1. Decay Data in View of Complex Applications Octavian Sima Physics Department, University of Bucharest Decay Data Evaluation Project Workshop May 12 – 14, 2008 Bucharest, Romania

2. Overview 1.Introduction – Complex applications? 2.Coincidence summing and decay data 3.Input decay data and joint emission probabilities 4.Computation of coincidence summing corrections 5.Uncertainties – demand for covariance matrix of decay data 6.Summary and conclusions Bucharest DDEP Workshop May 12 – 14 2008

3. 1. Introduction – Complex applications? Pierre Auger Observatory AGATA Bucharest DDEP Workshop May 12 – 14 2008

4. Source DetectorGamma spectrometry with HPGe detectors - is this a complex application from the point of view of decay data? Bucharest DDEP Workshop May 12 – 14 2008

5. Assessment of a sample by gamma-ray spectrometry: 1.Energy and efficiency calibration of the spectrometer - peak efficiency curve  (E), E=peak energy 2.Measurement of the spectrum of the sample 3.Computation of the count-rate R in the peaks of interest 4.Computation of the activity A: A=R(E)/[I(E)  (E)] where I(E)=absolute emission probability of the photon with energy E 5. Evaluation of the uncertainty u(A) of A Important: A and u(A) depend on a single decay parameter: I(E) and its uncertainty u(I) a single parameter characterizing the experimental set-up:  (E) and u(  ) Bucharest DDEP Workshop May 12 – 14 2008

6. Data source: Gamma-ray spectrum catalogue, INEEL Bucharest DDEP Workshop May 12 – 14 2008

7. 2. Coincidence summing and decay data Bucharest DDEP Workshop May 12 – 14 2008

8. Ba-133 EC decay E (keV) I  (per 100 Dis) 53.1622 2.14±0.03 79.6142 2.65 ±0.05 80.9979 32.9 ±0.3 160.6121 0.638 ±0.004 223.2368 0.453 ±0.003 276.3989 7.16 ±0.05 302.8508 18.34 ±0.13 356.0129 62.05 ±0.19 383.8485 8.94 ±0.06 Data source: Nucleide

9. Ex: 302 keV peak 1K  (EC4)-53-302-81 2 K  (EC4)-53-302-K  (81) 3 K  (EC4)-53-302-K  (81) 4 K  (EC4)-53-302-other(81) (other => no signal in detector) 5 K  (EC4)- K  (53)-302-81 6 K  (EC4)- K  (53)-302- K  (81) And so on, ending with 48 other(EC4)-other(53)-302-other(81) But: 302 keV photon is emitted together with other radiations! Other decay paths start by feeding the 383 keV level (EC3): 49 K  (EC3)-302-81 50, 51, 52, 53, 54, 55, 56, 57, 58, 59 60 other(EC3)-302-other(81) Bucharest DDEP Workshop May 12 – 14 2008

10. Each combination i has a specific joint emission probability pi ! I(302)=p1+p2+p3+…+p60 Each combination has a specific probability to contribute to the count-rate in the 302 keV peak, e.g. combination (1) K  (EC4)-53-302-81 =>  1=[1-  (K  )][1-  (53)]  (302) [1-  (81)]  (E)= total detection efficiency for photons of energy E The detector cannot resolve the signals produced by the photons emitted along a given decay path – a single signal, corresponding to the total energy delivered to the detector is produced Volume sources: more complex – effective total efficiency is needed Additional complication – angular correlation of photons  i coincidence losses from the 302 keV peak Bucharest DDEP Workshop May 12 – 14 2008

11. Ba-133 EC decay E (keV) I  (per 100 Dis) 53.1622 2.14±0.03 79.6142 2.65 ±0.05 80.9979 32.9 ±0.3 160.6121 0.638 ±0.004 223.2368 0.453 ±0.003 276.3989 7.16 ±0.05 302.8508 18.34 ±0.13 356.0129 62.05 ±0.19 383.8485 8.94 ±0.06 Data source: Nucleide

12. Sum peak contributions to the 302 keV peak: Combinations like: K  (EC4)-53-223-79-81 contribute to the 302 keV peak with a probability [1-  (K  )][1-  (53)]  (223)  (79) [1-  (81)] Other 59 similar contributions In the presence of coincidence summing R(E)   (E) I(E) A, but R(E) = Fc  (E) I(E) A Fc = coincidence summing correction factor, depends on: - decay scheme parameters - peak and total efficiency for the set of energies of all the photons Bucharest DDEP Workshop May 12 – 14 2008

13. Data source: Arnold and Sima, ARI 2004

14. Bucharest DDEP Workshop May 12 – 14 2008 Data source: Arnold and Sima, ARI 2004

15. Coincidence summing effects important in present day gamma-spectrometric measurements: - tendency to use high efficiency detectors - tendency to choose close-to-detector counting geometries The effects are present both for calibration and for measurement For activity assessment Fc for principal peaks But all peaks should be corrected: - interferences - problems in nuclide identification for automatic processing of spectra Bucharest DDEP Workshop May 12 – 14 2008

16. 3. Input decay data and joint emission probabilities Bucharest DDEP Workshop May 12 – 14 2008

17. Evaluation of Fc is very difficult for nuclides with complex decay schemes and for volume sources Methods developed for this purpose differ in the way in which - evaluate the necessary decay scheme parameters - evaluate the necessary peak and total efficiencies - combine the decay data with the efficiency data (1) Recursive formulae (Andreev et al, McCallum & Coote, Debertin & Schotzig, Morel et al, Jutier et al) (2) Matrix formalism (Semkow et al, Korun et al) (3) Generalized lists (Novkovic et al) (4) Monte Carlo simulation of the decay paths and of detection efficiencies (Decombaz et al) (5) Analytic evaluation of decay scheme parameters decoupled from Monte Carlo evaluation of efficiencies (Sima and Arnold) Bucharest DDEP Workshop May 12 – 14 2008

