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

A model to calculate particle-induced reaction cross sections with statistical Hauser-Feshbach theory including direct reactions is given. The energy average of the scattering matrix from the coupled-channels optical model is diagonalized by the transformation proposed by Engelbrecht and Weidenm¨uller [C. A. Engelbrecht and H. A. Weidenm¨uller, Phys. Rev. C 8, 859 (1973)]. The ensemble average of S-matrix elements in the diagonalized channel space is approximated by a model of Moldauer [P. A. Moldauer, Phys. Rev. C 12, 744 (1975)] using the newly parametrized channel degree-of-freedom νa to better describe the Gaussian orthogonal ensemble (GOE) reference calculations. The Moldauer approximation is confirmed by a Monte Carlo study using a randomly generated S matrix, as well as the GOE threefold integration formula. The method proposed is applied to the ²³⁸U(n,n') cross-section calculation in the fast-energy range, showing an enhancement in the inelastic scattering cross sections.