Application of the Laplace transform method for computational modelling of radioactive decay series

It is well known that when spent fuel is removed from the core, it is still composed of considerable amount of radioactive elements with significant half-lives. Most actinides, in particular plutonium, fall into this category, and have to be safely disposed of. One solution is to store the long-lived spent fuel as it is, by encasing and burying it deep underground in a stable geological formation. This implies estimating the transmutation of these radioactive elements with time. Therefore, we describe in this paper the application of the Laplace transform technique in matrix formulation to analytically solve initial value problems that mathematically model radioactive decay series. Given the initial amount of each type of radioactive isotopes in the decay series, the computer code generates the amount at a given time of interest, or may plot a graph of the evolution in time of the amount of each type of isotopes in the series. This computer code, that we refer to as the LTRadL code, where L is the number of types of isotopes belonging to the series, was developed using the Scilab free platform for numerical computation and can model one segment or the entire chain of any of the three radioactive series existing on Earth today. Numerical results are given to typical model problems to illustrate the computer code efficiency and accuracy. (orig.)