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This study presents accessible Wolfram Mathematica code to visualize radioactive decay chains, even when initial conditions are unknown. The tool helps analyze high-order progeny activities for health physicists and researchers.

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Area of Science:

  • Nuclear Physics
  • Radiochemistry
  • Health Physics

Background:

  • Studying high-order radioactive decay equations is complex due to variable assumptions and evolving parent/progeny activities.
  • Uncertainties and approximations can compromise the interpretation of decay analysis, especially when decay equilibrium is disturbed.
  • Arbitrary initial activities of radioactive progenies complicate accurate decay modeling.

Purpose of the Study:

  • To develop and present user-friendly Wolfram Mathematica code for visualizing time-activity plots of high-order radioactive decay progeny.
  • To address the challenge of analyzing decay chains with disturbed secular equilibrium and arbitrary initial progeny activities.
  • To provide a tool for health physicists and researchers to better understand and interpret radioactive decay processes.

Main Methods:

  • Expanded the Bateman equation for an un-replenished parent to calculate activity over time for up to 13 progenies.
  • Utilized the formula from Skrable et al., adapted for arbitrary initial concentrations and extended to the 13th progeny without parent production.
  • Developed code to generate activity vs. time plots and report cumulative disintegrations for user-specified periods.

Main Results:

  • Successfully created code to calculate and plot activity versus time for complex radioactive decay chains.
  • The code handles high-order progenies with arbitrary initial activities after secular equilibrium disturbance.
  • Cumulative disintegration calculations are provided for comparison with experimental counting measurements.

Conclusions:

  • The developed Wolfram Mathematica code offers a practical solution for analyzing disturbed radioactive decay equilibrium.
  • The tool enhances the study of high-order progeny activities, aiding in accurate interpretation of results.
  • The code is designed for accessibility, potentially benefiting health physicists and a broader scientific audience.