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Visualizing High-Order Decay after Disequilibria

Wilson, Charles A. IV1; Hendrickson, Katherine R.2; Hamideh, Amin M.3; Matthews, Kenneth L. II4; Wang, Wei-Hsung5

doi: 10.1097/HP.0000000000000926

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.

1J. Bennett Johnston Sr. Center for Advanced Microstructures and Devices (CAMD), Louisiana State University, 6980 Jefferson Highway, Baton Rouge, LA 70806;

2University of Florida Department of Industrial and Systems Engineering, 1819 Lewis Turner Blvd, Ft Walton Beach, FL 32547;

3Louisiana State University Radiation Safety Office, 112 Nuclear Science Building, Baton Rouge, LA 70803;

4Louisiana State University Department of Physics and Astronomy, 202 Nicholson Hall, Baton Rouge, LA 70803;

5Louisiana State University Center for Energy Studies, 1067 Energy, Coast and Environment Building, Baton Rouge, LA 70803.

The authors declare no conflicts of interest.

Charles A. Wilson IV is the radiation safety officer at Louisiana State University’s Center for Advanced Microstructures and Devices (CAMD). He is currently a doctoral candidate studying environmental health physics in the Department of Environmental Sciences at LSU. He earned his master’s degree in medical physics and health physics from LSU in 2012. Charles was President of the Deep South Chapter of the HPS and a former Chair of the HPS Student Support Committee. He presently serves as Chair of the Society Support Committee and member on the IRPA task force. His email is

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