1. 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
ICRM Dublin, Ireland
Applied Radiation and Isotopes 60 (2004)

2. Contents
Are the data correlated?
Efficiency Calibration
Example
Decay parameters

3. 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

4. Are the data correlated?

5. Are the data correlated?

6. Are the data correlated?
Some other cases:

7. 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

8. Efficiency Calibration
Typical efficiency curve
For energies above keV
Eg – Gamma Energy
Eb – Reference Energy

9. Efficiency Calibration
For example:
Using a Matrix notation:

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

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

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

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

14. Efficiency Calibration
Fitting Procedure
Quality of the fitting:
Interpolation:

15. 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

16. Example
Efficiency curve

17. 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
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)

18. 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

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

20. Example
Results: Uncertainties

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

22. Decay parameters
Decay Scheme
Constraints
Probability
& area

23. 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.

24. 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)
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)