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TDCRTDCRin a nutshellin a nutshell
P. Cassette, P. Cassette, LaboratoireLaboratoire National Henri Becquerel, FranceNational Henri Becquerel, France
Summary
• LSC in radionuclide metrology, free parameter model• The TDCR model• Examples of relations between efficiency and TDCR• Detection efficiency = TDCR?• Conclusions
LSC in radionuclide metrology, the free parameter model
A short history
• Invention of LSC: Kallman and Reynolds et al., 1950• LS theory: Birks, Voltz, Da Silva… sixties• Calculation models: Gibson, Gales, Houtermans… end of sixties• Precursor of the free parameter model: Kolarov, Vatin 1970• TDCR method: Pochwalski, Radoszewski, Broda 1979• CIEMAT/NIST: Grau Malonda, Coursey, 1982• Development of TDCR counters: France, Poland, South Africa, China in the eighties• Rapid development of the TDCR method since 1995• Commercial 3-PMT counters 2007…
TDCR in National Metrology Laboratories (2009)
If an electron with energy E is absorbed by the liquid scintillator, a Poisson-distributed random number of photons is emitted with a mean value m, function of E
( )!
/xemmxP
mx −
=
Probability of emission of x photons for an average value m(E)
1. Free parameter model: light emission
2. Free parameter model: light detection
The photons emitted are randomly distributed within the optical chamber of the counter and can create photoelectrons in photomultiplier tubes with an overall probability of ν.The resulting statistics of the number of photoelectrons createdis also Poisson-distributed with mean value νm
( )!
)(/y
emmyPmy ννν
−
=
Probability of emission of y photoelectrons for an average value νm(E)
3. Free parameter model: detection efficiency of an electron with energy E injected in a liquid scintillator
If the threshold of the detector is correctly adjusted, a photoelectron will produce a detectable pulse.
•The detection efficiency is the detection probability•The detection probability is the complement of the non-detection
probability.•Non-detection probability : probability of creation of 0
photoelectron when a mean value of νm is expected
mm
eemP νννε −−
−=−=−= 1!0
)(1)0(10
The detection efficiency is a function of a free parameter, νm, meaning the mean number of photoelectrons produced after the absorption of E
Relation between m and E
Experimental evidence:
• The number of photons emitted is not proportional to the energy released in the LS cocktail
• For a given energy, the number of photons emitted by alpha particles is lower than the one emitted by electrons
• The light emission is an inverse function of the stopping power of the incident particle
Birks formula (integral form) :
dxdEkB
dEEmE
+= ∫
1)(
0α
Mean number of photons emitted after absorption of E
Intrinsic light yield of the scintillator
Birks factor
Electron stopping power
Relation between m and E
4. Free parameter model: detection efficiency of electrons with energy spectrum S(E) injected in a liquid scintillator
∫ −−=E m dEeES
0)1)(( νε
with
dxdEkB
dEmE
+= ∫
10
α
να (fom) is the intrinsic efficiency of the detector (in number of photoelectrons per keV)
The knowledge of να allows the calculation of ε
The TDCR method
Calculation of νm using a LS counter with 3 PMT’s
Coincidence and dead-time unit
Time base
vial
PMTpreamplifiers
A
B
C
F
AB CA T F’BC D F
scalers
LSC TDCR Counter
DT
Free parameter model
TDCRcalculation algorithm
(numerical)
Activity
AbsorbedEnergySpectrum
AB, BC, AC
The TDCR method in short
Radionuclide with normalized spectrum density S(E)
Logical sum of double coincidences
3 PMT’s in coincidence
2 PMT’s in coincidence
Detection efficiency for S(E)Events
dEeESm
E 2302 )1()(max
ν
ε−
−= ∫
dEeESmE
T33
0)1()(max
ν
ε−
−= ∫
dEeeESmmE
D ))1(2)1(3)(( 33230
maxνν
ε −−−=−
∫
( )
( ) dEeeES
dEeESmm
E
mE
D
T
))1(2)1(3(
)1(
33230
330
max
max
νν
ν
εε
−−
−
−−−
−=
∫
∫
with
The ratio of triple to double detection efficiency is:
For a large number of recorded events, the ratio of frequencies converges towards the ratio of probabilities:
TDCRDT
D
T ==εε
dxdEkB
dEmE
+= ∫
10
α
Resolution algorithm:
Find a value of the free parameter (να) giving:
εT/εD calculated = T/D experimental
• Monoenergetic electrons: 1 analytical solution
• Pure-beta radionuclides: 1 solution
• Beta-gamma, electron capture: up to 3 solutions...
How many solutions ?
Detection efficiency (single energy)
3
2
)1()(27
2 TDCRTDCRD
+=ε
)1(3BCTLnm A −−=ν
Analytical solution
Similar PMT’s:
PMT’s with different quantum efficiencies:
a.s.o. for νB and νC
)2111(2
ACBCABT
BCABABACACBCTD
⋅⋅−
⋅+
⋅+
⋅=ε
( )( ) dEeeES
dEeESTDCR
EmEm
spectrum
Em
spectrum
)))1(2)1(3((
)1(3)(2)(
3)(
−−
−
−−−
−=∫
∫
Normalized energy spectrum S(E)
Numerical solution: find out νA (fom) to solve:
∫+
=E
dxdEkB
AdEEm0
13)( ν
with
Detection efficiency (multiple energies)
( )
( ) dEeeES
dEeeeESmm
E
mmmE
AB
TBA
CA
)1)(1(
)1)(1)(1(
330
3330
max
max
νν
ννν
εε
−−
−−−
−−
−−−=
∫
∫B
a.s.o. for and BC
T
εε
AC
T
εε
If the 3 PMT ’s are different (and they really are!)
