Tests of the Porter-Thomas Distribution for Reduced Partial Neutron Widths

Abstract

Given N data points drawn from a chi-square distribution, we use Bayesian inference to determine most likely values and N-dependent confidence intervals for the width sigma and the number k of degrees of freedom of that distribution. Using reduced partial neutron widths measured in a number of nuclei, a guessed value of sigma, and a maximum-likelihood approach (different from Bayesian inference), Koehler et al. and Koehler have determined the most likely k-values of chi-square distributions that fit the data. In all cases they find values for k that differ substantially from k = 1 (the value characterizing the Porter-Thomas distribution (PTD) predicted by random-matrix theory). The authors conclude that the validity of the PTD must be rejected with considerable statistical significance. We show that the value of sigma guessed in these papers lies far outside the Bayesian confidence interval for sigma, casting serious doubt on the results of and the conclusions drawn there. We also show that sigma and k must both be determined from the data. Comparison of the results with the Bayesian confidence intervals would then decide on acceptance or rejection of the PTD.