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