The TDCR method in LSC

P. Cassette

Laboratoire National Henri Becquerel

CEA/LNE, France

LIQUID SCINTILLATION USERS’ FORUM 2009

Summary

I. Some information on LSC

II. LSC in metrology: the free parameter model

III. The Triple to Double Coincidence Ratio method

IV. Uncertainty evaluation

V. Practical information

I. General information on LSC

LSC in short

• Mix the radioactive solution to measure with a LS cocktail

• place in a vial

• count the number of light flashes per unit of time

• calculate the detection efficiency

• activity = counting rate / detection efficiency

LS

vial

pulsesPMT

General composition of a LS-cocktail

Primary solvent 10 M

Secondary solvent (opt) 1,5 M

Primary fluor 10-2 M

Secondary fluor 10-3 M

Surfactants (opt) > 1M

Extractants (opt) 1-5 10-1 M

Energy transfer

radionuclide

solvent

Primary fluor

Fiat lux

α, β, γ, e-...

Organic phase

Aqueous phase

Non-radiative transfer

Radiative transfer

Detection efficiency

Energy Det. efficiency

Alpha particles 5000 keV 1

High-energy β- (90Y) 2283 keV max 0.99(800 average)

Medium-energy β- (63Ni) 65 keV max 0.7(17 average)

Low-energy β- (3H) 19 keV max 0.5(5.8 average)

Quenching

radionuclide

solvent

fluor

light

α, β, γ, e-...

Ionization

Chemical

Colour

Some numbers…

• The energy of a 5 keV electron, if totally

converted into light (425 nm) would

produce

• But typically, 99 % of the energy is

converted into heat

• At 5 keV, the light yield is even worse,

due to the ionization quenching process

• The quantum efficiency of a PMT is ~

25 %, the photocathode will emit

1700 photons

~17 photons

~ 7 photons

~ 2 photoelectrons

Light emitted

• Light flash duration: electrons ~ 5 ns

α ~ 10 ns

• Afterpulses during some µs (T+T reactions

and PMT afterpulses)

• Low global efficiency:

1 keV —> a few photons

• Blue, near-UV radiation

II. LSC in metrology, the free

parameter model

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

( )!

/x

emmxP

mx −

=

Probability of emission of x photons for an average value m(E)

1. Model of light emission

Light detection, the photomultiplier tube

2. Model of 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 created

is also Poisson-distributed with mean value νm

( )!

)(/

y

emmyP

my ννν

−

=

Probability of emission of y photoelectrons for an average value νm(E)

3. Detection efficiency of an electron injected

in a liquid scintillator with energy E

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

eem

Pν

ννε −

−

−=−=−= 1!0

)(1)0(1

0

3. Detection efficiency of an electron injected

in a liquid scintillator with energy E

me

νε −−=1

The detection efficiency is a function of a free

parameter, νm, meaning the mean number of

photoelectrons produced after the absorption of E

But generally, radionuclides do not produce monoenergetic electrons…

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) :

dx

dEkB

dEEm

E

+

= ∫1

)(0

α

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. Detection efficiency of an electron injected in a

liquid scintillator with an energy distribution S(E)

∫−−=

Em

dEeES0

)1)(( νε

with

dx

dEkB

dEm

E

+

= ∫1

0α

να is the intrinsic efficiency of the detector

(in number of photoelectrons per keV)

The knowledge of να allows the calculation of ε

III. 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

D

T

Free parameter

model

TDCR

calculation

algorithm

(numerical)

Activity

Absorbed

Energy

Spectrum

AB, BC, AC

The TDCR method in short

Logical sum of double

coincidences

3 PMT’s in coincidence

2 PMT’s in coincidence

1 PMT

Detection efficiency for EEvents

31 1

m

e

ν

ε−

−=

232 )1(

m

e

ν

ε−

−=

33 )1(

m

Te

ν

ε−

−=

3323 )1(2)1(3

mm

Dee

νν

ε −−−=−

LS counter with 3 similar PMT’s

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

dEeES

mE

23

02 )1()(

max

ν

ε−

−= ∫

dEeES

mE

T

33

0)1()(

max

ν

ε−

−= ∫

dEeeES

mmE

D))1(2)1(3)(( 3323

0

max

νν

ε −−−=−

∫

( )

( ) dEeeES

dEeES

mmE

mE

D

T

))1(2)1(3(

)1(

3323

0

33

0

max

max

νν

ν

ε

ε

−−

−

−−−

−=

∫

∫

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:

TDCRD

T

D

T ==ε

ε

dx

dEkB

dEm

E

+

= ∫1

0α

Resolution algorithm:

Find a value of the free parameter (να) giving:

εT/εD calculated = T/D experimental

Pure-beta radionuclides: 1 solution

Beta-gamma, electron capture: up to 3 solutions...

How many solutions ?

Pure beta

TDCR

Detection

efficiency

0 1

0

1

εD

εT

Mn-54

00,10,20,30,40,50,60,70,80,9

1

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

TDCR

De

tecti

on

eff

icie

ncy (

D)

Série1

Experimental

Region !

