Effects of Sample Size and Statistical Weights on Fluctuations in theC12(C12, α)Ne20Reactions

Absolute values of the differential cross sections for the reaction ${\mathrm{C}}^{12}({\mathrm{C}}^{12}, \alpha ){\mathrm{Ne}}^{20}$ to the ground and 1.63-MeV states are given at 100-keV energy intervals between 20.3- and 25.6-MeV bombarding energy at eight equally spaced angles between 3 and 73° in the laboratory, as well as some more detailed angular distributions at selected energies. Both differential cross sections and angle-integrated data are shown to fluctuate strongly with energy. A quantitative comparison between the properties of the fluctuations and the predictions of the statistical theory of the compound nucleus (used in the spirit of Ericson) is presented. The effects of making observations on a sample of finite size are illustrated in detail and are shown in some cases to lead to results that are readily mistaken for evidence of direct interaction. Fluctuations of cross sections involving sums of several incoherent components of different weights are calculated and compared with experiment and with the usual estimates based on equal weights. The proper weight coefficients for the calculation are derived from the treatment of the average cross sections in an accompanying paper. Agreement is found in all cases between observations and the statistical compound-nucleus picture although the finite-sample effects allow a contribution to the cross sections from direct reactions of 30% or less.