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Gamma ray spectrum its acquiring and analysis
1) Gamma ray spectrum
a) Common properties
b) Full absorption peak
c) Compton edges Compton continuum
d) Single and double escape peak annihilation peak
e) bdquoPile-upldquo background and summation peaks
f) Influence of surrounding material ndash backscattering peak
2) Analysis of gamma ray spectrum
a) Common characteristics
b) Peak shape fitting
c) Spectrum fitting
d) Energy calibration
e) Efficiency calibration
f) Self-absorption corrections
g) Correction on source thickness
h) Coincidence correction
1) Small detector limit ndash all secondary photons (from Compton scattering and annihilation) leave detector
2) Large detector limit ndash all secondary photons are absorbed
Ideal detector ndash no dead layers
Eγ lt 2mec2 Eγ gtgt 2mec2
All energy is absorbed at the detector
Good resolution (semiconductor) makes possible to see X-ray escape peaks from detector material
Ratio of areas of photo peakand Compton background
SFSC =σFσC
mean free path ofsecondary photons gtgtDetector size
(very large detector photons firstly interact at center)
Mean free path of secondary photons ltlt detector size
Full absorption peak (photo peak)
1) Gamma quanta interacting by photo effect2) Multiple Compton scattering3) Pair production and following absorption of annihilation photons
Compton edges
Ecm
EE
eC
2
22
2
Ecm
EE
eC
4
42
2
2
One Compton scattering to angle 180O
Two Compton scattering to angle 180O
Spectrum of 241Am source Spectrum of 60Co source
Spectrum between Compton edges and full absorption peak1) Multiple Compton scattering2) Compton scattering at bdquodead layerldquo before detector3) Annihilation photons are scattered by Compton scattering4) Incomplete charge collection5) Escape of characteristic KX - photons
Compton continuum
Many lines rarr Compton background changes only slowly
Compton background is almost not changing up to Compton edge
1
10
100
1000
10000
100000
1000000
0 1000 2000 3000 4000
čiacuteslo kanaacutelu
četn
ost
Spectrum with one line ndash 137Cs Spectrum with many lines ndash 152Eu
Single and double escape peak
Production of electron and positron pair rarr positron annihilation rarr two 511 keV photons rarr one or both escape
ESE = E ndash EA
EDE = E ndash 2EA kde EA = 511 keV
Characteristic KX rays of detector material
Broad peak ndash set of different transitions on K-shell
Important for low energies (photo effect is dominant)
X-ray escape lines
EVR = E ndash EK EKα(Ge) = 9885 keV EKβ(Ge) = 10981 keV
Annihilation peak ndash 511 keV ndash broad (electron and positron are not fully in the rest)
Important for lower energies and small detector volumes
0 0 0
])(1[)()(2])()(1)[()( dxxNdxxNxENdxxNENEN NNS
First contribution ndash stays on energy ESecond contribution ndash move to energy E (bdquopile-upldquo spectrum) from sum
τ ndash bdquosignal analysisldquoτN ndash bdquosignal creationldquo
One line rarr area of sum peak per time unit NSP = 2τN2
2) Correlated sums - right coincidences (from the same decay (reaction))
1) Uncorrelated sums - false coincidences (they are not from the same decay (reaction))
bdquoPile-up effectsldquo - summation
Depends on source decay schema
Influence of surrounding materials ndash backscattering peak
Compton scattering in material around sensitive detector volume ndash markedPeak in the background
Ecm
cmEE
e
eZR
22
2
1) Full absorption peaks are placed on relatively slowly varying background2) Good energy resolution (especially semiconductor) rarr single peaks occupy small space
Resolution of weak lines between intensive harr ratio between peak and Compton background
1
10
100
1000
10000
100000
0 2000 4000 6000
čiacuteslo kanaacutelu
četn
ost
Spectrum of gamma ray from 60Co source with backscattering peak and summation peaks
Common characteristic
EdEEFESEP )()()(
Observed spectrum ( S(Ersquo) ) is converted to
E le Eacute
Digitalization of analog signal
1
0)()(
k
k
W
WdEEPks
where Wk = Wk1 ndash Wk
0 is channel width ndash constant is assumed
F(EEacute) = G(EEacute) + B(EEacute)
where G(EEacute) ndash absorption of all energies B(EEacute) ndash incomplete energy conversion
Background and full absorption peaks are separated in this way
Background varies mostly slowly(exception is Compton edges)
We have discrete spectrum of monoenergetic lines
m
jjj EEaEC
1
)()(
where aj Ej are intensities and energies of j-th component
m
jjj
m
jjj EEBaEEGaEs
11
)()()(
m
jjj
m
jjj kkBakkGaks
11
)()()(
Measured spectrum
After digitalization
We use analysis of full absorption peaks for determination of intensities and energies
Approximation by Gauss curve (negligence of natural line width)
2
20
2
)(
2)(
EE
eS
xN
Natural width for X-ray is not negligible rarr its description by Lorentz curveGlobally convolution of Gauss and Lorentz curves
Eventually different types of step functions or tail to lower energies are added (see rec literature)
Background is approximated by linear function or by higher polynomial eventually by step
2
20 2
2)(
EE
EL
Detector efficiency determinationEfficiency to full absorption peak εF
Spectrum purity R = NFN0 NF - number of registration at full absorption peak N0 ndash total number of registered photons
Total efficiency εT
it is valid εF = RεT
Energy calibration
0001
0010
0100
100 1000 10000
E [keV]
e
Eu152
Co57
Eu154
Ba133
Cs137
Y88
Co60
Example of calibration curveof HPGe detector
Calibration lines (etalons standards) measured by crystal diffraction spectrometers
Common measurement of calibration and measured sources
Usage of cascade in decay schema
