with a refined width fluctuation correction for better cross section predictions.

Findings

Enhanced inelastic scattering cross sections for $^{238}$U(n,n')

Validation of Moldauer approximation via Monte Carlo simulations

Effective inclusion of direct reactions in statistical models

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 coupled-channels optical model is diagonalized by the transformation proposed by Engelbrecht and Weidenm\"{u}ller. The ensemble average of $S$-matrix elements in the diagonalized channel space is approximated by a model of Moldauer [Phys.Rev.C {\bf 12}, 744 (1975)] using newly parametrized channel degree-of-freedom $\nu_a$ 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.