Monte Carlo solutions for several problems in low level...
Transcript of 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
Bucharest Workshop 25 – 27 April 2007
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:
Bucharest Workshop 25 – 27 April 2007
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:
Bucharest Workshop 25 – 27 April 2007
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)
Bucharest Workshop 25 – 27 April 2007
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
Bucharest Workshop 25 – 27 April 2007
GESPECOR versus GEANT
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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
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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
Bucharest Workshop 25 – 27 April 2007
Bucharest Workshop 25 – 27 April 2007
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
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0 50 100 150 200 250
Energy (keV)
Cou
nts
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• Ba-133 point source
• Corrections in good agreement with experimental data (PTB)
Bucharest Workshop 25 – 27 April 2007
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
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1.0E+06
250 300 350 400 450 500Energy (keV)
Coun
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5758 59
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Bucharest Workshop 25 – 27 April 2007
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 ]
Bucharest Workshop 25 – 27 April 2007
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
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
Bucharest Workshop 25 – 27 April 2007
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
Bucharest Workshop 25 – 27 April 2007
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)
Bucharest 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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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
Bucharest Workshop 25 – 27 April 2007
Differences in photon cross sections in Al and H2O
XCOM versus GEANT
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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
Bucharest Workshop 25 – 27 April 2007
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)
Bucharest Workshop 25 – 27 April 2007
⇒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
Bucharest Workshop 25 – 27 April 2007
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
Bucharest Workshop 25 – 27 April 2007
- 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
Bucharest Workshop 25 – 27 April 2007
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
Bucharest Workshop 25 – 27 April 2007