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 PMT pulses
General composition of a LS-cocktail Primary solvent Secondary solvent (opt) Primary fluor Secondary fluor Surfactants (opt) Extractants (opt) 10 M 1,5 M 10-2 M 10-3 M > 1M 1-5 10-1 M
Energy transfer radionuclide Aqueous phase α, β, γ, e -... solvent Non-radiative transfer Organic phase Primary fluor Radiative transfer Fiat lux
Detection efficiency Energy Alpha particles 5000 kev 1 Det. efficiency High-energy β - ( 90 Y) 2283 kev max 0.99 (800 average) Medium-energy β - ( 63 Ni) 65 kev max 0.7 (17 average) Low-energy β - ( 3 H) 19 kev max 0.5 (5.8 average)
Quenching radionuclide α, β, γ, e -... solvent Ionization light fluor 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
1. Model of light emission 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 P ( x / m) = m x m e x! Probability of emission of x photons for an average value m(e)
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 P ( y / νm) = ν ( m) y νm y! e 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 ε νm ( νm) e = 1 P(0) = 1 = 1 0! 0 e νm
3. Detection efficiency of an electron injected in a liquid scintillator with energy E ε =1 e νm 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
Relation between m and E Birks formula (integral form) : m( E) = α 0 E 1+ de de kb dx Electron stopping power Birks factor Intrinsic light yield of the scintillator Mean number of photons emitted after absorption of E
4. Detection efficiency of an electron injected in a liquid scintillator with an energy distribution S(E) ε = E ν S( E)(1 e m ) de 0 with m = α 0 E 1+ de de kb dx 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
LSC TDCR Counter A vial B C F Coincidence and dead-time unit PMT preamplifiers AB CA T F BC D F Time base scalers
The TDCR method in short AB, BC, AC D T Free parameter model Absorbed Energy Spectrum TDCR calculation algorithm (numerical) Activity
LS counter with 3 similar PMT s Events Detection efficiency for E 1 PMT 2 PMT s in coincidence 3 PMT s in coincidence Logical sum of double coincidences ε D ε ε ε 1 = 1 e νm 3 νm 3 2 2 = (1 e ) T = (1 e = 3(1 e νm 3 ) 3 νm νm 3 2 3 ) 3 ) 2(1 e
Radionuclide with normalized spectrum density S(E) Events Detection efficiency for S(E) 2 PMT s in coincidence 3 PMT s in coincidence Logical sum of double coincidences = E νm max 3 ε 2 S( E)(1 e ) ε E T = 0 0 E max S( E)(1 e νm νm 3 ) 3 2 de de νm max 3 2 3 3 ε D = S( E)(3(1 e ) 2(1 e ) ) de 0
The ratio of triple to double detection efficiency is: εt ε D = 0 E max S 0 E max S ( E) (1 e νm νm 3 de νm 3 2 3 3 ( E) (3(1 e ) 2(1 e ) ) de ) 3 with For a large number of recorded events, the ratio of frequencies converges towards the ratio of probabilities: T D ε = T = TDCR ε D m = α 0 E de de 1+ kb dx
Resolution algorithm: Find a value of the free parameter (να) giving: ε T /ε D calculated = T/D experimental How many solutions? Pure-beta radionuclides: 1 solution Beta-gamma, electron capture: up to 3 solutions...
Pure beta 1 Detection efficiency ε D ε T 0 0 1 TDCR
Electron capture Mn-54 Detection efficiency (D) 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 Experimental Region! 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 Série1 TDCR
If the 3 PMT s are different And they really are!
If the 3 PMT s are different (and they really are!) εt ε AB = 0 E max S ( E) 0 E max (1 e S ν Am 3 )(1 e ν m ν Bm 3 )(1 e A B 3 3 ( E) (1 e )(1 e ) de ν m ν C m 3 ) de ε ε a.s.o. for T and BC εt ε AC
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 2 2 2 + + 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 Bad! Activity Good! Bad! Maximum value 0 Detection efficiency 1
Detection efficiency variation methods PMT defocusing coaxial grey filters spring, mesh, polarisers, LCD or use chemical quenching (destructive)
Example: 3 H source, defocusing Activity (kbq/g) Activity versus TDCR, E0=10 ev 122 120 118 116 114 112 110 0,3200 0,3400 0,3600 0,3800 0,4000 0,4200 TDCR Série1 Série2 Série3 Série4 Série5 Série6 Série7 Série8 Série9 Série10 Série11 Série12 Série13
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 )
Uncertainty evaluation method Model the measurement transfer function : y = f( x1, x2,... x n ) y is the result and x i are all the parameters used in the measurement : experimental, theoretical, etc. The combined standard uncertainty u c is calculated using : u c 2 y n 2 f i = 1 x i ( ) = u ( ) n1 n 2 f f x + i 2 x x u ( x i, x j) i= 1j= i+ 1 i j
Standard uncertainties on TDCR input parameters Experimental : Double coincidences : D Triple coincidences : T TDCR : T/D 2 2 2 2 2 1 1 2 2 2 1 2 ) )( ( 1 1 ) ( 1 1 ) ( 1 1 DT s D s T s s T T D D n s T T n s D D n s DT D T RCTD n i i i DT n i i T n i i D + + = = = = = = =
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 Radionuclide input data set average, standard deviation stat distribution law random number generator synthetic data set 1 synthetic data set 2 synthetic data set 3 synthetic data set n transfer function transfer function transfer function transfer function result 1 result 2 result 3 result n Calculation of average and standard deviation Average = result of measurement Standard deviation = standard uncertainty
Typical TDCR uncertainty budget Uncertainty component Weighing Counting statistics Background Detection efficiency Sources variability Total Relative uncertainty (k=1) ~ 0.1 % ALARA (e.g. 0.1 %) ALARA (e.g. 0.01 %) 0.1 % - 1 % function of E Generally ~ 0.2 % From a few 0.1 % to a few %
V. Practical information
TDCR counters in the world (2009) n 6 2 2 2 2
Examples of locally-made TDCR counters
Examples of optical chambers NPL LNHB
Commercial counter Hidex 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 locallymade 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