Monte Carlo solutions for several problems in low level...

Monte Carlo solutions for several problems in low level

underground gamma-ray spectrometryO. Sima and D. Arnold

Bucharest University and PTB Braunschweig

Bucharest Workshop 25 – 27 April 2007

Overview

1. Introduction - Low level gamma-ray spectrometry

2. Specific problems solved by Monte Carlo simulation

3. Validation

4. Conclusions


1. Introduction

• Broad range of samples (type, volume, matrix) • High efficiency detectors, high efficiency measurement

geometries • Severe requirements on quality control and quality assurance,

on detection limit • Automatic analysis of spectra

Gamma-ray spectrometry today:


Low level and ultra-low level gamma-ray spectrometry:

• purpose: the best detection limit

- very low background

- high efficiency detectors and measurement geometries

• Volume samples with various matrices: => self-attenuation effects=> sample specific efficiency

• High efficiency detectors and measurement geometries: => coincidence-summing effects=> nuclide specific efficiency

Experimental calibration possible in relatively few cases;expensive, problems with sources

Monte Carlo simulation able to cover all cases of interest in gamma ray spectrometryAfter validation, very useful to complement experimental

calibration

Difficulties in efficiency calibration:


2. Specific problems solved by Monte Carlo simulation

Evaluation of efficiency correction factors:

- self-attenuation corrections

- coincidence-summing corrections

- geometry corrections

Direct evaluation of efficiency

Background under the peaks

Spectrum simulation

= > GESPECORBucharest Workshop 25 – 27 April 2007

GESPECOR• GERMANIUM SPECTROSCOPY CORRECTION

FACTORS, authors O. Sima, D. Arnold, C. DovleteRealistic Monte Carlo simulation program

- detailed description of the physics processes (photon interactions: XCOM; electron interactions; bremsstrahlung)

- detailed description of the measurement arrangement- nuclear decay data: NUCLEIDE, ENDSF (250

nuclides in GESPECOR data base)- efficient algorithms – variance reduction techniques- user friendly interfaces- thoroughly tested at PTB (D. Arnold)





Coincidence summing:

- Summing out = Losses from peaks due to simultaneous detection of other photons (γ, X-ray) => apparent efficiency lower than corrected efficiency

- Summing in = additional counts in the peak no. 3 due to simultaneous complete energy absorption of photons 1 and 2 => apparent efficiency higher than corrected efficiency

Magnitude of coincidence-summing effects• Enhanced in high efficiency measurement conditions => important

in low level gamma-ray spectrometry• Depend on the detailed decay scheme of the nuclide (peak energy,

probability of emission of other photons in cascade, energy of the cascading photons)=> nuclide dependent efficiency

• Depend on the geometry (including surrounding materials), matrix⇒Difficult to evaluate: nuclear data + radiation transport

GESPECOR: automatic evaluation of decay data, variance reduction techniques implemented


GESPECOR versus GEANT

-14

-12

-10

-8

-6

-4

-2

0

2

10 100 1000 10000

Energy (keV)

% D

iffer

ence G 1

G 2

G 3

Peak Efficiency

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

Differences in photon cross sections in Ge

XCOM versus GEANT 3.21

-2

-1

0

1

2

3

4

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

iffer

ence Ge Photoeffect

Ge Compton

Ge Rayleigh

Ge Pair Production



GESPECOR: coincidence-summingSum peaks with X-rays (n-type HPGe)

Ba-133 spectrum - low energy part

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)

Cou

nts

1

2

3

4

5

6

7

89

1011

12

13

14

20

1516

1718

19

21 22

24

23 25 26

• Ba-133 point source

• Corrections in good agreement with experimental data (PTB)


GESPECOR: coincidence-summingSum peaks with X-rays (n-type HPGe)

• Ba-133 point source

• Corrections in good agreement with experimental data (PTB)

Ba-133 spectrum - high energy part

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 500Energy (keV)

Coun

ts

27

29

2830 31

32

3

34

35

37

3

3

3940

41

4243

44

45

46

47 48

49

50

52

51

53

54

55

56

5758 59

60

61

62


Are the small coincidence summing peaks present in the spectrum relevant?

