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Institute for Reference Materials and Measurements (IRMM) Geel, Belgium 230th ACS NM, Washington D.C., Aug 2005 Problems with the uncertainty budget of half-life measurements S. Pommé

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230th ACS NM - T1/2 2 Half-life Measurements Half-life determination by following the decay of a radioactive source The problem of data discrepancy; examples Autocorrelation causes underestimation of the uncertainty Example: the decay of Fe-55

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230th ACS NM - T1/2 3 Half-life of 109 Cd a selection of the ‘best’ data

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230th ACS NM - T1/2 4 Half-life of 134 Cs

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230th ACS NM - T1/2 5 Half-life of 54 Mn a selection of the ‘best’ data

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230th ACS NM - T1/ Houtermans Lagoutine Hoppes Morel Karmalitsyn Schötzig Van Ammel Days Half-life of 55 Fe a selection of the ‘best’ data

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230th ACS NM - T1/2 7 Why are uncertainties underestimated? ** by analogy with ‘It’s the economy, stupid!’ by James Carvil, advisor of Bill Clinton in the elections of 1992

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230th ACS NM - T1/2 8 Example: decay of 55 Fe fitted decay curve measured activity T 1/2 = d ± 1.4d

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230th ACS NM - T1/2 9 Procedure ‘uncertainty from fit’ 1) calculate the 2 –value, ensuring that it assumes its expectation value = the number of degrees of freedom 2) adjust the half-life so that 2 increases by a value of one 3) adopt as the standard deviation the square root of the amount by which the half-life was varied Bevington, P.R. Data Reduction and Error Analysis for the Physical Sciences; McGraw-Hill Book Company, New York, USA, 1969

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230th ACS NM - T1/2 10 Residuals 55 Fe add uncertainty component of % 2 / =3.5 2 / =1.0

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230th ACS NM - T1/2 11 Check of distribution of residuals BEFORE introducing extra uncertainty component AFTER 2 / =3.5 2 / =1.0

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230th ACS NM - T1/2 12 Half-life and uncertainty from least-squares fit => fit underestimates uncertainty!

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230th ACS NM - T1/2 13 Why?

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230th ACS NM - T1/2 14 Residuals 55 Fe: blow up uncertainty only including counting statistics => does not fully account for spread of data

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230th ACS NM - T1/2 15 Autocorrelated data are not random autocorrelation plot of the residuals

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230th ACS NM - T1/2 16 Alternative Procedure Subdivide instabilities according to frequency (low, medium, high) Apply new (simplified) uncertainty formula: n= the number of occurances of the effect n=1 for medium and low frequencies Add all components as square sum

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230th ACS NM - T1/2 17 Subdivide instabilities according to frequency noise, counting statistics, … => random effects geometrical reproducibility, ‘seasonal’ effects, short-lived impurity, … dead time, detector/source degradation, background subtraction, …

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230th ACS NM - T1/2 18 T 1/2 from combination of all data T 1/2

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230th ACS NM - T1/2 19 Realistic uncertainty

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230th ACS NM - T1/2 20

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230th ACS NM - T1/2 21 Residuals Ba-133 NIM A390 (1997) data scatter exceeds uncertainty => unidentified HIGH FREQUENCY component

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230th ACS NM - T1/2 22 Residuals Cs-134 NIM A390 (1997) MEDIUM FREQUENCY instability => fit underestimates uncertainty

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230th ACS NM - T1/2 23 Residuals Ce-144 NIM A390 (1997) sign of LOW FREQUENCY deviation => fit tends to hide it

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230th ACS NM - T1/2 24 Residuals Y-88 NIM A390 (1997) only a few measurement data => LACK OF INFORMATION

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230th ACS NM - T1/2 25 Residuals Cd-109 NIM A390 (1997) OVERESTIMATION of measurement uncertainty => overestimates uncertainty of half-life?

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230th ACS NM - T1/2 26 Residuals 99 Tc m electrometer range switching systematic deviation for short times ARI 60 (2004)

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230th ACS NM - T1/2 27 Conclusions perform many measurements with good statistical accuracy and carefully study the randomness of the residuals identify and quantify medium and low frequency instabilities separately and apply a conservative propagation factor to T 1/2 report in sufficient detail, for traceability Half-life measurements are NOT EASY !

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230th ACS NM - T1/2 28 Half-life of 93m Nb

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230th ACS NM - T1/2 29 Half-life of 152 Eu a selection of the ‘best’ data

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230th ACS NM - T1/2 30 Residuals Co-57 NIM A390 (1997) decreasing accuracy with time => extension of experiment becomes ineffective

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230th ACS NM - T1/2 31 Residuals Ba-133 and Eu-152 NIM A390 (1997) ‘independent’ measurements showing correlations => ‘medium term’ detector instability

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