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On the Validity of the Poisson Hypothesis for Low-Level Counting: Investigation of the Distributional Characteristics of Background Radiation with the Nist Individual Pulse Counting System1

Published online by Cambridge University Press:  18 July 2016

L. A. Currie
Affiliation:
Chemical Science and Technology Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, Maryland 20899 USA
E. M. Eijgenhuijsen
Affiliation:
Sandoz Pharma AG, Bau 360/816, CH-4000 Basel, Switzerland
G. A. Klouda
Affiliation:
Chemical Science and Technology Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, Maryland 20899 USA
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Abstract

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Does radioactive decay follow the Poisson distribution?—a fundamental question, to which the theoretical answer seems to be, Yes. On the practical side, the answer to this question impacts the best achievable precision in well-controlled counting experiments. There have been some noteworthy experimental tests of the Poisson assumption, using systems carefully designed for the analysis of individual pulses from stable radioactive sources; thus far, experiment supports theory. For low-level counting, the nature of the background distribution can be of profound practical importance, especially for very long counting experiments where validation by an adequate number of full replicates may be impracticable. One is tempted in such cases to assume that the variance is equal to the mean, in order to estimate the measurement uncertainty. Background radiation, however, has multiple components, only some of which are governed by the laws of radioactive decay.

A specially designed low-level gas counting system at NIST for interactive, retrospective individual pulse shape and time series analysis makes possible the investigation of the empirical distribution function of the background radiation, in a manner similar to the previous empirical distribution studies of radioactive decay. Benefits of individual pulse analysis are that there is no information loss due to averaging and that two independent tests of the Poisson hypothesis can be performed using data from a single, extended measurement period without the need for replication; namely, tests of the distribution of arrival times, expected to be uniform, and the distribution of inter-arrival times, expected to be exponential. For low-level counting the second test has a very interesting and very informative complement: the distribution of coincidence-anticoincidence inter-arrival times.

Key outcomes from the study were that: 1) nonstationarity in the mean background rate over extended periods of time could be compensated by an on-line paired counter technique, which is far preferable to the questionable practice of using an “error-multiplier” that presumes the wandering (nonstationary) background to be random; and 2) individual empirical pulse distributions differed from the ideal GM and Poisson processes by exhibiting giant pulses, a continuum of small pulses, afterpulses, and in certain circumstances bursts of pulses and transient relaxation processes. The afterpulses constituted ca. 8% of the anticoincidence background events, yet they escaped detection by the conventional distributional tests.

Type
Part 1: Methods
Copyright
Copyright © The American Journal of Science 

References

Berkson, J. 1975 Do radioactive decay events follow a random Poisson-Exponential? Journal of Applied Radiation and Isotopes 26: 543549.Google Scholar
Cannizzaro, F., Greco, G., Rizzo, S. and Sinagra, E. 1978 Results of the measurements carried out in order to verify the validity of the Poisson-Exponential distribution in radioactive decay events. Journal of Applied Radiation and Isotopes 29: 649652.Google Scholar
Cook, G. T., Scott, E. M., Wright, E. M. and Anderson, R. 1992 The statistics of low-level counting using the new generation of Packard liquid scintillation counters. In Long, A. and Kra, R. S., eds., Proceedings of the 14th International 14C Conference. Radiocarbon 34(3): 360365.Google Scholar
Cox, D. R. and Lewis, P. A. W. 1968 The Statistical Analysis of Series of Events. London, Methuen & Co.: 285 p.Google Scholar
Curtiss, L. F. Probability fluctuations in the rate of emission of α particles 1930 Journal of Research of the National Bureau of Standards 4: 595599.Google Scholar
Currie, L. A. et al. (ms.) 1997 Nature, impact, and spectroscopy of afterpulses in low-level counting systems.Google Scholar
Currie, L. A., Gerlach, R. W., Klouda, G. A., Ruegg, F. C. and Tompkins, G. B. 1983 Miniature signals and miniature counters: Accuracy assurance via microprocessors and multiparameter control techniques. In Stuiver, M. and Kra, R. S., eds., Proceedings of the 11th International 14C Conference. Radiocarbon 25 (2): 553–564.Google Scholar
Eijgenhuijsen, E. M. et al. (ms.) 1996 Design and development of a low-level counting system with individual pulse analysis.Google Scholar
Garfinkel, S. B. and Mann, W. B. 1968 A method for obtaining large numbers of measured time intervals in radioactive decay. Journal of Applied Radiation and Isotopes 19: 707709.Google Scholar
Jordan, D. and McBeth, G. W. 1978 An experimental test of Müller statistics for counting systems with non-extending dead time. Nuclear Instruments and Methods 155: 557562.Google Scholar
Kaihola, L., Polach, H. and Kojola, H. 1984 Time series analysis of low-level gas counting data. Radiocarbon 26(2): 159165.Google Scholar
Kern, J. 1963 Paramètres de la décharge Geiger. Helvetica Physica Acta 36: 1240.Google Scholar
Massart, D. L. et al. 1988 Chemometrics: A Textbook. Amsterdam, Elsevier: 488 p.Google Scholar
Mook, W. G. 1982 International comparison of proportional gas counters for 14C activity measurements. In Stuiver, M. and Kra, R. S., eds., Proceedings of the 11th International 14C Conference. Radiocarbon 25(2): 475484.Google Scholar
Narita, Y., Igarashi, R., Akagami, H. and Ozawa, Y. 1979 Suppression and utilization of spurious pulse occurrence in organic GM-counters. Nuclear Instruments and Methods in Physics Research 158: 161168.Google Scholar
Nicholson, W. L. 1966 Statistics of net-counting-rate estimation with dominant background corrections. Nucleonics 24: 118121.Google Scholar
Theodórsson, P. 1992 Quantifying background components of low-level gas proportional counters. In Long, A. and Kra, R. S., eds., Proceedings of the 14th International 14C Conference. Radiocarbon 34(3): 420427.Google Scholar