  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.
