Čerenkov counting and liquid scintillation counting of 36 Cl Karsten Kossert, Ole Nähle Physikalisch-Technische Bundesanstalt (PTB), Braunschweig, Germany and Agustín Grau Carles Instituto de Física Fundamental (CSIC), Madrid, Spain LSC 2010, Advances in Liquid Scintillation Spectrometry, Paris, 6-10 September 2010 Physikalisch-Technische Bundesanstalt
Motivation The application of a new TDCR-Čerenkov technique for the activity determination of 36 Cl revealed discrepancies with liquid scintillation counting. This discrepancy indicates errors in the computation of the beta emission spectrum.
The TDCR-Čerenkov method
Basics Charged particles produce Čerenkov light when traveling in a transparent dielectric medium with v>c/n Electrons: m 0 = 511 kev/c 2 v/c=β>1/n 1 β = 1 E / 511+ 1 2 At threshold: β=1/n E = th 1 511 1 1 (1 2 ) n in kev
Basics E th 1 = 511 1 1 (1 2 ) n in kev 700 600 water: n = 1.333 E th = 261.6 kev E th in kev 500 400 300 200 100 0 1,0 1,2 1,4 1,6 1,8 2,0 refractive index n
Basics Cherenkov light emission has a directional character (not isotropic) cos θ = 1 nβ 40 35 30 θ in 25 20 15 10 5 0 0 500 1000 1500 2000 2500 3000 3500 Energy in kev water: n = 1.333 θ max = 41.4
Basics According to the Frank and Tamm theory the number of photons per unit path is given by dk 1 1 1 = 2παFS 1 2 2 dx λ1 λ2 n β - α FS is the fine structure constant - n is the refractive index of the medium (here non-dispersive) - β=v/c - λ 1 and λ 2 are the lower and upper limit of the wavelength region
A new TDCR-Cherenkov technique Number of photons is computed by numerical (Romberg) integration E E dk 1 k( E) = de dx ρd E / dx th where dk 1 1 1 = 2παFS 1 2 2 dx λ1 λ2 n β 700 600 500 The electron stopping powers de/dx are taken from the ESTAR database (NIST) ( ) k E 400 300 200 100 0 0 500 1000 1500 2000 2500 3000 3500 4000 E in kev
A new TDCR-Cherenkov technique - Assumption: The number of created photoelectrons follows the Poisson statistics, i.e. we can apply a free parameter model. E 0 th qk ( E) α1 qk ( E) α2 qk ( E) α3 ( )( )( ) ε T = N( E) 1 e 1 e 1 e de E E 0 th qk ( E) α1 qk ( E) α2 ( )( ) ε D = N( E) 1 e 1 e E qk ( E) α 3 3 ( )( ) ( )( ) 1 qk ( E) α qk ( E) α 2 qk ( E) α 1 e 1 e 1 e 1 e qk ( E ) α1 qk ( E) α2 qk ( E) α3 ( )( )( ) E + + 2 1 e 1 e 1 e d
A new TDCR-Cherenkov technique E 0 th qk ( E) α1 qk ( E) α2 qk ( E) α3 ) ( )( )( ) ε T = N( E) 1 e 1 e 1 e de E E 0 th qk ( E) α1 qk ( E) α2 ( )( ) ε D = N( E) 1 e 1 e E qk ( E) α 3 3 ( )( ) ( )( ) 1 qk ( E) α qk ( E) α 2 qk ( E) α 1 e 1 e 1 e 1 e qk ( E ) α1 qk ( E) α2 qk ( E) α3 ) ( )( )( ) E + + 2 1 e 1 e 1 e d The anisotropy is described with only one parameter α: 3 3 α 1 = α α 2 = (1 α ) α α 3 = 1 (1 α) α α 2 2 For α=1/3 the formulas are similar to the TDCR formulas for LS.
