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Problems with the uncertainty budget of half-life measurements

Problems with the uncertainty budget of half-life measurements. S. Pommé. 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

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Problems with the uncertainty budget of half-life measurements

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  1. Problems with the uncertainty budget of half-life measurements S. Pommé

  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 230th ACS NM - T1/2

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

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

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

  6. Half-life of 55Fe 1020 1010 1000 Days 990 980 970 Morel Hoppes Schötzig Lagoutine Van Ammel Karmalitsyn Houtermans a selection of the ‘best’ data 230th ACS NM - T1/2

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

  8. Example: decay of 55Fe measured activity fitted decay curve T1/2=1005.0 d ± 1.4d 230th ACS NM - T1/2

  9. Procedure ‘uncertainty from fit’ • calculate the c2–value, ensuring that it assumes its expectation value = the number of degrees of freedom • adjust the half-life so that c2 increases by a value of one • 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 230th ACS NM - T1/2

  10. Residuals 55Feadd uncertainty component of 0.0175% c2/n=3.5 c2/n=1.0 230th ACS NM - T1/2

  11. Check of distribution of residuals BEFORE introducing extrauncertainty component AFTER c2/n=3.5 c2/n=1.0 230th ACS NM - T1/2

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

  13. Why? least-squares fit requires RANDOMNESS 230th ACS NM - T1/2

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

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

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

  19. Realistic uncertainty 230th ACS NM - T1/2

  20. Some examples from literature 230th ACS NM - T1/2

  21. Residuals Ba-133 data scatter exceeds uncertainty => unidentified HIGH FREQUENCY component NIM A390 (1997) 267-273 230th ACS NM - T1/2

  22. Residuals Cs-134 MEDIUM FREQUENCY instability => fit underestimates uncertainty NIM A390 (1997) 267-273 230th ACS NM - T1/2

  23. Residuals Ce-144 sign of LOW FREQUENCY deviation => fit tends to hide it NIM A390 (1997) 267-273 230th ACS NM - T1/2

  24. Residuals Y-88 only a few measurement data => LACK OF INFORMATION NIM A390 (1997) 267-273 230th ACS NM - T1/2

  25. Residuals Cd-109 OVERESTIMATION of measurement uncertainty => overestimates uncertainty of half-life? NIM A390 (1997) 267-273 230th ACS NM - T1/2

  26. Residuals 99Tcm systematic deviation for short times electrometer range switching ARI 60 (2004) 317-323 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 T1/2 • report in sufficient detail, for traceability Half-life measurements are NOT EASY ! 230th ACS NM - T1/2

  28. Half-life of 93mNb 230th ACS NM - T1/2

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

  30. Residuals Co-57 decreasing accuracy with time => extension of experiment becomes ineffective NIM A390 (1997) 267-273 230th ACS NM - T1/2

  31. Residuals Ba-133 and Eu-152 ‘independent’ measurements showing correlations => ‘medium term’ detector instability NIM A390 (1997) 267-273 230th ACS NM - T1/2

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