Certificated calibration sources
Details see recommended literature
Primary standard 198Au 4118044(11) keV λ = 30107788(11) fmSimilar also for 192Ir 169Yb a 170Tm ndash primary calibration sources Eγ = f(k)
polynomialmostlyto secondorder
log-log imaging log εF = f(log Eγ)
Absolute activity determination
Number of detected electrons nβ = Aεβ
Number of detected gamma photons nγ = Aεγ
Assumptions ndash every decay one beta and one gamma conversion coefficient is negligible one detector cleanly for electrons (gas) second detects only gamma photons
Number of coincidences of electron and photon detections nc = Aεβεγ
cn
nnA
Afterwards absolute activity of source is
4π proportionalcounter
NaI(Tl)
Photomultiplier
Source
nβ
nγ
nc
Correction on uncertainty of source position and thickness
2212
Rd
d
Selfabsorption correction
Coincidence correction
d
d
R
d
R
d
R
d
R
d
1
2
2
2
2
11ee
xeII 0
]1[0
0
0D
D
x
x eD
IdxeII
DA e
D
I
IK
1
0
Gamma intensity decreasing done by absorption (μ ndash linear absorption coefficient)
Source with homogenous thickness D is assumed
correction coefficient is
Equation for solid angle
and then
Details see recommended literature and exercise
Details see recommended literature
1) Small detector limit ndash all secondary photons (from Compton scattering and annihilation) leave detector
2) Large detector limit ndash all secondary photons are absorbed
Ideal detector ndash no dead layers
Eγ lt 2mec2 Eγ gtgt 2mec2
All energy is absorbed at the detector
Good resolution (semiconductor) makes possible to see X-ray escape peaks from detector material
Ratio of areas of photo peakand Compton background
SFSC =σFσC
mean free path ofsecondary photons gtgtDetector size
(very large detector photons firstly interact at center)
Mean free path of secondary photons ltlt detector size
Full absorption peak (photo peak)
1) Gamma quanta interacting by photo effect2) Multiple Compton scattering3) Pair production and following absorption of annihilation photons
Compton edges
Ecm
EE
eC
2
22
2
Ecm
EE
eC
4
42
2
2
One Compton scattering to angle 180O
Two Compton scattering to angle 180O
Spectrum of 241Am source Spectrum of 60Co source
Spectrum between Compton edges and full absorption peak1) Multiple Compton scattering2) Compton scattering at bdquodead layerldquo before detector3) Annihilation photons are scattered by Compton scattering4) Incomplete charge collection5) Escape of characteristic KX - photons
Compton continuum
Many lines rarr Compton background changes only slowly
Compton background is almost not changing up to Compton edge
1
10
100
1000
10000
100000
1000000
0 1000 2000 3000 4000
čiacuteslo kanaacutelu
četn
ost
Spectrum with one line ndash 137Cs Spectrum with many lines ndash 152Eu
Single and double escape peak
Production of electron and positron pair rarr positron annihilation rarr two 511 keV photons rarr one or both escape
ESE = E ndash EA
EDE = E ndash 2EA kde EA = 511 keV
Characteristic KX rays of detector material
Broad peak ndash set of different transitions on K-shell
Important for low energies (photo effect is dominant)
X-ray escape lines
EVR = E ndash EK EKα(Ge) = 9885 keV EKβ(Ge) = 10981 keV
Annihilation peak ndash 511 keV ndash broad (electron and positron are not fully in the rest)
Important for lower energies and small detector volumes
0 0 0
])(1[)()(2])()(1)[()( dxxNdxxNxENdxxNENEN NNS
First contribution ndash stays on energy ESecond contribution ndash move to energy E (bdquopile-upldquo spectrum) from sum
τ ndash bdquosignal analysisldquoτN ndash bdquosignal creationldquo
One line rarr area of sum peak per time unit NSP = 2τN2
2) Correlated sums - right coincidences (from the same decay (reaction))
1) Uncorrelated sums - false coincidences (they are not from the same decay (reaction))
bdquoPile-up effectsldquo - summation
Depends on source decay schema
Influence of surrounding materials ndash backscattering peak
Compton scattering in material around sensitive detector volume ndash markedPeak in the background
Ecm
cmEE
e
eZR
22
2
1) Full absorption peaks are placed on relatively slowly varying background2) Good energy resolution (especially semiconductor) rarr single peaks occupy small space
Resolution of weak lines between intensive harr ratio between peak and Compton background
1
10
100
1000
10000
100000
0 2000 4000 6000
čiacuteslo kanaacutelu
četn
ost
Spectrum of gamma ray from 60Co source with backscattering peak and summation peaks
Common characteristic
EdEEFESEP )()()(
Observed spectrum ( S(Ersquo) ) is converted to
E le Eacute
Digitalization of analog signal
1
0)()(
k
k
W
WdEEPks
where Wk = Wk1 ndash Wk
0 is channel width ndash constant is assumed
F(EEacute) = G(EEacute) + B(EEacute)
where G(EEacute) ndash absorption of all energies B(EEacute) ndash incomplete energy conversion
Background and full absorption peaks are separated in this way
Background varies mostly slowly(exception is Compton edges)
We have discrete spectrum of monoenergetic lines
m
jjj EEaEC
1
)()(
where aj Ej are intensities and energies of j-th component
m
jjj
m
jjj EEBaEEGaEs
11
)()()(
m
jjj
m
jjj kkBakkGaks
11
)()()(
Measured spectrum
After digitalization
We use analysis of full absorption peaks for determination of intensities and energies
Approximation by Gauss curve (negligence of natural line width)
2
20
2
)(
2)(
EE
eS
xN
Natural width for X-ray is not negligible rarr its description by Lorentz curveGlobally convolution of Gauss and Lorentz curves
Eventually different types of step functions or tail to lower energies are added (see rec literature)
Background is approximated by linear function or by higher polynomial eventually by step
