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Andrew Parker Lancaster University Engineering Department Utilising a Bayesian Combination Model to Enhance Gamma-ray Detection Precision

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Borderline Waste – A Management Problem “...where wastes are borderline between disposal categories the higher standard should be adopted for characterisation purposes.” – Nuclear Decommissioning Authority Waste type Disposal cost per-cubic- metre LLW£1,700 ILW£67,000 Table 1: The disposal cost per-cubic-metre, taken from LLWR at Drigg and NDA budget information Andrew Parker, Lancaster University Engineering Dept, 2011

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Gamma-ray Detectors Sodium Iodide Scintillator NaI Sodium Iodide Scintillator NaI Hyper-pure Germanium Semiconductor HPGe Hyper-pure Germanium Semiconductor HPGe High detection efficiency Cheap to produce Poor energy resolution Good energy resolution Insensitive to temperature change Poor detection efficiency relative to NaI. Andrew Parker, Lancaster University Engineering Dept, 2011 LLW: Waste that has activity... less than 12 GBq per tonne of gamma radioactivity

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Bayesian Normal-Normal Model Posterior Mean Posterior Variance Bayes’ Rule Prior Likelihood Posterior Value Andrew Parker, Lancaster University Engineering Dept, 2011 Assuming the detectors’ results are normally distributed with Means and Standard Deviations (M, τ ) & (Y, σ ) respectively.

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Combination of Count Data Am keV Cs keV Co keV Co keV Mean StDev Example of Cs137 photopeak Levenberg-Marquardt fitting method applied to photopeaks. Table 3: Shows the Bayesian mean and standard deviation for the selected isotopes, having used all 15 result sets from each detector HPGe (M, τ )NaI (Y, σ ) Mean St Dev Table 2: Mean and standard deviation of Cs counts with the two detectors Andrew Parker, Lancaster University Engineering Dept, 2011

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Precision Comparison Results NaIHPGe CV for 137 Cs 0.43%1.34% CV for Cs 137N1 = 1N1 = 5N1 = 15 N2 = 10.70%0.27%0.13% N2 = 50.50%0.31%0.17% N2 =150.33%0.26%0.18% WhereN1 = Number of sets of data used from Sodium Iodide (NaI) N2 = Number of sets of data used from Hyper-pure Germanium (HPGe) Table 4: CV for single detector results Table 5: CV for the Bayesian method with varying values of N1 & N2 Coefficient of Variation (CV) Andrew Parker, Lancaster University Engineering Dept, 2011

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Visual Comparison Figure 2: Plot showing the distributions of each detector alone and the plot of the Bayesian method using all available results for Cs 137. Normalised to zero. Bayesian MethodNaIHPGe

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Conclusions Under certain conditions the method has shown to reduce the normal distribution dispersion and therefore the precision of the result. By obtaining a higher degree of precision the technique offers lower uncertainty when determining an accurate estimate for the activity of a source. When fewer results were used the model shows higher levels of dispersion compared to that of a single detector. Andrew Parker, Lancaster University Engineering Dept, 2011 Thank you for listening, any questions related to the work? Andrew Parker

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