A new TDCR-Cherenkov technique Nuclide TDCR ε D,exp ε D,calc (ε D,calc -ε D,exp )/ ε D,exp in % ε D,calc (ε D,calc -ε D,exp )/ ε D,exp in % (α=0.41) α(e ) (x=0.655) 32 P 0.7931 0.68725 0.6858-0.21 0.6878 0.07 89 Sr 0.7630 0.59285 0.5909-0.33 0.5930 0.03 90 Y 0.8745 0.76966 0.7699 0.03 0.7710 0.18 106 Rh 0.9277 0.88083 0.8829 0.23 0.8834 0.29 204 Tl 0.3830 0.13410 0.1307-2.53 0.1327-1.08 K. Kossert, Applied Radiation and Isotopes 68 (2010) 1116-1120
A new TDCR-Cherenkov technique The new method works excellent for several beta emitters, but calculations for 36 Cl yield discrepancies up to 10%.
A new TDCR-Cherenkov technique The method was extended and improved: - Wavelength-dependent PMT response curves are taken into account - Wavelength-dependent refractive index (dispersion) is taken into account - PMT asymmetries are taken into account (3 free parameters and Downhill Simplex algorithm) But: discrepancies for 36 Cl remained. quantum efficiency in % refractive index of water 10 1 0.1 0.01 100 200 300 400 500 600 700 1.48 1.47 1.46 1.45 1.44 1.43 1.42 1.41 1.4 1.39 1.38 1.37 1.36 1.35 1.34 1.33 1.32 HAMAMATSU R331-05, 2" HAMAMATSU R331, 2" BURLE 8850, 2" wavelength in nm Fit used in this work Eq. 1 from Thormahlen et al. 200 300 400 500 600 700 λ in nm
36 Cl beta spectrum Beta transition is 2 nd forbidden (non-unique) Decay scheme from DDEP: www.nucleide.org N(W)dW = AW(W 2-1) 1/2 (W 0 -W) 2 F(Z,W) C(W) dw A=g 2 /2π 3 ); W is the total electron energy in units of the rest mass; W 0 is the maximum value for W; F(Z,W) is the Fermi function taking into account distortion due to nuclear charge; C(W) is the shape factor function
36 Cl beta spectrum Determination of 36 Cl beta spectrum: Reich and Schüpferling, 1974 Sadler and Behrens, 1993 Grau Malonda and Grau Carles, 1998 Grau Carles, 2005 Rotzinger et al., 2008 This work 4π-Si(Li) spectrometer theory shape-factor derived from Sadler and Behrens LS cutoff energy yield method cryogenic magnetic calorimeters derived from exp. data of Rotzinger et al.
36 Cl beta spectrum 0.03 probability in arbitrary units 0.02 0.01 Fit of exp. data from Rotzinger et al. (2008) Grau Carles (2005) Grau Malonda and Grau Carles (1998) 0 0 100 200 300 400 500 600 700 Energy in kev 36 Cl shape-factor function as determined in this work using experimental data: C(W)=1-1.326W+0.6328W 2
Experimental details LS sample composition: 15 ml Ultima Gold TM + 1 ml water, glass vials, quenching agent: Nitromethane Čerenkov samples: 12 ml HCl (1 mol/l) in PE vials Preparation by difference weighing of a pycnometer with traceable balances
LS measurements Reference activity was determined by means of LS counting using CIEMAT/NIST efficiency tracing and TDCR. Efficiency was computed with MICELLE2 using kb = 0.0075 cm/mev. Counters: - Wallac 1414 - TriCarb 2800 - TDCR system of PTB
LS measurements For TDCR, efficiency reduction is necessary. Results: CN: 9.029(27) kbq g -1 TDCR: 9.047(27) kbq g -1 1.00 1.00 1.00 0.75 a) 0.75 b) 0.75 c) (a i -a mean )/ a mean in % 0.50 0.25 0.00-0.25-0.50 (a i -a mean )/ a mean in % 0.50 0.25 0.00-0.25-0.50 (a i -a mean )/ a mean in % 0.50 0.25 0.00-0.25-0.50-0.75-0.75-0.75-1.00 0.225 0.250 0.275 0.300 0.325 0.350 0.375 0.400 ε tracer -1.00 0.275 0.300 0.325 0.350 0.375 0.400 0.425 0.450 0.475 ε tracer -1.00 0.982 0.983 0.984 0.985 0.986 0.987 0.988 0.989 0.990 TDCR