Yes, especially in low background measurements:• Corrections factors for the main peaks required for activity

determination, but:• All features of the spectra should be correctly described

(including small peaks and pure sum peaks)- peak interference- nuclide identification problems=> more important in low background measurements!

• Present day tendency: completely automatic analysis of spectra => requires improvement [Arnold, Blaauw, Fazinic, Kolotov, Nucl. Instrum. Meth. A 536 (2005) 196 ]


Efficiency transfer for volume sources with slightly different geometry

• actual geometry slightly different from the reference geometry– identical containers but different filling height

• Transfer factor: – Monte Carlo simulation based on a correlated sampling technique– simultaneous computation of each efficiency

Actual geometry Reference SimulationBucharest Workshop 25 – 27 April 2007

- at low energy, weak dependence of scattered photon energy on angle

e.g. 45 keV: all cases with scattering angle <30° have E>44.5 keV

⇒ Should it be included in the peak efficiency definition? (in programs like GEANT the efficiency is usually defined by the number of counts in a given region of the peak)

⇒ it might be also influenced by the environment of the

measurement, not only by the source, detector and media

in betweenBucharest Workshop 25 – 27 April 2007

Background under the peaks: Small angle scattering in the source and other media

Scatteringmedium

3. Validation

Monte Carlo techniques are well established, but

- are the detector data perfectly known ?

- are the interaction data absolutely correct ?

- is the calculation model perfect ?

⇒Validation required

⇒ Comparison of selected experimental results with calculation,

adjustment of some parameters in case of discrepancy


Comparison between GESPECOR and GEANT 3.21

ICRM Gamma-ray spectrometry Working Group action:

Comparison of Monte Carlo simulation evaluation of the efficiency for 3 geometries:

1. Point source and a bare crystal;

2. Point source and a realistic Ge detector

3. Volume source and a realistic Ge detector


Results

Comparison between our results obtained with GESPECOR and with GEANT:

- in geometry 1 reasonable agreement- in geometry 2 and 3 higher discrepancies, especially at low energies

Agreement of the results for geometry 1 implies that cross sections are in accord?

- no, in geometry 1 at low energy the detector is practically an „infinitely thick“ detector, irrespective to the exact values of the cross sections.- in fact, important differences between XCOM and GEANT cross sections, especially in photoelectric cross section (XCOM – from NIST, Berger and Hubbell)


Differences in photon cross sections in Ge

XCOM versus GEANT 3.21

-2

-1

0

1

2

3

4

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

iffer

ence Ge Photoeffect

Ge Compton

Ge Rayleigh

Ge Pair Production


Differences in photon cross sections in Al and H2O

XCOM versus GEANT

0

1

2

3

4

5

6

7

8

9

10

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

iffer

ence

Al Photoeffect

H2O Photoeffect


Effect of the differences in cross sections in the case of geometry 1:- at 45 keV, peak efficiency is changed by 0.08% and totalefficiency is changed by 0.07% if artificial Ge density equal to 6 g/cm^3 (instead of 5.323) is used in GEANT calculations

Effect of differences in cross sections in the case of other geometries:- at 45 keV, if in GEANT the dead layer density is changedfrom 5.323 g/cm^3 to 5.565 and the Al density is changed from 2.7 g/cm^3 to 2.828, the XCOM and GEANT 3.21 cross sections become equal

=> change in peak efficiency –12.6% (G2)=> change in total efficiency –12.2% (G2)

- at 45 keV if in GESPECOR the cross sections are modifed artificially to be equal to the GEANT cross sections, the differences between GESPECOR and GEANT decreaseto 0.5% (G2) and 1.2% (G3) (Ge X-Ray escape excluded)


⇒At low energy photon attenuation in the media between the emission point and the sensitive volume of the detector aremost important

=> dependence on the photon cross sections (especially for photoeffect)

⇒Which cross sections are the best?==========================

Effect of the low energy cut-off:- in GESPECOR 1.9 keV for photons, 10 keV for

electrons- in GEANT 3.21 10 keV for photons, 10 keV for

electronsComputations with GEANT also with 15 and 20 keV low energy

cut-off=> small change in peak efficiency, practically no changein total efficiency Bucharest Workshop 25 – 27 April 2007

