Algorithm for Computational Age Dating of Nuclear Material for Nuclear Forensic Purposes

The parent and daughter nuclides in a radioactive decay chain arrive at secular equilibrium once they have a large half-life difference. The characteristics of this equilibrium state can be used to estimate the production time of nuclear materials. In this study, a mathematical model and algorithm that can be applied to radio-chronometry using the radioactive equilibrium relationship were investigated, reviewed, and implemented. A Bateman equation that can analyze the decay of radioactive materials over time was used for the mathematical model. To obtain a differential-based solution of the Bateman equation, an algebraic numerical solution approach and two different matrix exponential functions (Moral and Levy) were implemented. The obtained result was compared with those of commonly used algorithms, such as the Chebyshev rational approximation method and WISE Uranium. The experimental analysis confirmed the similarity of the results. However, the Moral method led to an increasing calculation uncertainty once there was a branching decay, so this aspect must be improved. The time period corresponding to the production of nuclear materials or nuclear activity can be estimated using the proposed algorithm when uranium or its daughter nuclides are included in the target materials for nuclear forensics.