Statistical distributions neutron widths

For the high-energy unresolved resonances, statistical methods have to be applied. The radiation width can be assumed to be constant, but the neutron widths show a Porter-Thomas [22] distribution. The probability for Tn to be in an interval dFn is... 

Except for the resonances, which have been experimentally resolved at neutron energies up to 4 keV, the locations and widths of the individual resonances are not known in the energy range of interest for fast reactors. Thus, one must consider a general resonance k selected from the sequence and average over statistical distributions for the widths of this and the other resonances, and the location of others in the sequence with respect to it. If the resonances of a particular sequence, say sequence (1), are unresolved, then... 

A further argument concerns the parameter v for the neutron width distribution, as obtained by the maximum likelihood method from the three experiments. For both of the earlier experiments, v is amazingly close to the theoretical value of one, although the statistical uncertainty is at least 10%. Garg et al. 47) report that they found v = 0.89, if all the levels are counted, and v = 1.13, if the uncertain levels are excluded. One could speculate that inclusion of about half of the uncertain levels would yield the desired value v = 1, which corresponds to an average spacing of about 19.3 eV. Thus, one could favor a value in the range 18.5 to 19.3 eV for use in calculations. 

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