2
20 2
2)(
EE
EL
Detector efficiency determinationEfficiency to full absorption peak εF
Spectrum purity R = NFN0 NF - number of registration at full absorption peak N0 ndash total number of registered photons
Total efficiency εT
it is valid εF = RεT
Energy calibration
0001
0010
0100
100 1000 10000
E [keV]
e
Eu152
Co57
Eu154
Ba133
Cs137
Y88
Co60
Example of calibration curveof HPGe detector
Calibration lines (etalons standards) measured by crystal diffraction spectrometers
Common measurement of calibration and measured sources
Usage of cascade in decay schema
Certificated calibration sources
Details see recommended literature
Primary standard 198Au 4118044(11) keV λ = 30107788(11) fmSimilar also for 192Ir 169Yb a 170Tm ndash primary calibration sources Eγ = f(k)
polynomialmostlyto secondorder
log-log imaging log εF = f(log Eγ)
Absolute activity determination
Number of detected electrons nβ = Aεβ
Number of detected gamma photons nγ = Aεγ
Assumptions ndash every decay one beta and one gamma conversion coefficient is negligible one detector cleanly for electrons (gas) second detects only gamma photons
Number of coincidences of electron and photon detections nc = Aεβεγ
cn
nnA
Afterwards absolute activity of source is
4π proportionalcounter
NaI(Tl)
Photomultiplier
Source
nβ
nγ
nc
Correction on uncertainty of source position and thickness
2212
Rd
d
Selfabsorption correction
Coincidence correction
d
d
R
d
R
d
R
d
R
d
1
2
2
2
2
11ee
xeII 0
]1[0
0
0D
D
x
x eD
IdxeII
DA e
D
I
IK
1
0
Gamma intensity decreasing done by absorption (μ ndash linear absorption coefficient)
Source with homogenous thickness D is assumed
correction coefficient is
Equation for solid angle
and then
Details see recommended literature and exercise
Details see recommended literature
Full absorption peak (photo peak)
1) Gamma quanta interacting by photo effect2) Multiple Compton scattering3) Pair production and following absorption of annihilation photons
Compton edges
Ecm
EE
eC
2
22
2
Ecm
EE
eC
4
42
2
2
One Compton scattering to angle 180O
Two Compton scattering to angle 180O
Spectrum of 241Am source Spectrum of 60Co source
Spectrum between Compton edges and full absorption peak1) Multiple Compton scattering2) Compton scattering at bdquodead layerldquo before detector3) Annihilation photons are scattered by Compton scattering4) Incomplete charge collection5) Escape of characteristic KX - photons
Compton continuum
Many lines rarr Compton background changes only slowly
Compton background is almost not changing up to Compton edge
1
10
100
1000
10000
100000
1000000
0 1000 2000 3000 4000
čiacuteslo kanaacutelu
četn
ost
Spectrum with one line ndash 137Cs Spectrum with many lines ndash 152Eu
Single and double escape peak
Production of electron and positron pair rarr positron annihilation rarr two 511 keV photons rarr one or both escape
ESE = E ndash EA
EDE = E ndash 2EA kde EA = 511 keV
Characteristic KX rays of detector material
Broad peak ndash set of different transitions on K-shell
Important for low energies (photo effect is dominant)
X-ray escape lines
EVR = E ndash EK EKα(Ge) = 9885 keV EKβ(Ge) = 10981 keV
Annihilation peak ndash 511 keV ndash broad (electron and positron are not fully in the rest)
Important for lower energies and small detector volumes
0 0 0
])(1[)()(2])()(1)[()( dxxNdxxNxENdxxNENEN NNS
First contribution ndash stays on energy ESecond contribution ndash move to energy E (bdquopile-upldquo spectrum) from sum
τ ndash bdquosignal analysisldquoτN ndash bdquosignal creationldquo
One line rarr area of sum peak per time unit NSP = 2τN2
2) Correlated sums - right coincidences (from the same decay (reaction))
1) Uncorrelated sums - false coincidences (they are not from the same decay (reaction))
bdquoPile-up effectsldquo - summation
Depends on source decay schema
Influence of surrounding materials ndash backscattering peak
Compton scattering in material around sensitive detector volume ndash markedPeak in the background
Ecm
cmEE
e
eZR
22
2
1) Full absorption peaks are placed on relatively slowly varying background2) Good energy resolution (especially semiconductor) rarr single peaks occupy small space
Resolution of weak lines between intensive harr ratio between peak and Compton background
1
10
100
1000
10000
100000
0 2000 4000 6000
čiacuteslo kanaacutelu
četn
ost
Spectrum of gamma ray from 60Co source with backscattering peak and summation peaks
Common characteristic
EdEEFESEP )()()(
Observed spectrum ( S(Ersquo) ) is converted to
E le Eacute
Digitalization of analog signal
1
0)()(
k
k
W
WdEEPks
where Wk = Wk1 ndash Wk
0 is channel width ndash constant is assumed
F(EEacute) = G(EEacute) + B(EEacute)
where G(EEacute) ndash absorption of all energies B(EEacute) ndash incomplete energy conversion
Background and full absorption peaks are separated in this way
Background varies mostly slowly(exception is Compton edges)
We have discrete spectrum of monoenergetic lines
m
jjj EEaEC
1
)()(
where aj Ej are intensities and energies of j-th component
m
jjj
m
jjj EEBaEEGaEs
11
)()()(
m
jjj
m
jjj kkBakkGaks
11
)()()(
Measured spectrum
After digitalization
We use analysis of full absorption peaks for determination of intensities and energies
Approximation by Gauss curve (negligence of natural line width)
2
20
2
)(
2)(
EE
eS
xN
Natural width for X-ray is not negligible rarr its description by Lorentz curveGlobally convolution of Gauss and Lorentz curves
Eventually different types of step functions or tail to lower energies are added (see rec literature)
Background is approximated by linear function or by higher polynomial eventually by step
