Functional approach to statistical theories of nuclear reactions

Nuclear reactions for equivalent channels are considered in the framework of the entropy approach. We show that in the limit of many open channels, the resulting partition function may be expressed in terms of a functional integral whose trajectories are labelled by the eigenvalue density of the S matrix. A saddle-point method is used to establish a linear integral equation for the eigenvalue density function of largest probability. This function can then be used to express all averages of physical interest. As an example, a particular partition function which has no transition points is used to determine cross sections and the enhancement factor. We find good agreement with other theories.