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.
Categories: nucl-th