2
20 2
2)(
EE
EL
Detector efficiency determinationEfficiency to full absorption peak εF
Spectrum purity R = NFN0 NF - number of registration at full absorption peak N0 ndash total number of registered photons
Total efficiency εT
it is valid εF = RεT
Energy calibration
0001
0010
0100
100 1000 10000
E [keV]
e
Eu152
Co57
Eu154
Ba133
Cs137
Y88
Co60
Example of calibration curveof HPGe detector
Calibration lines (etalons standards) measured by crystal diffraction spectrometers
Common measurement of calibration and measured sources
Usage of cascade in decay schema
Certificated calibration sources
Details see recommended literature
Primary standard 198Au 4118044(11) keV λ = 30107788(11) fmSimilar also for 192Ir 169Yb a 170Tm ndash primary calibration sources Eγ = f(k)
polynomialmostlyto secondorder
log-log imaging log εF = f(log Eγ)
Absolute activity determination
Number of detected electrons nβ = Aεβ
Number of detected gamma photons nγ = Aεγ
Assumptions ndash every decay one beta and one gamma conversion coefficient is negligible one detector cleanly for electrons (gas) second detects only gamma photons
Number of coincidences of electron and photon detections nc = Aεβεγ
cn
nnA
Afterwards absolute activity of source is
4π proportionalcounter
NaI(Tl)
Photomultiplier
Source
nβ
nγ
nc
Correction on uncertainty of source position and thickness
2212
Rd
d
Selfabsorption correction
Coincidence correction
d
d
R
d
R
d
R
d
R
d
1
2
2
2
2
11ee
xeII 0
]1[0
0
0D
D
x
x eD
IdxeII
DA e
D
I
IK
1
0
Gamma intensity decreasing done by absorption (μ ndash linear absorption coefficient)
Source with homogenous thickness D is assumed
correction coefficient is
Equation for solid angle
and then
Details see recommended literature and exercise
Details see recommended literature
Spectrum between Compton edges and full absorption peak1) Multiple Compton scattering2) Compton scattering at bdquodead layerldquo before detector3) Annihilation photons are scattered by Compton scattering4) Incomplete charge collection5) Escape of characteristic KX - photons
Compton continuum
Many lines rarr Compton background changes only slowly
Compton background is almost not changing up to Compton edge
1
10
100
1000
10000
100000
1000000
0 1000 2000 3000 4000
čiacuteslo kanaacutelu
četn
ost
Spectrum with one line ndash 137Cs Spectrum with many lines ndash 152Eu
Single and double escape peak
Production of electron and positron pair rarr positron annihilation rarr two 511 keV photons rarr one or both escape
ESE = E ndash EA
EDE = E ndash 2EA kde EA = 511 keV
Characteristic KX rays of detector material
Broad peak ndash set of different transitions on K-shell
Important for low energies (photo effect is dominant)
X-ray escape lines
EVR = E ndash EK EKα(Ge) = 9885 keV EKβ(Ge) = 10981 keV
Annihilation peak ndash 511 keV ndash broad (electron and positron are not fully in the rest)
Important for lower energies and small detector volumes
0 0 0
])(1[)()(2])()(1)[()( dxxNdxxNxENdxxNENEN NNS
First contribution ndash stays on energy ESecond contribution ndash move to energy E (bdquopile-upldquo spectrum) from sum
τ ndash bdquosignal analysisldquoτN ndash bdquosignal creationldquo
One line rarr area of sum peak per time unit NSP = 2τN2
2) Correlated sums - right coincidences (from the same decay (reaction))
1) Uncorrelated sums - false coincidences (they are not from the same decay (reaction))
bdquoPile-up effectsldquo - summation
Depends on source decay schema
Influence of surrounding materials ndash backscattering peak
Compton scattering in material around sensitive detector volume ndash markedPeak in the background
Ecm
cmEE
e
eZR
22
2
1) Full absorption peaks are placed on relatively slowly varying background2) Good energy resolution (especially semiconductor) rarr single peaks occupy small space
Resolution of weak lines between intensive harr ratio between peak and Compton background
1
10
100
1000
10000
100000
0 2000 4000 6000
čiacuteslo kanaacutelu
četn
ost
Spectrum of gamma ray from 60Co source with backscattering peak and summation peaks
Common characteristic
EdEEFESEP )()()(
Observed spectrum ( S(Ersquo) ) is converted to
E le Eacute
Digitalization of analog signal
1
0)()(
k
k
W
WdEEPks
where Wk = Wk1 ndash Wk
0 is channel width ndash constant is assumed
F(EEacute) = G(EEacute) + B(EEacute)
where G(EEacute) ndash absorption of all energies B(EEacute) ndash incomplete energy conversion
Background and full absorption peaks are separated in this way
Background varies mostly slowly(exception is Compton edges)
We have discrete spectrum of monoenergetic lines
m
jjj EEaEC
1
)()(
where aj Ej are intensities and energies of j-th component
m
jjj
m
jjj EEBaEEGaEs
11
)()()(
m
jjj
m
jjj kkBakkGaks
11
)()()(
Measured spectrum
After digitalization
We use analysis of full absorption peaks for determination of intensities and energies
Approximation by Gauss curve (negligence of natural line width)
2
20
2
)(
2)(
EE
eS
xN
Natural width for X-ray is not negligible rarr its description by Lorentz curveGlobally convolution of Gauss and Lorentz curves
Eventually different types of step functions or tail to lower energies are added (see rec literature)
Background is approximated by linear function or by higher polynomial eventually by step
2
20 2
2)(
EE
EL
Detector efficiency determinationEfficiency to full absorption peak εF
Spectrum purity R = NFN0 NF - number of registration at full absorption peak N0 ndash total number of registered photons
Total efficiency εT
it is valid εF = RεT
Energy calibration
0001
0010
0100
100 1000 10000
E [keV]
e
Eu152
Co57
Eu154
Ba133
Cs137
