Solving the Fermi equation for Modeling Nuclear Decay: Approaches, Assumptions, and Limitations in the Context of the Thomas-Dirac Distribution

Ruben Cornelius Siagian, Budiman Nasution, Jubaidah Jubaidah

Abstract


This study explores a sophisticated probabilistic model for radioactive decay, emphasizing decay probability in small time intervals. Equation (1), with decay constant and time interval (dt), is central. Integration yields Equations (2), (3), and (4), describing total decay (N) over larger intervals (T). The Poisson distribution links to Equation (5), depicting decay events with average rate. In radioactive decay, the binomial distribution is relevant for independent nuclei (R). Equations (7) and (8) outline the probability of observing (N) decays, utilizing the binomial distribution and coefficient. Equation (9) simplifies via the Poisson distribution and factorial (n), notably eliminating (R-N). This reveals the efficiency of representing binomial distribution properties. The study extends to analyzing radiotracers in nuclear medicine through visualized data, revealing properties like half-life and decay constants on graphs. Graphical analysis identifies time's role in deviation from true values, offering insights into radiotracer reliability. This amalgamation of probabilistic methods and radiotracer analysis significantly contributes to understanding and applying radioactive decay concepts in diverse scientific and medical contexts.


Keywords


Uranium Decay; Fermi Equation; Numerical Methods; Boltzmann Distribution; Materials Properties

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DOI: https://doi.org/10.31284/j.iptek.2023.v27i2.4424

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