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vantages compared to using a energy-independent threshold. First, p -wave contamination is eliminated equally effectively at all energies. This is because the penetrability factor for p -waves differs from s -waves by (to good approximation) a factor of E$_{n}$ . Second, experiment thresholds have approximately this same energy dependence; thus, possible diffusiveness of the instrumental threshold can be surmounted equally effectively at all energies. Third, statistical precision of the analysis is maximized by allowing the largest p -wave-free set of s -wave resonances to be included. 

Analyzing a data set comprised of many different nuclides such as the NDE involves at least two additional potential pitfalls. First, as is evident from Fig. 3, the apparent sensitivities of the various experiments from which the NDE was derived differ by several orders of magnitude. Therefore, if the entire NDE were analyzed as a single set (as was done in Ref. [2]), the threshold must be at least as high as the highest apparent individual threshold. But doing this will substantially reduce the statistical precision of the result and at least partially negate the reason for assembling the NDE in the first place. Second, for a given set of data and threshold, the ML-estimated average reduced neutron width might be substantially different from the one estimated from the data (e.g., from a simple average or by assuming ν = 1). Therefore, it is important to include the average reduced width as a parameter in the ML analysis. Furthermore, the difference between these two estimated values will likely vary from one NDE nuclide to the next. For these two reasons, it is important that separate ML analyses be made for each NDE nuclide. 

To minimize the effects of the above problems, I have done separate ML analyses for each nuclide in the NDE using (a range of) separate energy-dependent thresholds, and then combined these individual results for comparison to theory. 

## IV. AN IMPROVED ML ANALYSIS OF THE NDE NEUTRON WIDTHS 

The analysis technique was briefly described in Ref. [23]. Each resonance λ has an energy E$_{λ}$ and reduced neutron width g Γ 0 λ $_{n}$. The probability density function (PDF) f ( x | ν ) for a χ 2 distribution is given by, 

<img src='content_image/343883.jpg'>

