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 coupledchannels optical model is diagonalized by the transformation proposed by Engelbrecht and Weidenmüller. The ensemble average of S-matrix elements in the diagonalized channel space is approximated by a model of Moldauer [Phys.Rev.C 12, 744 (1975)] using newly parametrized channel degree-of-freedom νa 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.

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It is argued that spectral features of quantal systems with random interactions can be given a geometric interpretation. This conjecture is investigated in the context of two simple models: a system of randomly interacting d bosons and one of randomly interacting fermions in a j=7/2 shell. In both examples the probability for a given state to become the ground state is shown to be related to a geometric property of a polygon or polyhedron which is entirely determined by particle number, shell size, and symmetry character of the states. Extensions to more general situations are discussed

We present new analytical results concerning the spectral distributions for (2 × 2) random real symmetric matrices which generalise the Wigner surmise.