18. Decay data extracted from Nucleide or ENSDF - we have developed an automatic procedure for extracting the data and compiling a specific library – KORDATEN (initially developed by Debertin and Schotzig) - the procedure includes several checks, e.g. - transition assignment (already allocated, uncertainty matching) - intensity balance - conversion coefficients - the program issues warnings if something might be questionable KORDATEN includes about 225 nuclides Our method: Bucharest DDEP Workshop May 12 – 14 2008

19. BA-133 EC 31.692 0.894 4.53 0.104 0.000 5.000E-04 0.000E+00 0.000E+00 STABLE 80.998 7.000E-01 8.800E-01 0.000E+00 6.280E-03 160.612 3.000E-01 7.900E-01 0.000E+00 1.720E-04 383.849 1.370E+01 7.734E-01 1.761E-01 4.200E-05 437.011 8.620E+01 6.720E-01 2.520E-01 1.500E-04 2 1 80.998 3.290E+01 1.740E+00 1.460E+00 2.200E-01 3 1 160.612 6.380E-01 3.100E-01 2.400E-01 5.400E-02 3 2 79.614 2.650E+00 1.770E+00 1.515E+00 2.040E-01 4 1 383.849 8.940E+00 2.030E-02 1.690E-02 2.730E-03 4 2 302.851 1.834E+01 4.430E-02 3.810E-02 4.960E-03 4 3 223.237 4.530E-01 9.950E-02 8.530E-02 1.130E-02 5 2 356.013 6.205E+01 2.560E-02 2.110E-02 3.510E-03 5 3 276.399 7.160E+00 5.690E-02 4.610E-02 8.550E-03 5 4 53.162 2.140E+00 6.020E+00 4.930E+00 8.600E-01 Bucharest DDEP Workshop May 12 – 14 2008

20. Computation of joint emission probability of groups of photons Search of all the decay paths (Sima and Arnold, ARI 2008): the decay scheme is considered an oriented graph the levels are the nodes of the graph the transitions are the edges of the graph the problem of finding the decay paths is equivalent with finding the paths with specific properties in the graph - a fast algorithm of the breadth-first type was implemented Joint emission probabilities can be computed for any nuclide with less than 100 levels -radiations considered: gamma photons, K , K  X-rays, annihilation photons Bucharest DDEP Workshop May 12 – 14 2008

21. 4. Computation of coincidence summing corrections Bucharest DDEP Workshop May 12 – 14 2008

22. GESPECOR GERMANIUM SPECTROSCOPY CORRECTION FACTORS, authors O. Sima, D. Arnold, C. Dovlete Realistic Monte Carlo simulation program Fc depends on detection efficiency and on decay data - detailed description of the measurement arrangement - nuclear decay data: NUCLEIDE, ENDSF (225 nuclides in GESPECOR data base) - efficient algorithms – variance reduction techniques - user friendly interfaces - thoroughly tested at PTB (D. Arnold) Bucharest DDEP Workshop May 12 – 14 2008

23. Peak Efficiency Bucharest Workshop 25 – 27 April 2007 Bucharest DDEP Workshop May 12 – 14 2008

24. Differences in photon cross sections in Ge Bucharest Workshop 25 – 27 April 2007 Bucharest DDEP Workshop May 12 – 14 2008

27. 5. Uncertainties – demand for covariance matrix of decay data Bucharest DDEP Workshop May 12 – 14 2008

28. Contributions to the uncertainty of the value of Fc: uncertainty of the efficiencies - sensitivity of the values to changes in the detector parameters coupled with the uncertainty of the parameters - validation of the Monte Carlo model of the detector provides reasonable tolerance limits for the parameters of the detector for which the uncertainty cannot be directly estimated - statistical uncertainty of the Monte Carlo sampling - uncertainty resulting from the imperfection of the model Bucharest DDEP Workshop May 12 – 14 2008

29. uncertainty of the decay data: - Fc depends simultaneously on many parameters of the decay scheme p1, p2, … pk, each with uncertainty u1, u2, … uk; - the dependence on pi is complex => difficult an analytic evaluation of the uncertainty of Fc resulting from the uncertainty of the decay data => Monte Carlo evaluation of this contribution:  generate n random sets (p1, p2, … pk) in which each pi is randomly sampled from a gaussian distribution with appropriate mean and sigma=ui  repeated computations of the decay data files for the generated sets of decay parameters Bucharest DDEP Workshop May 12 – 14 2008

30. Attention: ======= Fc depends simultaneously on many decay scheme parameters The decay scheme parameters are correlated  A correct uncertainty budget for Fc cannot be obtained without the complete covariance matrix of the decay scheme parameters! Bucharest DDEP Workshop May 12 – 14 2008

31. 6. Summary and conclusions Bucharest DDEP Workshop May 12 – 14 2008

32. High quality decay data are extremely important The presently existing evaluations do satisfy most of the needs of current applications like gamma-ray spectrometry The evaluations are especially suited for cases when only one piece of data is required for obtaining the quantity of interest; the uncertainty of the evaluated decay data can then be safely applied for obtaining the uncertainty of the quantity of interest Bucharest DDEP Workshop May 12 – 14 2008

33. In the case of coincidence summing effects the computation of the correction factor requires using simultaneously many decay data values. When many decay data values are simultaneously required for the computation of the quantity of interest then the uncertainty of the quantity cannot be reliably estimated without the covariance matrix of the decay data Present day gamma-spectrometry measurements tend to increase the coincidence summing effects The covariance matrix of the decay data becomes more and more necessary Bucharest DDEP Workshop May 12 – 14 2008

34. Thank you !