Use of the Dyson-Mehta Δ3 statistic as a test of missing levels

Peter D. Georgopulos and Harry S. Camarda
Phys. Rev. C 24, 420 – Published 1 August 1981
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Abstract

We have performed Monte Carlo calculations examining the sensitivity of the Δ3 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 Δ3 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 Δ3 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 Δ3 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.

[NUCLEAR REACTIONS Statistical theory and fluctuations Δ3 statistic, Monte Carlo calculations, Dyson and Wigner's statistical theory. Effects of missing levels on the Δ3 statistic. Examination of experimental data.]

  • Received 21 November 1980

DOI:https://doi.org/10.1103/PhysRevC.24.420

©1981 American Physical Society

Authors & Affiliations

Peter D. Georgopulos and Harry S. Camarda

  • Pennsylvania State University, Delaware County Campus, 25 Yearsley Mill Road, Media, Pennsylvania 19063

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Vol. 24, Iss. 2 — August 1981

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