Electron capture

If the 3 PMT ’s are different

And they really are !

( )

( ) dEeeES

dEeeeES

mmE

mmmE

AB

T

BA

CA

)1)(1(

)1)(1)(1(

33

0

333

0

max

max

νν

ννν

ε

ε

−−

−−−

−−

−−−=

∫

∫B

a.s.o. for and

BC

T

ε

ε

AC

T

ε

ε

If the 3 PMT ’s are different (and they really are!)

3 equations, 3 unknown…

Resolution method: minimize:

e.g. using the downhill simplex algorithm

This calculation gives the detection efficiency and the relative

Efficiency of each PMT

222

−+

−+

−

Ac

T

BC

T

AB

T

AC

T

BC

T

AB

T

ε

ε

ε

ε

ε

ε

How to choose the best kB parameter

(or any other parameter in the model)?

Change detection efficiency: if the parameters are OK, the

calculated activity must remain the same

(i.e. the calculation model must compensate any variation in

detection efficiency)

Detection efficiency variation

Activity

Detection efficiency

Maximum value

10

Good !

Bad !

Bad !

Detection efficiency variation methods

• PMT defocusing

• coaxial grey filters

• spring, mesh, polarisers, LCD …

• or use chemical quenching (destructive)

Activity versus TDCR, E0=10 eV

110

112

114

116

118

120

122

0,3200 0,3400 0,3600 0,3800 0,4000 0,4200

TDCR

Ac

tiv

ity

(k

Bq

/g)

Série1

Série2

Série3

Série4

Série5

Série6

Série7

Série8

Série9

Série10

Série11

Série12

Série13

Example: 3H source, defocusing

IV Uncertainty evaluation

“A measurement without uncertainty is not a measurement”

Uncertainty evaluation method

(GUM)

1. Model the measurement

(get the transfer function between input quantities and

measurement result)

2. Evaluate standard uncertainties of input quantities

(experimental data, parameters, etc.) and covariances between

input quantities

3. Combine the standard uncertainties and covariances

4. Expand uncertainty (if you really need it…)

y f x x xn= ( , ,... )1 2

The combined standard uncertainty uc is calculated using :

( ) ( )uc2 y

f

xii

nu xi=

=

∑ ⋅∂

∂1

22 + ⋅ ⋅

= +=

−

∑∑211

1 ∂

∂

∂

∂

f

x

f

xu x x

ij i

n

i

n

ji j( , )

Uncertainty evaluation method

Model the measurement transfer function :

y is the result and xi are all the parameters used in the

measurement : experimental, theoretical, etc.

Standard uncertainties on TDCR input

parameters

Experimental :

• Double coincidences : D

• Triple coincidences : T

• TDCR : T/D

22

2

2

2

1

1

22

2

1

2

))((1

1

)(1

1

)(1

1

DT

s

D

s

T

ss

TTDDn

s

TTn

s

DDn

s

DTDTRCTD

n

i iiDT

n

i iT

n

i iD

++=

−−−

=

−−

=

−−

=

∑

∑

∑

=

=

=

The TDCR transfer function is not

analytical

Result of a bisection or minimisation algorithm

So, how to combine the standard uncertainties ?

1. Numerical evaluation of the partial derivatives

2. Monte Carlo simulation

Monte Carlo method

result 1

transfer function

synthetic data set 1

result 2

transfer function

synthetic data set 2

result 3

transfer function

synthetic data set 3

result n

transfer function

synthetic data set n

random number generator

Radionuclide input data set

average, standard deviation

stat distribution law

Calculation of average and standard deviation

Average = result of measurement

Standard deviation = standard uncertainty

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

V. Practical information

TDCR counters in the world (2009)

2

6

2

2

n

2

Examples of locally-made TDCR counters

Examples of optical chambers

NPL LNHB

Commercial counterHidex 300 SL

•TDCR is just used as a quenching indicator

•No efficiency calculation model provided

•Under evaluation by LNHB and PTB

Too early to decide if this counter can be used for the TDCR method

… but evaluation results will come soon

Available software

Available:• TDCRB02 (POLATOM/LNHB)

http://www.nucleide.org/ICRM_LSC_WG/icrmsoftware.htm

• TDCR07 and variants (LNHB)

philippe.cassette@cea.fr

• EFFY5 (CIEMAT)

And,

many programs made by NIST, BIPM, PTB, NMISA,…

but probably using the same models…

Conclusions

• The TDCR method is a mature LSC standardization technique

widely used within the international radionuclide metrology

community and well suitable for the standardization of pure-beta

and some electron-capture radionuclides

• The models and programs are available

• Up to now, this technique was restricted to specific locally-

made 3 PMT’s counters… But this could change soon if

commercial counter are found to be suitable for the application of

this technique

•There is an international community (in the National Metrology

Institutes) improving models, instruments and software

More information: http://www.nucleide.org/icrm.htm