TDCR in a nutshell P. Cassette, Laboratoire National 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)
1. Free parameter model: 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)
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 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. 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 ε νm ( νm) e = 1 P(0) = 1 = 1 0! 0 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
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. Free parameter model: detection efficiency of electrons with energy spectrum S(E) injected in a liquid scintillator ε ν = E S( E)(1 e m ) de with 0 m = α 0 E 1+ de kb de dx 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
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
Radionuclide with normalized spectrum density S(E) Events Detection efficiency for S(E) 2 PMT s in coincidence 3 PMT s in coincidence E νm max 3 ε 2 = S( E)(1 e ) ε T = 0 0 E max S( E)(1 e νm 3 ) 3 2 de de Logical sum of double coincidences ε D = 0 E max S( E)(3(1 e νm 3 ) 2 2(1 e νm 3 ) 3 ) de
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 ε T = D m = α TDCR 0 E 1+ de kb de dx
Resolution algorithm: Find a value of the free parameter (να) giving: ε T /ε D calculated = T/D experimental How many solutions? Monoenergetic electrons: 1 analytical solution Pure-beta radionuclides: 1 solution Beta-gamma, electron capture: up to 3 solutions...
Detection efficiency (single energy) Similar PMT s: Analytical solution εd = 2 27( TDCR) (1 + 2 TDCR) 3 PMT s with different quantum efficiencies: mν A = 3Ln(1 T BC ) a.s.o. for ν B and ν C εd = T 2 1 ( BC AC + 1 AC AB + 1 AB BC 2 AB T BC AC )
Detection efficiency (multiple energies) Normalized energy spectrum S(E) Numerical solution: find out νa (fom) to solve: TDCR = spectrum S spectrum S ( E) (1 e m( E ) de ( ) m( E ) 2 m( E ) 3 E ((3(1 e ) 2(1 e ) )) de ) 3 with m( E) ν = 3 E 0 1 AdE de + kb dx
( ) ( ) de e e E S de e e e E S m m E m m m E AB T B A C A ) )(1 (1 ) )(1 )(1 (1 3 3 0 3 3 3 0 max max ν ν ν ν ν 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!) 2 2 2 + + Ac T BC T AB T AC T BC T AB T ε ε ε ε ε ε Solution, 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 Detection efficiency 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 TDCR
3 H H-3, detection efficiency vs. TDCR Detection efficiency 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 TDCR
14 C C-14, detection efficiency vs. TDCR 1 0.95 Detection efficiency 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 TDCR
90 Y Y-90, figure of merit and detection efficiency vs. TDCR 2 fom and detection efficiency 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 Detection efficiency D fom 0.988 0.99 0.992 0.994 0.996 0.998 1 TDCR
90 Y Y-90, detection efficiency vs. TDCR 1 0.999 Detection efficiency 0.998 0.997 0.996 0.995 0.994 0.993 0.992 0.99 0.992 0.994 0.996 0.998 1 TDCR
18 F F-18, detection efficiency vs. TDCR 0.97 Detection efficiency 0.965 0.96 0.955 0.95 0.945 0.94 0.95 0.96 0.97 0.98 0.99 1 TDCR
18 F F-18, detection efficiency vs. TDCR 0.97 Detection efficiency 0.969 0.968 0.967 0.966 0.965 0.99 0.992 0.994 0.996 0.998 1 TDCR Zoom in the high-efficiency region
64 Cu (β +, β -, e.c.) Cu-64, detection efficiency vs. TDCR 1 0.95 Detection efficiency 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0.75 0.8 0.85 0.9 0.95 1 TDCR
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 %
Detection efficiency=tdcr (± 15 %)?
Not true for monoenergetic electrons (and quasi-monoenergetic spectra like 55 Fe) 27( TDCR) (1 + ( TDCR)) 2 ε D =! 3 εd = TDCR only if TDCR=1 or TDCR = (3 3-5)/4 6 kev, TDCR as detection efficiency, relative bias 60.00% 50.00% Relative bias % 40.00% 30.00% 20.00% 10.00% 0.00% 0 0.1 0.2 0.3 0.4 0.5 0.6 TDCR
Not bad for 3 H (if the detection efficiency is not too small) H-3: TDCR as detection efficiency, relative bias 70.00% 60.00% Relative bias % 50.00% 40.00% 30.00% 20.00% 10.00% 0.00% 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 TDCR
True for 63 Ni Ni-63, TDCR as detection efficiency, relative bias 3.50% 3.00% Relative bias % 2.50% 2.00% 1.50% 1.00% 0.50% 0.00% 0.3 0.4 0.5 0.6 0.7 0.8 0.9 TDCR
Fair for 14 C (experimental TDCR is generally > 0.9) C-14, TDCR as detection efficiency, relative bias 14.00% 12.00% Relative bias % 10.00% 8.00% 6.00% 4.00% 2.00% 0.00% 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 TDCR
Very good (albeit useless) for 90 Y Y-90, TDCR as detection efficiency, relative bias 0.25% 0.20% Relative bias % 0.15% 0.10% 0.05% 0.00% 0.99 0.992 0.994 0.996 0.998 1 TDCR
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. 54 Mn, 64 Cu). In this case, TDCR cannot be used as a quenching index.
TDCR as a quenching indicator Example of spectrum with low-energy peak S(E) S(E) Unquenched spectrum Nb of photons Quenched spectrum Nb of photons Quenching increases T decreases D decreases (but more than T) So: T D If increases
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
Optimum threshold level Threshold