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) „Pile-up“ background and summation peaks
f) Influence of surrounding material – 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
Ideal detector – no dead layers, ...
1) Small detector limit – all secondary photons (from Compton scattering and
annihilation) leave detector
mean free path of
secondary photons
>>
Detector size
Eγ < 2·mec2
Eγ >> 2·mec2
Ratio of areas of photo peak
and Compton background:
SF/SC =σF/σC
Good resolution (semiconductor) makes possible to see X-ray escape peaks from detector material
2) Large detector limit – all secondary photons are absorbed
(very large detector, photons firstly interact at center)
Mean free path of secondary
photons << detector size
All energy is absorbed at the detector
Full absorption peak (photo peak)
1) Gamma quanta interacting by photo effect
2) Multiple Compton scattering
3) Pair production and following absorption of annihilation photons
Spectrum of 241Am source
Spectrum of 60Co source
Compton edges
2  E
2
One Compton scattering to angle 180O:
Two Compton scattering to angle 180O:
EC 
mec  2  E
2
4  E
2
E 2C 
mec  4  E
2
Spectrum between Compton edges and full absorption peak:
1) Multiple Compton scattering
2) Compton scattering at „dead layer“ before detector
3) Annihilation photons are scattered by Compton scattering
4) Incomplete charge collection
5) Escape of characteristic KX - photons
Compton continuum
Compton background is almost not changing up to Compton edge
Many lines → Compton background changes only slowly
1000000
četnost
100000
10000
1000
100
10
1
0
1000
2000
3000
4000
číslo kanálu
Spectrum with one line – 137Cs
Spectrum with many lines – 152Eu
Single and double escape peak
Production of electron and positron pair → positron annihilation → two 511 keV
photons → one or both escape
ESE = E – EA
EDE = E – 2·EA kde EA = 511 keV
Annihilation peak – 511 keV – broad (electron and positron are not fully in the rest)
Characteristic KX rays of detector material
Broad peak – set of different transitions on K-shell
Important for low energies (photo effect is dominant)
X-ray escape lines
Important for lower energies and small detector volumes
EVR = E – EK
EKα(Ge) = 9.885 keV EKβ(Ge) = 10.981 keV
„Pile-up effects“ - summation
1) Uncorrelated sums - false coincidences (they are not from the same decay (reaction))
τ – „signal analysis“
τN – „signal creation“

N S ( E )  N ( E )[ 1  (   N )  N ( x ) dx ]  2
0


 N ( E  x ) N ( x ) dx [1    N ( x ) dx ]
N
0
0
First contribution – stays on energy E
Second contribution – move to energy E („pile-up“ spectrum) from sum
One line → area of sum peak per time unit:
NSP = 2·τ·N2
2) Correlated sums - right coincidences (from the same decay (reaction))
Depends on source decay schema
Influence of surrounding materials – backscattering peak
Compton scattering in material around sensitive detector volume – marked
Peak in the background:
100000
2
mec  2  E
10000
2
Spectrum of gamma ray from
60Co source with backscattering
peak and summation peaks
četnost
E ZR 
E mec
1000
100
10
1
0
2000
4000
6000
číslo kanálu
1) Full absorption peaks are placed on relatively slowly varying background
2) Good energy resolution (especially semiconductor) → single peaks occupy
small space
Resolution of weak lines between intensive ↔ ratio between peak and Compton
background
Common characteristic
Observed spectrum ( S(E’) ) is converted to:
P(E ) 
 S ( E ) F ( E , E ) d E 
E ≤ E´
Digitalization of analog signal:
1
s(k ) 

Wk
0
P ( E ) dE
Wk
where Wk = Wk1 – Wk0 is channel width – constant is assumed
F(E,E´) = G(E,E´) + B(E,E´)
where G(E,E´) – absorption of all energies
B(E,E´) – incomplete energy conversion Background varies mostly slowly
(exception is Compton edges)
Background and full absorption peaks are separated in this way
We have discrete spectrum of monoenergetic lines:
m
C (E ) 
a
j
 (E  E j )
j 1
where aj, Ej are intensities and energies of j-th component
m
s(E ) 
Measured spectrum:

m
a j G (E, E j ) 
j 1
m
s(k ) 
After digitalization:
a
j 1
a
j
 B(E, E j )
j 1
m
j
 G (k , k j ) 
a
j
 B (k , k j )
j 1
We use analysis of full absorption peaks for determination of intensities and energies.
Approximation by Gauss curve (negligence of natural line width)
N (x) 
S

2

e
( E  E0 )
2 
2
2
Eventually different types of step functions or tail
to lower energies are added (see rec. literature)
Natural width for X-ray is not negligible → its description by Lorentz curve

Globally: convolution of Gauss and Lorentz curves
L(E ) 
2


2
 E  E 0 2  
2
Background is approximated by linear function or by higher polynomial, eventually by step
Energy calibration
Calibration lines (etalons, standards) measured by crystal diffraction spectrometers:
Primary standard: 198Au 411.8044(11) keV λ = 3010.7788(11) fm
Similar also for 192Ir, 169Yb a 170Tm – primary calibration sources
Common measurement of calibration and measured sources
Usage of cascade in decay schema
Eγ = f(k)
polynomial,
mostly
to second
order
Detector efficiency determination
Total efficiency εT
Spectrum purity
Efficiency to full absorption peak εF
R = NF/N0
NF - number of registration at full absorption peak
N0 – total number of registered photons
it is valid: εF = R·εT
0.100
e
Eu152
Co57
Certificated calibration sources
Eu154
log-log imaging: log εF = f(log Eγ)
Ba133
0.010
Cs137
Y88
Details see recommended literature
Co60
Example of calibration curve
of HPGe detector
0.001
100
1000
10000
E [keV]
Absolute activity determination
Assumptions – every decay one beta and one gamma
conversion coefficient is negligible
one detector cleanly for electrons (gas)
second detects only gamma photons
Number of detected electrons:
nβ = Aεβ
Number of detected gamma photons:
nγ = Aεγ
Number of coincidences of
electron and photon detections:
4π proportional
counter
nβ
nc = A·εβεγ
Source
Afterwards absolute activity of source is:
NaI(Tl)
nc
A
n  n
nc
Photomultiplier
nγ
Correction on uncertainty of source
position and thickness:
Equation for solid angle:
e
and then:
e

  2  1 




2
2 
d R 
d
2
2

d 
d
d 

   1  2   1  2   

R 
R
R 
 



1
d d
R d
Details see recommended literature
Selfabsorption correction:
Gamma intensity decreasing done by absorption (μ – linear absorption coefficient):
I  I 0e
  x
Source with homogenous thickness D is assumed:
D
I  I 0
e
x0
  x
dx 
I 0
D
[1  e
 D
]
correction coefficient is:
Coincidence correction:
Details see recommended literature and exercise
KA 
I 0
I

D
1 e
 D