Theory of compound-nucleus reactions: Gaussian versus non-Gaussian statistics of its parameters

A theory of compound-nucleus reactions is formulated which is valid for most of the physical situations: from the domain of isolated to the domain of overlapping resonances. We allow for a more general than Gaussian statistics of the resonance decay amplitudes. The energy spectrum is parametrized in terms of a variable σ/sub p/ that measures its stiffness. The following results are obtained: We formulate a condition under which Hauser-Feshbach expressions emerge. They include an elastic enhancement factor W. This factor essentially depends on the fourth moment of the decay amplitudes and the stiffness parameter σ/sub p/. Within our model, σ/sub p/ is given by requiring Wigner's level repulsion. If, in addition, one specializes to the Gaussian statistics of the decay amplitudes, the present results yield the analytical solution to the earlier Monte Carlo simulations. In the same limit, we find agreement with experimental results on W that are available for the regimes of well-isolated and of strongly overlapping resonances