Y88
Co60
Example of calibration curveof HPGe detector
Calibration lines (etalons standards) measured by crystal diffraction spectrometers
Common measurement of calibration and measured sources
Usage of cascade in decay schema
Certificated calibration sources
Details see recommended literature
Primary standard 198Au 4118044(11) keV λ = 30107788(11) fmSimilar also for 192Ir 169Yb a 170Tm ndash primary calibration sources Eγ = f(k)
polynomialmostlyto secondorder
log-log imaging log εF = f(log Eγ)
Absolute activity determination
Number of detected electrons nβ = Aεβ
Number of detected gamma photons nγ = Aεγ
Assumptions ndash every decay one beta and one gamma conversion coefficient is negligible one detector cleanly for electrons (gas) second detects only gamma photons
Number of coincidences of electron and photon detections nc = Aεβεγ
cn
nnA
Afterwards absolute activity of source is
4π proportionalcounter
NaI(Tl)
Photomultiplier
Source
nβ
nγ
nc
Correction on uncertainty of source position and thickness
2212
Rd
d
Selfabsorption correction
Coincidence correction
d
d
R
d
R
d
R
d
R
d
1
2
2
2
2
11ee
xeII 0
]1[0
0
0D
D
x
x eD
IdxeII
DA e
D
I
IK
1
0
Gamma intensity decreasing done by absorption (μ ndash linear absorption coefficient)
Source with homogenous thickness D is assumed
correction coefficient is
Equation for solid angle
and then
Details see recommended literature and exercise
Details see recommended literature
Single and double escape peak
Production of electron and positron pair rarr positron annihilation rarr two 511 keV photons rarr one or both escape
ESE = E ndash EA
EDE = E ndash 2EA kde EA = 511 keV
Characteristic KX rays of detector material
Broad peak ndash set of different transitions on K-shell
Important for low energies (photo effect is dominant)
X-ray escape lines
EVR = E ndash EK EKα(Ge) = 9885 keV EKβ(Ge) = 10981 keV
Annihilation peak ndash 511 keV ndash broad (electron and positron are not fully in the rest)
Important for lower energies and small detector volumes
0 0 0
])(1[)()(2])()(1)[()( dxxNdxxNxENdxxNENEN NNS
First contribution ndash stays on energy ESecond contribution ndash move to energy E (bdquopile-upldquo spectrum) from sum
τ ndash bdquosignal analysisldquoτN ndash bdquosignal creationldquo
One line rarr area of sum peak per time unit NSP = 2τN2
2) Correlated sums - right coincidences (from the same decay (reaction))
1) Uncorrelated sums - false coincidences (they are not from the same decay (reaction))
bdquoPile-up effectsldquo - summation
Depends on source decay schema
Influence of surrounding materials ndash backscattering peak
Compton scattering in material around sensitive detector volume ndash markedPeak in the background
Ecm
cmEE
e
eZR
22
2
1) Full absorption peaks are placed on relatively slowly varying background2) Good energy resolution (especially semiconductor) rarr single peaks occupy small space
Resolution of weak lines between intensive harr ratio between peak and Compton background
1
10
100
1000
10000
100000
0 2000 4000 6000
čiacuteslo kanaacutelu
četn
ost
Spectrum of gamma ray from 60Co source with backscattering peak and summation peaks
Common characteristic
EdEEFESEP )()()(
Observed spectrum ( S(Ersquo) ) is converted to
E le Eacute
Digitalization of analog signal
1
0)()(
k
k
W
WdEEPks
where Wk = Wk1 ndash Wk
0 is channel width ndash constant is assumed
F(EEacute) = G(EEacute) + B(EEacute)
where G(EEacute) ndash absorption of all energies B(EEacute) ndash incomplete energy conversion
Background and full absorption peaks are separated in this way
Background varies mostly slowly(exception is Compton edges)
We have discrete spectrum of monoenergetic lines
m
jjj EEaEC
1
)()(
where aj Ej are intensities and energies of j-th component
m
jjj
m
jjj EEBaEEGaEs
11
)()()(
m
jjj
m
jjj kkBakkGaks
11
)()()(
Measured spectrum
After digitalization
We use analysis of full absorption peaks for determination of intensities and energies
Approximation by Gauss curve (negligence of natural line width)
2
20
2
)(
2)(
EE
eS
xN
Natural width for X-ray is not negligible rarr its description by Lorentz curveGlobally convolution of Gauss and Lorentz curves
Eventually different types of step functions or tail to lower energies are added (see rec literature)
Background is approximated by linear function or by higher polynomial eventually by step
2
20 2
2)(
EE
EL
Detector efficiency determinationEfficiency to full absorption peak εF
Spectrum purity R = NFN0 NF - number of registration at full absorption peak N0 ndash total number of registered photons
Total efficiency εT
it is valid εF = RεT
Energy calibration
0001
0010
0100
100 1000 10000
E [keV]
e
Eu152
Co57
Eu154
Ba133
Cs137
Y88
Co60
Example of calibration curveof HPGe detector
Calibration lines (etalons standards) measured by crystal diffraction spectrometers
Common measurement of calibration and measured sources
Usage of cascade in decay schema
Certificated calibration sources
Details see recommended literature
Primary standard 198Au 4118044(11) keV λ = 30107788(11) fmSimilar also for 192Ir 169Yb a 170Tm ndash primary calibration sources Eγ = f(k)
polynomialmostlyto secondorder
log-log imaging log εF = f(log Eγ)
Absolute activity determination
Number of detected electrons nβ = Aεβ
Number of detected gamma photons nγ = Aεγ
Assumptions ndash every decay one beta and one gamma conversion coefficient is negligible one detector cleanly for electrons (gas) second detects only gamma photons
Number of coincidences of electron and photon detections nc = Aεβεγ
cn
nnA
Afterwards absolute activity of source is
4π proportionalcounter
NaI(Tl)
