Visualizing High-Order Decay after Disequilibria

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Abstract

High-order decay equations are often difficult to study without significant care taken with variables and assumptions. As parent and progeny activities evolve over time, the effects of uncertainties and approximations confound the quality and interpretation of results. Of particular concern is the situation when decay equilibrium has been disturbed and progenies have arbitrary initial activities. To address this, code was created using Wolfram Mathematica to visualize the time-activity plots of the high order progenies of naturally occurring radioactive material after secular equilibrium is disturbed. The Bateman equation for an un-replenished parent was expanded to calculate activity vs. time for up to 13 progenies at different initial activities. The code uses the formula of Skrable et al., without parent production, expanded to the 13th progeny with arbitrary initial concentration. The code calculates and plots activity vs. time; it also reports the cumulative disintegrations of each progeny over a user-specified time period for comparison to counting measurements. The code could also be modified to incorporate additional production or branched decay schemes. We believe this code may be useful to health physicists and is intended to be accessible for anyone’s use. This paper presents the code with explanations and examples on how to use it.

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