LS measurements Standard uncertainty components for LS counting Component Standard deviation of the mean (samples:5 (4 for TDCR); repetition per sample for each counter: 8) Weighing Dead time Background Time of measurements (starting time and duration (life-time)) Adsorption Radionuclide impurities (none detected) 3 H activity/tdcr value and fit Decay data (endpoint energy and beta shape-factor function) Ionization quenching Quenching indicator (SQP(E), tsie) PMT asymmetry Decay correction Square root of the sum of quadratic components u(a)/a in % CIEMAT/ TDCR NIST 0.02 0.02 0.10 0.03 0.01 0.05 0.05 0.01 0.25 0.01 0.02 0.10 0.01 0.30 0.01 0.02 0.03 0.03 0.01 0.05 0.05 0.01 0.25 0.01 -- 0.10 0.01 0.29
Seasonal effects? Alburger et al. (1986) measured 36 Cl and 32 Si/ 32 P with an endwindow gas-flow proportional counter. Seasonal fluctuations of the decay-corrected counting rates in the order of 3 10-3 were observed with a maximum in February and minimum in August. Jenkins et al. (2009) developed a contentious explanation: A correlation between the decay constant and the Earth-Sun distance (corresponds to a change of the solar neutrino flux). Our LS-TDCR measurements were started in Dec. 2009 and some repetitions were made in summer 2010 to detect potential seasonal effects.
Seasonal effects? 10-14 Dec. 2009 measurement 14-16 June 2010 measurement 6-12 July 2010 measurement Comparison (Dec. July) Sample No. a 1 in kbq g -1 a 2 in kbq g -1 a 3 in kbq g -1 Deviation (a 1 - a 3 )/a 1 in % 2 3 4 5 Mean 9.0482(29) 9.0459(14) 9.0461(17) 9.0486(23) 9.0472 9.0543(27) 9.0470(25) 9.0498(28) 9.0482(25) 9.0498 9.0507(14) 9.0481(7) 9.0483(7) 9.0502(4) 9.0493-0.0272(351) -0.0253(170) -0.0238(205) -0.0169(259) -0.0233(246) Deviation between the Dec. and the July measurements: about (2.3±2.5) 10-4. We can exclude seasonal variations of the decay rate of 36 Cl in the stated order. The measurements will be continued.
Čerenkov counting results of 36 Cl Shape factor C(W) Reference α=1.11, n=1.341, no dispersion ε D, Č, calc x in % α=1.07, n=1.331, dispersion for water ε D, Č, calc x in % α=1.0, n=1.341, dispersion for water ε D, Č, calc x in % 1-1.326W +0.6328W 2 1-1.875W +1.375W 2 1-1.167W +0.884W 2 This work (with exp. data from Rotzinger et al. (2008)) Grau Malonda and Grau Carles (1998) Grau Carles (2005) 0.2121 0.2330 0.2032-2.40 7.19-6.49 0.2124 0.2333 0.2036-2.26 7.35-6.32 0.2177 0.2391 0.2010 0.16 10.01-3.84 x = ( ε ε ) / ε D, Č, calc D, Č, exp D, Č, exp Reasonable agreement is obtained with the new shape-factor function. Theoretical prediction from Sadler and Behrens (1993) can be ruled out.
Summary A new shape-factor function was derived for 36 Cl. The results of LS measurements and TDCR-Čerenkov counting are in reasonable agreement when using the new shape-factor function. This confirms the results from Rotzinger et al. (2008). From our LS-TDCR data we find no evidence for a correlation of the decay rate and the Earth-Sun distance.
Outlook Potential application of the new TDCR-Čerenkov method: - measurement of radionuclides for nuclear medicine (e.g. 32 P, 89 Sr, 90 Y) - measurements in environmental radioactivity (e.g. 210 Pb, Sr isotopes) - due to the large sensitivity on shape-factors the method can provide useful information on beta spectra (as shown for 36 Cl) - preliminary tests indicate that the method can also be applied with the new Hidex-TDCR counter - further effects must be investigated, e.g. bremsstrahlung and direct interaction of electrons with PMTs (see e.g., full MC approach from Bobin et al. (2010)) The recent extensions and improvements as well as a computer program will be published soon.
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