Photomultiplier
Source
nβ
nγ
nc
Correction on uncertainty of source position and thickness
2212
Rd
d
Selfabsorption correction
Coincidence correction
d
d
R
d
R
d
R
d
R
d
1
2
2
2
2
11ee
xeII 0
]1[0
0
0D
D
x
x eD
IdxeII
DA e
D
I
IK
1
0
Gamma intensity decreasing done by absorption (μ ndash linear absorption coefficient)
Source with homogenous thickness D is assumed
correction coefficient is
Equation for solid angle
and then
Details see recommended literature and exercise
Details see recommended literature
0 0 0
])(1[)()(2])()(1)[()( dxxNdxxNxENdxxNENEN NNS
First contribution ndash stays on energy ESecond contribution ndash move to energy E (bdquopile-upldquo spectrum) from sum
τ ndash bdquosignal analysisldquoτN ndash bdquosignal creationldquo
One line rarr area of sum peak per time unit NSP = 2τN2
2) Correlated sums - right coincidences (from the same decay (reaction))
1) Uncorrelated sums - false coincidences (they are not from the same decay (reaction))
bdquoPile-up effectsldquo - summation
Depends on source decay schema
Influence of surrounding materials ndash backscattering peak
Compton scattering in material around sensitive detector volume ndash markedPeak in the background
Ecm
cmEE
e
eZR
22
2
1) Full absorption peaks are placed on relatively slowly varying background2) Good energy resolution (especially semiconductor) rarr single peaks occupy small space
Resolution of weak lines between intensive harr ratio between peak and Compton background
1
10
100
1000
10000
100000
0 2000 4000 6000
čiacuteslo kanaacutelu
četn
ost
Spectrum of gamma ray from 60Co source with backscattering peak and summation peaks
Common characteristic
EdEEFESEP )()()(
Observed spectrum ( S(Ersquo) ) is converted to
E le Eacute
Digitalization of analog signal
1
0)()(
k
k
W
WdEEPks
where Wk = Wk1 ndash Wk
0 is channel width ndash constant is assumed
F(EEacute) = G(EEacute) + B(EEacute)
where G(EEacute) ndash absorption of all energies B(EEacute) ndash incomplete energy conversion
Background and full absorption peaks are separated in this way
Background varies mostly slowly(exception is Compton edges)
We have discrete spectrum of monoenergetic lines
m
jjj EEaEC
1
)()(
where aj Ej are intensities and energies of j-th component
m
jjj
m
jjj EEBaEEGaEs
11
)()()(
m
jjj
m
jjj kkBakkGaks
11
)()()(
Measured spectrum
After digitalization
We use analysis of full absorption peaks for determination of intensities and energies
Approximation by Gauss curve (negligence of natural line width)
2
20
2
)(
2)(
EE
eS
xN
Natural width for X-ray is not negligible rarr its description by Lorentz curveGlobally convolution of Gauss and Lorentz curves
Eventually different types of step functions or tail to lower energies are added (see rec literature)
Background is approximated by linear function or by higher polynomial eventually by step
2
20 2
2)(
EE
EL
Detector efficiency determinationEfficiency to full absorption peak εF
Spectrum purity R = NFN0 NF - number of registration at full absorption peak N0 ndash total number of registered photons
Total efficiency εT
it is valid εF = RεT
Energy calibration
0001
0010
0100
100 1000 10000
E [keV]
e
Eu152
Co57
Eu154
Ba133
Cs137
Y88
Co60
Example of calibration curveof HPGe detector
Calibration lines (etalons standards) measured by crystal diffraction spectrometers
Common measurement of calibration and measured sources
Usage of cascade in decay schema
Certificated calibration sources
Details see recommended literature
Primary standard 198Au 4118044(11) keV λ = 30107788(11) fmSimilar also for 192Ir 169Yb a 170Tm ndash primary calibration sources Eγ = f(k)
polynomialmostlyto secondorder
log-log imaging log εF = f(log Eγ)
Absolute activity determination
Number of detected electrons nβ = Aεβ
Number of detected gamma photons nγ = Aεγ
Assumptions ndash every decay one beta and one gamma conversion coefficient is negligible one detector cleanly for electrons (gas) second detects only gamma photons
Number of coincidences of electron and photon detections nc = Aεβεγ
cn
nnA
Afterwards absolute activity of source is
4π proportionalcounter
NaI(Tl)
Photomultiplier
Source
nβ
nγ
nc
Correction on uncertainty of source position and thickness
2212
Rd
d
Selfabsorption correction
Coincidence correction
d
d
R
d
R
d
R
d
R
d
1
2
2
2
2
11ee
xeII 0
]1[0
0
0D
D
x
x eD
IdxeII
DA e
D
I
IK
1
0
Gamma intensity decreasing done by absorption (μ ndash linear absorption coefficient)
Source with homogenous thickness D is assumed
correction coefficient is
Equation for solid angle
and then
Details see recommended literature and exercise
Details see recommended literature
Influence of surrounding materials ndash backscattering peak
Compton scattering in material around sensitive detector volume ndash markedPeak in the background
Ecm
cmEE
e
eZR
22
2
1) Full absorption peaks are placed on relatively slowly varying background2) Good energy resolution (especially semiconductor) rarr single peaks occupy small space
Resolution of weak lines between intensive harr ratio between peak and Compton background
1
10
100
1000
10000
100000
0 2000 4000 6000
čiacuteslo kanaacutelu
četn
ost
Spectrum of gamma ray from 60Co source with backscattering peak and summation peaks
Common characteristic
EdEEFESEP )()()(
Observed spectrum ( S(Ersquo) ) is converted to
E le Eacute
Digitalization of analog signal
1
0)()(
k
k
W
WdEEPks
where Wk = Wk1 ndash Wk
0 is channel width ndash constant is assumed
F(EEacute) = G(EEacute) + B(EEacute)
where G(EEacute) ndash absorption of all energies B(EEacute) ndash incomplete energy conversion
Background and full absorption peaks are separated in this way