Is the 10 keV energy cut-off of no importance?Ge K X-Rays: Kα2 9.85543 (51.49%),

Kα1 9.88653 (100%), Kβ3 10.9781 Kβ1 10.9822

Kβ5” 11.0748 (22.37), Kβ2 11.101 (0.49%)

=> 6.63 times higher probability of X Rays with E < 10 keVthan with E > 10 keV

If in GESPECOR the simulation of Ge X-Rays is prohibitted, the discrepancy in geometry 1 at low energies between GESPECOR and GEANT is much reduced


4. ConclusionsMonte Carlo methods are very useful for assisting in gamma ray spectrometry calibration problemsBest results in the case of the evaluation of efficiency correction factors => robust results, not sensitive to detector data and other imperfections of the model and data

- self-attenuation corrections- coincidence summing corrections- small geometry differences

Direct evaluation of the efficiency => less robust- good detector data are required;- good cross sections ( most important: photoelectric cross sections)- proper values of the simulation parameters (energy cut)

-Validation requiredBucharest Workshop 25 – 27 April 2007

M. C. Simulations of detector efficiencies

GESPECOR and GEANT 3.21-2 sets of results:

- first set: peak efficiency defined as in experimental work(1/10 from the peak height: 96.82 % from Gaussian)

- second set: ideal peak efficiency (the complete Gaussian)

GESPECOR-User friendly MC software for solving problems in gamma ray spectrometry with Ge detectors:

- self-attenuation- coincidence summing- peak and total efficiency


- in measurement: based on a region of interest from the peak,e.g. between 1/10 from the peak height (for a Guassian shape, 96.82% from the ideal peak)

- in simulations peak width is not normally reproduced – it depends on charge production and collection etc. Possible to apply a Gaussian spread of the energy deposited in the sensitivevolume of the detector, assuming that the peak has a Gaussianshape or simply to take 0.9682 from the ideal efficiency.

- possible practical definitions in simulations based on:- interactions in the sensitive volume without any energy lost

outside the sensitive volume- the number of counts in a suitably defined energy bin

- important to have a consistent use of the definition of the peak,especially when coincidence summing effects are present

Peak efficiency definition


Monte Carlo simulation is very useful to complement experimental calibrations- experimental calibration possible in relatively few cases;

expensive, problems with sources - Monte Carlo simulation capable to cover all cases of interest

in gamma ray spectrometry- Problems: requires good knowledge of the experimental setup,

especially detector data, good cross sections and appropriatecorrespondence between the simulated quantities and the quantities applied in experimental data

- Flexibility, user friendliness and short computing times

ICRM Gamma WG Meeting Paris Nov. 2006

GESPECOR physicsPhoton cross sections:

- for each material 100 points between 1.9 keV and 4 MeV; in addition, values before and after each X-Ray absorption edge, on the basis of XCOM- log-log interpolation- very good accord with XCOM (also in the close vicinity of absorption edges)

Electron processes:- multiple scattering (Moliere, third function included), orfaster semiempirical method- bremsstrahlung: fast algorithm, sampling using Walker algorithm- energy loss fluctuations neglected- delta electron production neglected- energy cut: 10 keV Bucharest Workshop 25 – 27 April 2007

GESPECOR – variance reduction- Peak and total efficiency evaluated separately:

-peak efficiency: photon history stopped when energy lost outsidethe sensitive volume of the detector-materials between the point of emission and the sensitivevolume of the detector : attenuating media-emission from source: focalized towards the detector

-total efficiency: photon history stopped at the first interaction inthe sensitive volume of the detector

- Always force the first interaction in the detector- Whenever possible use mean values instead of random sampling

(e.g. use probability of the emission of groups of photons instead of random simulation of decay cascades in coincidence summing computations)

- Use efficient sampling (Walker, interpolation)Bucharest Workshop 25 – 27 April 2007

Computing times: ACER Notebook, Pentium M Centrino 1.4 GHz

GESPECOR GEANTGeometry 1 Peak efficiency: 3 min 1100 minTotal efficiency: 3 min Geometry 2 Peak efficiency: 4 min 2150 min Total efficiency: 15 min Geometry 3 Peak efficiency: 8 min 17000 minTotal efficiency: 60 min


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