222
⎟⎟⎠
⎞⎜⎜⎝
⎛−+⎟⎟
⎠
⎞⎜⎜⎝
⎛−+⎟⎟
⎠
⎞⎜⎜⎝
⎛−
Ac
T
BC
T
AB
T
ACT
BCT
ABT
εε
εε
εεSolution, minimize:
This gives the detection efficiency and fom for of each PMT
Examples of calculations for various radionuclides
• Calculation using figure of merit (fom) value between 0.1 and 2. photoelectrons/ keV
• Similar PMT’s
• Program TDCR07c (see your LSC2010 memory key!)
• kB value: 0.01 cm/MeV
Monoenergetic emission
6 kev, detection efficiency vs. TDCR
00.1
0.20.3
0.40.50.6
0.70.8
0.91
0 0.1 0.2 0.3 0.4 0.5 0.6
TDCR
Det
ectio
n ef
ficie
ncy
3H
H-3, detection efficiency vs. TDCR
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
TDCR
Dete
ctio
n ef
ficie
ncy
14C
C-14, detection efficiency vs. TDCR
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
TDCR
Dete
ctio
n ef
ficie
ncy
90YY-90, figure of merit and detection efficiency vs. TDCR
00.2
0.40.6
0.81
1.21.4
1.61.8
2
0.988 0.99 0.992 0.994 0.996 0.998 1
TDCR
fom
and
det
ectio
n ef
ficie
ncy
Detection efficiency D
fom
90Y
Y-90, detection efficiency vs. TDCR
0.992
0.993
0.994
0.995
0.996
0.997
0.998
0.999
1
0.99 0.992 0.994 0.996 0.998 1
TDCR
Dete
ctio
n ef
ficie
ncy
18FF-18, detection efficiency vs. TDCR
0.945
0.95
0.955
0.96
0.965
0.97
0.94 0.95 0.96 0.97 0.98 0.99 1
TDCR
Dete
ctio
n ef
ficie
ncy
18FF-18, detection efficiency vs. TDCR
0.965
0.966
0.967
0.968
0.969
0.97
0.99 0.992 0.994 0.996 0.998 1
TDCR
Dete
ctio
n ef
ficie
ncy
Zoom in the high-efficiency region
64Cu(β+, β-, e.c.)
Cu-64, detection efficiency vs. TDCR
0.50.55
0.60.65
0.70.750.8
0.850.9
0.951
0.75 0.8 0.85 0.9 0.95 1
TDCR
Dete
ctio
n ef
ficie
ncy
Typical TDCR uncertainty budget
From a few 0.1 % to a few %Total
Generally ~ 0.2 %Sources variability
0.1 % - 1 % function of EDetection efficiency
ALARA (e.g. 0.01 %)Background
ALARA (e.g. 0.1 %)Counting statistics
~ 0.1 %Weighing
Relative uncertainty (k=1)Uncertainty component
Detection efficiency=TDCR (± 15 %) ?
6 keV, TDCR as detection efficiency, relative bias
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
0 0.1 0.2 0.3 0.4 0.5 0.6
TDCR
Rela
tive
bias
%
Not true for monoenergetic electrons (and quasi-monoenergetic spectra like 55Fe)
3
2
))(1()(27
TDCRTDCRD
+=ε ! εD = TDCR only if TDCR=1
or TDCR = (3⌦3-5)/4
H-3: TDCR as detection efficiency, relative bias
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
TDCR
Rela
tive
bias
%
Not bad for 3H (if the detection efficiency is not too small)
Ni-63, TDCR as detection efficiency, relative bias
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
3.50%
0.3 0.4 0.5 0.6 0.7 0.8 0.9
TDCR
Rel
ativ
e bi
as %
True for 63Ni
C-14, TDCR as detection efficiency, relative bias
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95
TDCR
Rela
tive
bias
%
Fair for 14C (experimental TDCR is generally > 0.9)
Y-90, TDCR as detection efficiency, relative bias
0.00%
0.05%
0.10%
0.15%
0.20%
0.25%
0.99 0.992 0.994 0.996 0.998 1
TDCR
Rela
tive
bias
%
Very good (albeit useless) for 90Y
Is TDCR a good quenching indicator?
Advantages:• TDCR is representative of the light emission process of the radionuclide to measure • no need for an external source
Drawbacks:• TDCR is not a robust quenching indicator for high efficiency sources (but this is not really a problem…)• for some radionuclides, several values of detection efficiency can correspond to one value of TDCR (e.g. 54Mn, 64Cu). In this case, TDCR cannot be used as a quenching index.
TDCR as a quenching indicatorExample of spectrum with low-energy peak
S(E)
Nb of photons
S(E)
Nb of photons
Unquenched spectrum
Quenched spectrum
Quenching increases
• T decreases
• D decreases (but more than T)
So: increases…DT
If
Conclusions
If you have a 3-PMT LS counter, you can generally use it like any other LS counter with the TDCR value as a quenching indicator…
But
You can also do precise metrology using the TDCR method, i.e. by calculating the detection efficiency from the TDCR value!
What 3-PMT LS counter can be used for implementing the TDCR method?
• The counter must be linear (in counting rate)• The afterpulses must be correctly processed• The detection threshold must be adjusted under the single electron response of the PMT’s
… but this is also the qualities expected for a 2-PMT LS counter to be used for radioactivity metrology!
With an extending-type dead-time unit and live-time clock, a LS counter can be linear (without any dead-time correction) and afterpulse interference can be safely removed (see literature)
Thank you for your attention
LSC afterpulses
Threshold
Optimum threshold level
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