Decay Data in View of Complex Applications Octavian Sima Physics Department, University of Bucharest Decay Data Evaluation Project Workshop May 12

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Decay Data in View of Complex ApplicationsOctavi
an SimaPhysics Department, University of
BucharestDecay Data Evaluation Project
WorkshopMay 12 14, 2008Bucharest, Romania
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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

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1. Introduction Complex applications?
Pierre Auger Observatory
AGATA
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Source
Detector
Gamma spectrometry with HPGe detectors
- is this a complex application from the point
of view of decay data?
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• Assessment of a sample by gamma-ray spectrometry
• Energy and efficiency calibration of the
  spectrometer
• - peak efficiency curve ?(E), Epeak energy
• Measurement of the spectrum of the sample
• Computation of the count-rate R in the peaks of
  interest
• Computation of the activity A

AR(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(?)

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Data source Gamma-ray spectrum catalogue, INEEL
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2. Coincidence summing and decay data
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Ba-133 EC decay E (keV) I? (per 100 Dis)
53.1622 2.140.03 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
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Ex 302 keV peak
But 302 keV photon is emitted together with
other radiations!

1. K?(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 gt 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)
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)
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Each combination i has a specific joint emission
probability pi !
I(302)p1p2p3p60
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
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 gt ?11-?(K?)1-?(53)
?(302) 1-?(81) ?(E) total detection
efficiency for photons of energy E
?i lt ?(302) gt coincidence losses from the 302
keV peak
Volume sources more complex effective total
efficiency is needed Additional complication
angular correlation of photons
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Ba-133 EC decay E (keV) I? (per 100 Dis)
53.1622 2.140.03 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
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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
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Data source Arnold and Sima, ARI 2004
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Data source Arnold and Sima, ARI 2004
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• 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

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3. Input decay data and joint emission
probabilities
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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)
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Our method

• 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

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BA-133 EC 31.692 0.894 4.53
0.104 0.000 5.000E-04 0.000E00 0.000E00
STABLE 80.998 7.000E-01 8.800E-01 0.000E00
6.280E-03 160.612 3.000E-01 7.900E-01 0.000E00
1.720E-04 383.849 1.370E01 7.734E-01 1.761E-01
4.200E-05 437.011 8.620E01 6.720E-01 2.520E-01
1.500E-04 2 1 80.998 3.290E01 1.740E00
1.460E00 2.200E-01 3 1 160.612 6.380E-01
3.100E-01 2.400E-01 5.400E-02 3 2 79.614
2.650E00 1.770E00 1.515E00 2.040E-01 4 1
383.849 8.940E00 2.030E-02 1.690E-02
2.730E-03 4 2 302.851 1.834E01 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
6.205E01 2.560E-02 2.110E-02 3.510E-03 5 3
276.399 7.160E00 5.690E-02 4.610E-02
8.550E-03 5 4 53.162 2.140E00 6.020E00
4.930E00 8.600E-01
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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

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4. Computation of coincidence summing corrections
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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)

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Peak Efficiency
Bucharest Workshop 25 27 April 2007
Bucharest Workshop 25 27 April 2007
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Differences in photon cross sections in Ge
Bucharest Workshop 25 27 April 2007
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5. Uncertainties demand for covariance matrix
of decay data
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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

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• 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 gt difficult
  an analytic evaluation of the uncertainty of Fc
  resulting from the
• uncertainty of the decay data
• gt 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 sigmaui
• repeated computations of the decay data files for
  the generated sets of decay parameters

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• 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!

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6. Summary and conclusions
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• 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

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• 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

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Thank you !