Background varies mostly slowly(exception is Compton edges)
We have discrete spectrum of monoenergetic lines
m
jjj EEaEC
1
)()(
where aj Ej are intensities and energies of j-th component
m
jjj
m
jjj EEBaEEGaEs
11
)()()(
m
jjj
m
jjj kkBakkGaks
11
)()()(
Measured spectrum
After digitalization
We use analysis of full absorption peaks for determination of intensities and energies
Approximation by Gauss curve (negligence of natural line width)
2
20
2
)(
2)(
EE
eS
xN
Natural width for X-ray is not negligible rarr its description by Lorentz curveGlobally convolution of Gauss and Lorentz curves
Eventually different types of step functions or tail to lower energies are added (see rec literature)
Background is approximated by linear function or by higher polynomial eventually by step
2
20 2
2)(
EE
EL
Detector efficiency determinationEfficiency to full absorption peak εF
Spectrum purity R = NFN0 NF - number of registration at full absorption peak N0 ndash total number of registered photons
Total efficiency εT
it is valid εF = RεT
Energy calibration
0001
0010
0100
100 1000 10000
E [keV]
e
Eu152
Co57
Eu154
Ba133
Cs137
Y88
Co60
Example of calibration curveof HPGe detector
Calibration lines (etalons standards) measured by crystal diffraction spectrometers
Common measurement of calibration and measured sources
Usage of cascade in decay schema
Certificated calibration sources
Details see recommended literature
Primary standard 198Au 4118044(11) keV λ = 30107788(11) fmSimilar also for 192Ir 169Yb a 170Tm ndash primary calibration sources Eγ = f(k)
polynomialmostlyto secondorder
log-log imaging log εF = f(log Eγ)
Absolute activity determination
Number of detected electrons nβ = Aεβ
Number of detected gamma photons nγ = Aεγ
Assumptions ndash every decay one beta and one gamma conversion coefficient is negligible one detector cleanly for electrons (gas) second detects only gamma photons
Number of coincidences of electron and photon detections nc = Aεβεγ
cn
nnA
Afterwards absolute activity of source is
4π proportionalcounter
NaI(Tl)
Photomultiplier
Source
nβ
nγ
nc
Correction on uncertainty of source position and thickness
2212
Rd
d
Selfabsorption correction
Coincidence correction
d
d
R
d
R
d
R
d
R
d
1
2
2
2
2
11ee
xeII 0
]1[0
0
0D
D
x
x eD
IdxeII
DA e
D
I
IK
1
0
Gamma intensity decreasing done by absorption (μ ndash linear absorption coefficient)
Source with homogenous thickness D is assumed
correction coefficient is
Equation for solid angle
and then
Details see recommended literature and exercise
Details see recommended literature
Common characteristic
EdEEFESEP )()()(
Observed spectrum ( S(Ersquo) ) is converted to
E le Eacute
Digitalization of analog signal
1
0)()(
k
k
W
WdEEPks
where Wk = Wk1 ndash Wk
0 is channel width ndash constant is assumed
F(EEacute) = G(EEacute) + B(EEacute)
where G(EEacute) ndash absorption of all energies B(EEacute) ndash incomplete energy conversion
Background and full absorption peaks are separated in this way
Background varies mostly slowly(exception is Compton edges)
We have discrete spectrum of monoenergetic lines
m
jjj EEaEC
1
)()(
where aj Ej are intensities and energies of j-th component
m
jjj
m
jjj EEBaEEGaEs
11
)()()(
m
jjj
m
jjj kkBakkGaks
11
)()()(
Measured spectrum
After digitalization
We use analysis of full absorption peaks for determination of intensities and energies
Approximation by Gauss curve (negligence of natural line width)
2
20
2
)(
2)(
EE
eS
xN
Natural width for X-ray is not negligible rarr its description by Lorentz curveGlobally convolution of Gauss and Lorentz curves
Eventually different types of step functions or tail to lower energies are added (see rec literature)
Background is approximated by linear function or by higher polynomial eventually by step
2
20 2
2)(
EE
EL
Detector efficiency determinationEfficiency to full absorption peak εF
Spectrum purity R = NFN0 NF - number of registration at full absorption peak N0 ndash total number of registered photons
Total efficiency εT
it is valid εF = RεT
Energy calibration
0001
0010
0100
100 1000 10000
E [keV]
e
Eu152
Co57
Eu154
Ba133
Cs137
Y88
Co60
Example of calibration curveof HPGe detector
Calibration lines (etalons standards) measured by crystal diffraction spectrometers
Common measurement of calibration and measured sources
Usage of cascade in decay schema
Certificated calibration sources
Details see recommended literature
Primary standard 198Au 4118044(11) keV λ = 30107788(11) fmSimilar also for 192Ir 169Yb a 170Tm ndash primary calibration sources Eγ = f(k)
polynomialmostlyto secondorder
log-log imaging log εF = f(log Eγ)
Absolute activity determination
Number of detected electrons nβ = Aεβ
Number of detected gamma photons nγ = Aεγ
Assumptions ndash every decay one beta and one gamma conversion coefficient is negligible one detector cleanly for electrons (gas) second detects only gamma photons
Number of coincidences of electron and photon detections nc = Aεβεγ
cn
nnA
Afterwards absolute activity of source is
4π proportionalcounter
NaI(Tl)
Photomultiplier
Source
nβ
nγ
nc
Correction on uncertainty of source position and thickness
2212
Rd
d
Selfabsorption correction
Coincidence correction
d
d
R
d
R
d
R
d
R
d
1
2
2
2
2
11ee
xeII 0
]1[0
0
0D
D
x
x eD
IdxeII
DA e
D
I
IK
1
0
Gamma intensity decreasing done by absorption (μ ndash linear absorption coefficient)
Source with homogenous thickness D is assumed
correction coefficient is
Equation for solid angle
and then
Details see recommended literature and exercise
Details see recommended literature
We have discrete spectrum of monoenergetic lines
m
jjj EEaEC
