Statistical theory of nuclear cross section fluctuations

Abstract

The method of “random matrices”, employed originally in the study of energy level distributions of complex systems, is applied to the analysis of nuclear cross section averages and fluctuations in the continuum region. A generalization of the “orthogonal” ensemble of random unitary symmetric matrices introduced by Dyson is postulated as the underlying statistical ensemble of collision matrices from which averages and variances of nuclear reaction cross sections may be calculated. Analytical results are obtained only in the asymptotic limit N > 1, where N is the number of open channels, i.e., the dimension of the matrices considered. Effects due to energy resolution of the measuring apparatus and to “direct” or fast processes as well as to slow processes such as compound nucleus formation are considered. The method has the advantage of yielding results that are invariant with respect to a transformation of channel-representation, e.g., from channel-spin s to projectile momentum j. Consistency with unitarity is achieved by treating the collision matrix as the basic random variable rather than one or more of its matrix elements. The discussion is limited to angle-integrated cross sections corresponding to given values of spin and parity, but the extension to the more general case is straightforward.