In this work, we addressed the inhomogeneity problem in gamma spectrometry caused by hot particles, which are dispersed into environment from large nuclear reactor accidents such as at Chernobyl and Fukushima. Using M...In this work, we addressed the inhomogeneity problem in gamma spectrometry caused by hot particles, which are dispersed into environment from large nuclear reactor accidents such as at Chernobyl and Fukushima. Using Monte Carlo simulation, we have determined the response of a gamma spectrometer to individual and grouped hot particles randomly distributed in a soil matrix of 1-L and 0.6-L sample containers. By exploring the fact that the peak-to-total ratio of efficiencies in gamma spectrometry is an empirical parameter, we derived and verified a power-law relationship between the peak efficiency and peak-to-total ratio. This enabled creation of a novel calibration model which was demonstrated to reduce the bias range and bias standard deviation, caused by measuring hot particles, by several times, as compared with the homogeneous calibration. The new model is independent of the number, location, and distribution of hot particles in the samples. In this work, we demonstrated successful performance of the model for a single-peak <sup>137</sup>Cs radionuclide. An extension to multi-peak radionuclide was also derived.展开更多
In gamma spectrometry of voluminous samples, inhomogeneous distribution of radioactivity caused by the presence of hot particles can create significant Bias in the results of activity determinations. We developed a no...In gamma spectrometry of voluminous samples, inhomogeneous distribution of radioactivity caused by the presence of hot particles can create significant Bias in the results of activity determinations. We developed a novel method to reduce this Bias using the gamma-peak ratio. We show that the peak area ratio of two gamma peaks of different energies, emitted by the same radionuclide, is a sensitive measure of emitting source location and thus the inhomogeneity. A new calibration formula was then derived for true gamma efficiency <em>p<sub>i</sub></em> as a function of efficiency ratio <em>p<sub>i</sub></em>/<em>p<sub>j</sub></em> of two peaks. This approach was verified by Monte Carlo simulations for a sample of 1-L volume containing from 1 up to 2048 of hot particles randomly distributed in a soil matrix. A <sup>152</sup>Eu radionuclide was selected for calculations and we used various combinations of two gamma spectral peaks selected from three gamma energies of 121.8, 344.3, and 1408.0 keV. This new method is shown to reduce the Bias range and Bias standard deviation by several times when compared with the traditional homogeneous calibration applied to measuring hot particles. The method is independent of the number, location, and distribution of hot particles in the samples, and can be applied to a mixture of radionuclides. It complements our previous calibration model based on the peak-to-total ratio.展开更多
We describe two new derivations of the chi-square distribution. The first derivation uses the induction method, which requires only a single integral to calculate. The second derivation uses the Laplace transform and ...We describe two new derivations of the chi-square distribution. The first derivation uses the induction method, which requires only a single integral to calculate. The second derivation uses the Laplace transform and requires minimum assumptions. The new derivations are compared with the established derivations, such as by convolution, moment generating function, and Bayesian inference. The chi-square testing has seen many applications to physics and other fields. We describe a unique version of the chi-square test where both the variance and location are tested, which is then applied to environmental data. The chi-square test is used to make a judgment whether a laboratory method is capable of detection of gross alpha and beta radioactivity in drinking water for regulatory monitoring to protect health of population. A case of a failure of the chi-square test and its amelioration are described. The chi-square test is compared to and supplemented by the t-test.展开更多
文摘In this work, we addressed the inhomogeneity problem in gamma spectrometry caused by hot particles, which are dispersed into environment from large nuclear reactor accidents such as at Chernobyl and Fukushima. Using Monte Carlo simulation, we have determined the response of a gamma spectrometer to individual and grouped hot particles randomly distributed in a soil matrix of 1-L and 0.6-L sample containers. By exploring the fact that the peak-to-total ratio of efficiencies in gamma spectrometry is an empirical parameter, we derived and verified a power-law relationship between the peak efficiency and peak-to-total ratio. This enabled creation of a novel calibration model which was demonstrated to reduce the bias range and bias standard deviation, caused by measuring hot particles, by several times, as compared with the homogeneous calibration. The new model is independent of the number, location, and distribution of hot particles in the samples. In this work, we demonstrated successful performance of the model for a single-peak <sup>137</sup>Cs radionuclide. An extension to multi-peak radionuclide was also derived.
文摘In gamma spectrometry of voluminous samples, inhomogeneous distribution of radioactivity caused by the presence of hot particles can create significant Bias in the results of activity determinations. We developed a novel method to reduce this Bias using the gamma-peak ratio. We show that the peak area ratio of two gamma peaks of different energies, emitted by the same radionuclide, is a sensitive measure of emitting source location and thus the inhomogeneity. A new calibration formula was then derived for true gamma efficiency <em>p<sub>i</sub></em> as a function of efficiency ratio <em>p<sub>i</sub></em>/<em>p<sub>j</sub></em> of two peaks. This approach was verified by Monte Carlo simulations for a sample of 1-L volume containing from 1 up to 2048 of hot particles randomly distributed in a soil matrix. A <sup>152</sup>Eu radionuclide was selected for calculations and we used various combinations of two gamma spectral peaks selected from three gamma energies of 121.8, 344.3, and 1408.0 keV. This new method is shown to reduce the Bias range and Bias standard deviation by several times when compared with the traditional homogeneous calibration applied to measuring hot particles. The method is independent of the number, location, and distribution of hot particles in the samples, and can be applied to a mixture of radionuclides. It complements our previous calibration model based on the peak-to-total ratio.
文摘We describe two new derivations of the chi-square distribution. The first derivation uses the induction method, which requires only a single integral to calculate. The second derivation uses the Laplace transform and requires minimum assumptions. The new derivations are compared with the established derivations, such as by convolution, moment generating function, and Bayesian inference. The chi-square testing has seen many applications to physics and other fields. We describe a unique version of the chi-square test where both the variance and location are tested, which is then applied to environmental data. The chi-square test is used to make a judgment whether a laboratory method is capable of detection of gross alpha and beta radioactivity in drinking water for regulatory monitoring to protect health of population. A case of a failure of the chi-square test and its amelioration are described. The chi-square test is compared to and supplemented by the t-test.
