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A model to calculate particle-induced reaction cross sections withstatistical Hauser-Feshbach theory including direct reactions is given. Theenergy average of scattering matrix from the coupled-channels optical model isdiagonalized by the transformation proposed by Engelbrecht andWeidenm\"{u}ller. The ensemble average of $S$-matrix elements in thediagonalized 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) referencecalculations. Moldauer approximation is confirmed by a Monte Carlo study usingrandomly generated $S$-matrix, as well as the GOE three-fold integrationformula. The method proposed is applied to the $^{238}$U(n,n') cross sectioncalculation in the fast energy range, showing an enhancement in the inelasticscattering cross sections.

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