Use of the Dyson-MehtaΔ3statistic as a test of missing levels

Abstract

We have performed Monte Carlo calculations examining the sensitivity of the ${\ensuremath{\Delta}}_{3}$ statistic to missing levels for both single populations and two randomly mixed populations of neutron resonance data. Our results are presented in easy to use graphical form. By calculating ${\ensuremath{\Delta}}_{3}$ for the experimental data and then comparing it with the graphs, the most probable number of missed levels can be determined. We present results for 20, 60, and 100 observed single population levels and 20, 60, 100, 150, and 200 observed levels for two mixed populations and illustrate the use of these graphs by examining recently published neutron resonance data. We have also examined the sensitivity of the ${\ensuremath{\Delta}}_{3}$ statistic to spurious or added levels for both single and mixed populations and indicate how to estimate the number of spurious levels contained in a complete sequence of levels. Relations which express the average ${\ensuremath{\Delta}}_{3}$ and its standard deviation in terms of missing levels were found from our Monte Carlo results. They can be used to extend the range of the graphs, and have been found to apply under certain conditions to spurious levels as well. Finally, the results presented here are also useful when comparing the predictions of random matrix theory with experiment.