A Unified Formulation of Nuclear Fluctuation Theory

The statistical theory of fluctuations was initiated by ERICSON 1 in 1960 in the appendix of his review article on the statistical model of the compound nucleus. This was at a time when nuclear fluctuations had not yet been observed or recognized as such in scattering experiments. ERICSON pointed out that the excitation functions and angular distributions of nuclear reactions involving a compound nucleus in its region of overlapping resonances should exhibit in high resolution experiments a specific kind of irregular fluctuations. As in the case of noise in electrical circuits or radio waves 2 or other kinds of stochastic processes, one will consider these fluctuations as a single realization of an imaginary large ensemble of stochastic functions. One can then try to investigate, if not its details, so at least its statistical properties. Later ERICSON3 gave a detailed account of the fluctuation theory by extending essentially the former theories of the average compound cross sections to the consideration of its variances and covariances. The assumption of many overlapping levels turned out to be very important in getting fairly simple results on these higher moments of the cross section.