The Interplay Between the Statistical Correlations of g-ray Emission Probabilities and Efficiency Calibration * Ruy M. Castro 1,2, Vito R. Vanin 3, Paulo.

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Presentation transcript:

The Interplay Between the Statistical Correlations of g-ray Emission Probabilities and Efficiency Calibration * Ruy M. Castro 1,2, Vito R. Vanin 3, Paulo R. Pascholati 3, Nora L. Maidana 3 1 IEAv - CTA, São José dos Campos, Brasil 2 DMAF - UNITAU, Taubaté, Brasil 3 LAL - IFUSP, São Paulo, Brasil * Presented in: 14th International Conference on Radionuclide Metrology and its Applications ICRM2003 - Dublin, Ireland Applied Radiation and Isotopes 60 (2004) 185-190 http://dx.doi.org/10.1016/j.apradiso.2003.11.014

Contents Are the data correlated? Efficiency Calibration Example Decay parameters

Are the data correlated? Analyzing the 152Eu published data ~ 32 experiments with the most intense transitions REF Relative Pg (P1408keV = 100 %) 121 keV 244 keV 344 keV 411 keV 1 145,0 ± 4,1 39,4 ± 1,3 128,2 ± 3,6 10,14 ± 0,54 2 138,5 ± 6,4 36,2 ± 1,8 ± 5,9 10,32 ± 0,51 3 132,9 ± 4,0 35,8 ± 1,0 ± 3,8 10,77 ± 0,38 4 144,6 ± 4,7 36,4 ± 1,2 ± 4,2 10,59 ± 0,27 5 141,0 36,6 ± 1,1 127,2 10,71 ± 0,11 6 140,6 ± 2,8 ± 0,6 ± 2,6 10,55 ± 0,22 7 136,9 ± 0,3 127,1 ± 0,7 10,84 ± 0,07 8 136,7 36,5 ± 0,4 126,9 ± 0,9 10,73 ± 0,10

Are the data correlated?

Are the data correlated?

Are the data correlated? Some other cases:

Are the data correlated? Efficiency e - Efficiency Area - Peak area F - Factor Activity Normalization Constant Reference area Pg - Emission probability Usually: Area, F and P are independent Area is uncorrelated Pg are correlated for a multi gamma source, but their correlation coefficients are generally unknown

Efficiency Calibration Typical efficiency curve For energies above 150-200 keV Eg – Gamma Energy Eb – Reference Energy

Efficiency Calibration For example: Using a Matrix notation:

Efficiency Calibration Fitting Procedure Problem: How to obtain V? What is V? Variance in Y due to: peak area, factor and emission probability

Efficiency Calibration Variance in Y due to Area: VY-Area

Efficiency Calibration Variance in Y due to F: VY-F

Efficiency Calibration Variance in Y due to Pg: VY-Pg

Efficiency Calibration Fitting Procedure Quality of the fitting: Interpolation:

Example Typical efficiency calibration Relative efficiency 1 multi gamma-ray source - 152Eu (partially know covariance) 2 105 Bq Activity 20 cm source-detector distance 2 h of measurement (live time) Pile-up rejection and dead time correction Relative efficiency

Example Efficiency curve

Example Calibration Data Energy Ig Correlation Matrix (keV) 344 411 778 1089 1299 0,26689(13) 1 0,10 0,32 0,15 -0,07 0,02229(3) 0,31 0,72 -0,08 779 0,1303(8) 0,45 -0,20 0,01712(3) -0,12 0,01612(8) Energy Ig Correlation Matrix (keV) 121 244 4445-2 44415-9 867 964 1085 1112 1212 1408 0,2875(6) 1 -0,68 -0,70 -0,69 -0,75 -1 -0,65 -0,62 -0,53 0,0773(9) 0,76 0,62 0,69 0,68 0,59 0,52 0,00316(4) 0,74 0,75 0,0263(3) 0,73 0,58 0,0422(5) 0,61 0,57 0,49 0,1448(16) 0,66 0,53 0,1004(12) 0,64 0,1339(17) 0,55 0,01432(20) 0,51 0,208(3)

Example Variance Matrix Variance Matrix (x 106) VY-P (x 106) 153 7 92 244 344 411 444 778 867 964 1085 1089 1112 1212 1299 1408 153 7 92 96 102 98 104 94 11 8 41 9 6 122 90 85 86 82 87 66 12 1 179 103 99 91 141 105 163 110 192 106 97 332 111 227 VY-P (x 106) 244 344 411 444 778 867 964 136 85 86 89 1 2 3 92 83 79 38 140 97 122

Example Results: Without covariances With covariances a0 = 0,1537(23)

Example Results: Uncertainties

Decay parameters Decay Scheme Peak Areas + corrections Pg and corrections dependents of the decay parameters

Decay parameters Decay Scheme Constraints Probability & area

Conclusion The emission probabilities of a multi gamma source are correlated The emission probabilities and efficiencies are dependents. Should use branching ratios and feeding fractions instead of gamma intensities.

References Ruy M. Castro , Vito R. Vanin , Otaviano Helene , Paulo R. Pascholati , Nora L. Maidana , Mauro S. Dias and Marina F. Koskinas, The Interplay Between the Statistical Correlations of g-ray Emission Probabilities and Efficiency Calibration, Applied Radiation and Isotopes 60 (2004) 185-190 http://dx.doi.org/10.1016/j.apradiso.2003.11.014 Vito R. Vanin and Otaviano Helene, Covariance Analysis Within the Framework of the Least-squares Method in Update of X Ray and Gamma Ray Data Standards for Detector Calibration and Other applications, International Atomic Energy Agency, Viena (2007)