1
)()(
where aj Ej are intensities and energies of j-th component
m
jjj
m
jjj EEBaEEGaEs
11
)()()(
m
jjj
m
jjj kkBakkGaks
11
)()()(
Measured spectrum
After digitalization
We use analysis of full absorption peaks for determination of intensities and energies
Approximation by Gauss curve (negligence of natural line width)
2
20
2
)(
2)(
EE
eS
xN
Natural width for X-ray is not negligible rarr its description by Lorentz curveGlobally convolution of Gauss and Lorentz curves
Eventually different types of step functions or tail to lower energies are added (see rec literature)
Background is approximated by linear function or by higher polynomial eventually by step
2
20 2
2)(
EE
EL
Detector efficiency determinationEfficiency to full absorption peak εF
Spectrum purity R = NFN0 NF - number of registration at full absorption peak N0 ndash total number of registered photons
Total efficiency εT
it is valid εF = RεT
Energy calibration
0001
0010
0100
100 1000 10000
E [keV]
e
Eu152
Co57
Eu154
Ba133
Cs137
Y88
Co60
Example of calibration curveof HPGe detector
Calibration lines (etalons standards) measured by crystal diffraction spectrometers
Common measurement of calibration and measured sources
Usage of cascade in decay schema
Certificated calibration sources
Details see recommended literature
Primary standard 198Au 4118044(11) keV λ = 30107788(11) fmSimilar also for 192Ir 169Yb a 170Tm ndash primary calibration sources Eγ = f(k)
polynomialmostlyto secondorder
log-log imaging log εF = f(log Eγ)
Absolute activity determination
Number of detected electrons nβ = Aεβ
Number of detected gamma photons nγ = Aεγ
Assumptions ndash every decay one beta and one gamma conversion coefficient is negligible one detector cleanly for electrons (gas) second detects only gamma photons
Number of coincidences of electron and photon detections nc = Aεβεγ
cn
nnA
Afterwards absolute activity of source is
4π proportionalcounter
NaI(Tl)
Photomultiplier
Source
nβ
nγ
nc
Correction on uncertainty of source position and thickness
2212
Rd
d
Selfabsorption correction
Coincidence correction
d
d
R
d
R
d
R
d
R
d
1
2
2
2
2
11ee
xeII 0
]1[0
0
0D
D
x
x eD
IdxeII
DA e
D
I
IK
1
0
Gamma intensity decreasing done by absorption (μ ndash linear absorption coefficient)
Source with homogenous thickness D is assumed
correction coefficient is
Equation for solid angle
and then
Details see recommended literature and exercise
Details see recommended literature
Detector efficiency determinationEfficiency to full absorption peak εF
Spectrum purity R = NFN0 NF - number of registration at full absorption peak N0 ndash total number of registered photons
Total efficiency εT
it is valid εF = RεT
Energy calibration
0001
0010
0100
100 1000 10000
E [keV]
e
Eu152
Co57
Eu154
Ba133
Cs137
Y88
Co60
Example of calibration curveof HPGe detector
Calibration lines (etalons standards) measured by crystal diffraction spectrometers
Common measurement of calibration and measured sources
Usage of cascade in decay schema
Certificated calibration sources
Details see recommended literature
Primary standard 198Au 4118044(11) keV λ = 30107788(11) fmSimilar also for 192Ir 169Yb a 170Tm ndash primary calibration sources Eγ = f(k)
polynomialmostlyto secondorder
log-log imaging log εF = f(log Eγ)
Absolute activity determination
Number of detected electrons nβ = Aεβ
Number of detected gamma photons nγ = Aεγ
Assumptions ndash every decay one beta and one gamma conversion coefficient is negligible one detector cleanly for electrons (gas) second detects only gamma photons
Number of coincidences of electron and photon detections nc = Aεβεγ
cn
nnA
Afterwards absolute activity of source is
4π proportionalcounter
NaI(Tl)
Photomultiplier
Source
nβ
nγ
nc
Correction on uncertainty of source position and thickness
2212
Rd
d
Selfabsorption correction
Coincidence correction
d
d
R
d
R
d
R
d
R
d
1
2
2
2
2
11ee
xeII 0
]1[0
0
0D
D
x
x eD
IdxeII
DA e
D
I
IK
1
0
Gamma intensity decreasing done by absorption (μ ndash linear absorption coefficient)
Source with homogenous thickness D is assumed
correction coefficient is
Equation for solid angle
and then
Details see recommended literature and exercise
Details see recommended literature
Absolute activity determination
Number of detected electrons nβ = Aεβ
Number of detected gamma photons nγ = Aεγ
Assumptions ndash every decay one beta and one gamma conversion coefficient is negligible one detector cleanly for electrons (gas) second detects only gamma photons
Number of coincidences of electron and photon detections nc = Aεβεγ
cn
nnA
Afterwards absolute activity of source is
4π proportionalcounter
NaI(Tl)
Photomultiplier
Source
nβ
nγ
nc
Correction on uncertainty of source position and thickness
2212
Rd
d
Selfabsorption correction
Coincidence correction
d
d
R
d
R
d
R
d
R
d
1
2
2
2
2
11ee
xeII 0
]1[0
0
0D
D
x
x eD
IdxeII
DA e
D
I
IK
1
0
Gamma intensity decreasing done by absorption (μ ndash linear absorption coefficient)
Source with homogenous thickness D is assumed
correction coefficient is
Equation for solid angle
and then
Details see recommended literature and exercise
Details see recommended literature
Correction on uncertainty of source position and thickness
2212
Rd
d
Selfabsorption correction
Coincidence correction
d
d
R
d
R
d
R
d
R
d
1
2
2
2
2
11ee
xeII 0
]1[0
0
0D
D
x
x eD
IdxeII
DA e
D
I
IK
1
0
Gamma intensity decreasing done by absorption (μ ndash linear absorption coefficient)
Source with homogenous thickness D is assumed
correction coefficient is
Equation for solid angle
and then
Details see recommended literature and exercise
Details see recommended literature
