Reduced Width Amplitude Distributions and Random Sign Rules in R-Matrix Theory

Abstract

A multivariate reduced width amplitude distribution is derived from quite general assumptions of level independence and of functional form invariance of the distribution. The multivariate distribution reduces to the well-known Gaussian singlet distribution (one degree of freedom) and moreover allows for the possibility of channel-channel reduced width amplitude correlations. Such correlations, which cannot be represented by a singlet distribution, may be especially relevant to partial fission reduced width amplitudes. In particular, it is noted that in statistical theory complete correlation or anticorrelation between two random variables implies a linear relation between them. The multivariate distribution is then used as a basis for a more precise statement of the ``random sign'' rules of R-matrix theory than hitherto given. It is pointed out that these rules imply a linear averaging over the multivariate reduced width amplitude distribution (in addition to the usual linear energy average) and are not merely consequences of the equiprobability of positive and negative signs for the reduced width amplitudes. The influence of the energy eigenvalue distribution and of variable reduced width amplitude statistics is discussed. It is emphasized that the multivariate reduced width amplitude distribution is relevant to any reaction theory in which level widths are defined even though it is phrased here in the language of R-matrix theory.