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

Decay Data in View of Complex Applications

Octavian SimaPhysics Department, University of Bucharest

Decay Data Evaluation Project Workshop

May 12 – 14, 2008Bucharest, Romania

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

1. Introduction – Complex applications?

Pierre Auger Observatory AGATA


Source

Detector Gamma spectrometry with HPGe detectors

- is this a complex application from the point of view of decay data?


Assessment of a sample by gamma-ray spectrometry:1. Energy and efficiency calibration of the spectrometer

- peak efficiency curve (E), E=peak energy2. Measurement of the spectrum of the sample3. Computation of the count-rate R in the peaks of interest4. 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()


Data source: Gamma-ray spectrum catalogue, INEELBucharest DDEP Workshop May 12 – 14 2008

2. Coincidence summing and decay data


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 ±0.3160.6121 0.638 ±0.004223.2368 0.453 ±0.003276.3989 7.16 ±0.05302.8508 18.34 ±0.13356.0129 62.05 ±0.19383.8485 8.94 ±0.06

Data source: Nucleide

Ex: 302 keV peak

1 K(EC4)-53-302-812 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)-302-816 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)


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 thecount-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 neededAdditional complication – angular correlation of photons

i < (302) => coincidence losses from the 302 keV peak


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 ±0.3160.6121 0.638 ±0.004223.2368 0.453 ±0.003276.3989 7.16 ±0.05302.8508 18.34 ±0.13356.0129 62.05 ±0.19383.8485 8.94 ±0.06

Data source: Nucleide

Sum peak contributions to the 302 keV peak:

Combinations like:K(EC4)-53-223-79-81 contribute to the 302 keV peakwith a probability [1-(K)][1-(53)] (223) (79) [1-(81)]

Other 59 similar contributions

In the presence of coincidence summingR(E) (E) I(E) A, butR(E) = Fc (E) I(E) AFc = coincidence summing correction factor, depends on: - decay scheme parameters - peak and total efficiency for the set of energies of all the photons


1.0E+02

1.0E+03

1.0E+04

1.0E+05

1.0E+06

1.0E+07

0 50 100 150 200 250

Energy (keV)

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

1.0E+00

1.0E+01

1.0E+02

1.0E+03

1.0E+04

1.0E+05

1.0E+06

250 300 350 400 450 500

Energy (keV)

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2830 31

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

Coincidence summing effects important in present daygamma-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


3. Input decay data and joint emission probabilities


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 fromMonte Carlo evaluation of efficiencies (Sima and Arnold)


Decay data extracted from Nucleide or ENSDF - we have developed an automatic procedure for extractingthe 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:


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-01Bucharest DDEP Workshop May 12 – 14 2008

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


4. Computation of coincidence summing corrections


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)


GESPECOR versus GEANT

-14

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Energy (keV)

% D

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G 2

G 3

Peak Efficiency

Bucharest Workshop 25 – 27 April 2007Bucharest Workshop 25 – 27 April 2007


Differences in photon cross sections in Ge

XCOM versus GEANT 3.21

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-1

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1

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5

0.00E+00 5.00E-01 1.00E+00 1.50E+00 2.00E+00 2.50E+00 3.00E+00 3.50E+00

Energy (MeV)

% D

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ren

ce Ge Photoeffect

Ge Com pton

Ge Rayleigh

Ge Pair Production

Bucharest Workshop 25 – 27 April 2007




5. Uncertainties – demand for covariance matrix of decay data


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


• 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


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!


6. Summary and conclusions


• High quality decay data are extremely important

• The presently existing evaluations do satisfy mostof the needs of current applications like gamma-rayspectrometry

• The evaluations are especially suited for cases whenonly one piece of data is required for obtaining thequantity of interest; the uncertainty of the evaluateddecay data can then be safely applied for obtaining the uncertainty of the quantity of interest


• 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


Thank you !

Documents

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