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Method of False Rates for Radioactive Decay Chain Calculation
International Journal of Systems Science and Applied Mathematics
Volume 5, Issue 3, September 2020, Pages: 27-31
Received: Dec. 18, 2019; Accepted: Dec. 31, 2019; Published: Sep. 14, 2020
Author
Michael Erle Lord, Intera Inc., Boulder, CO, USA
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Abstract
Many engineering applications involving radioactive materials requires the time history of the radioactivity of nuclides within a decay chain. The system of differential equations with initial conditions or initial value problem describing radioactive decay of a parent and daughter nuclides was posited by Ernest Rutherford who was awarded a Noble Prize in 1910 for this work. Harry Bateman (1910) provided an analytic solution to the radioactive decay chain problem with the constraint that initial inventory of all daughter elements is zero. Required data for the decay chain calculation consists of the parent and all daughters’ radioactive half-life. The half-life for essentially all radionuclides has been established and is available from multiple sources. Solutions other than Bateman’s (non-zero initial conditions) can be computed analytically but become unwieldy for longer decay chains. For this reason, many applications use a numerical solution. However, a numerical solution can require constraints on the time step size. The proposed method of false rates provides a unique algorithm for the decay chain activities. The method treats the decay chain with arbitrary initial conditions and the calculation is analytic or exact. The method is unexpectedly simplistic. An example decay chain calculation compares the solutions by the method of false rates with a numerical method. The comparison is a verification of the method of false rates calculation. The method of false rates is easily coded as a stand-alone application or as a sub-module of a more general code such as a contaminant transport model.
Keywords
Decay Chain, Activity, Differential Equations, Decay Rate, Half-Life, False Rate
Michael Erle Lord, Method of False Rates for Radioactive Decay Chain Calculation, International Journal of Systems Science and Applied Mathematics. Vol. 5, No. 3, 2020, pp. 27-31. doi: 10.11648/j.ijssam.20200503.11
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