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최소자승법을 이용한 다수 베타 방출 핵종 혼합물의 방사능 분석
선광일,남욱원,공경남,김창규,이동명,이상국 대한방사선 방어학회 2001 방사선방어학회지 Vol.26 No.4
베타선 스펙트럼의 최대 에너지가 확실하게 구별되는 2개의 핵종만을 포함하는 혼합시료의 경우에는 최대 에너지가 다르다는 점을 이용하여 손쉽게 각 핵종의 방사능값을 측정할 수 있다. 그러나 3개 이상의 베타 방출 핵종이 포함된 혼합물에 대해서는 각 핵종의 스펙트럼이 서로 겹치기 때문에 이러한 방법으로 구해진 방사능값은 신뢰도가 떨어지게 된다. 따라서, 본 연구에서는 최소자승법을 이용하여 혼합물의 중첩된 베타선 스펙트럼을 각각 분리 정량분석할 수 있는 밥법을 제시하였다. 또한, 실제로 4개의 베타 방출 핵종 ^3H, ^14C, ^16Cl, 90Sr)이 혼합된 사료를 조제하여 본 분석법을 검증한 결과 최고치 Reference value)와 분석치가 7% 이내에서 잘 일치함을 보였다. It is possible to count and perform quench correction on two β-label samples so long as the maximum β-energies are sufficiently different. However, when the coventional technique is applied to the radioassay of a mixture of more than three nuclides, the reliability of the activiteis determined is considerably reduced, resulting from the large overlapping of liquid scintillation pulse height distributions of ezch nuclide. A technique that allows the activities of multiple β-labeled samples to be radioassayed was proposed by using the least square method. The technique was applied to mixture samples of ^3H, ^14C, ^16Cl, and ^90Sr. The analytical values were in good agreement with the reference values within 7% relstive error.
선광일,Seon, Kwang-Il 한국천문학회 2005 天文學論叢 Vol.20 No.1
When we measure a source signal in the presence of a background rate that has been independently measured, the usual approach is to obtain an estimate of the background rate by observing an empty part of the sky, and an estimate of the source signal plus background rate by observing the region where a source signal is expected. The source signal rate is then estimated by subtracting the background rate from the source signal plus background rate. However, when the rates or their observation times are small, this procedure can lead to negative estimates of the source signal rate, even when it should produce a positive value. By applying the Bayesian approach, we solve the problem and prove that the most probable value of source signal rate is zero when the observed total count is smaller than the expected background counts. It is also shown that the results from the conventional method is consistent with the most probable value obtained from the Bayesian approach when the source signal is large or the observation time is long enough.
선광일,이대희,Seon, Kwang-Il,Lee, Dae-Hee 한국천문학회 2005 天文學論叢 Vol.20 No.1
We are often faced with the task of having to estimate the amplitude of a source signal in the presence of a background. In the simplest case, the background can be taken as being flat, and of unknown magnitude B, and the source signal of interest assumed to be the amplitude A of a peak of known shape and position. We present a robust method to find the most probable values of A and B by applying the one-dimensional Newton-Raphson method. In the derivation of the formula, we adopted the Bayesian statistics and assmumed Poisson distribution so that the results could be applied to the analysis of very weak signals, as observed in FIMS (Far-ultraviolet IMaging Spectrogaph).