Comparison of numerical and exact analyses in a neutron activation and decay chain

A method for solving a set of coupled linear first-order ordinary differential equations as it applies to neutron activation and subsequent radioisotope decay chains was developed that is easy to implement and accurate enough for most preliminary engineering design calculations. The method is applied to a specific radioisotope production scheme to evaluate the yield of the desired isotope as well as production of secondary and tertiary contaminant radioisotopes. An analytical closed-form solution was also derived for the same activation and decay chain to provide a basis for comparison; the analytical solution was benchmarked against several limiting cases to validate the equations. Results of the simulation involving the numerical approach were compared to the exact analytical solution. The numerical solution, while obviously not exact, is found to be close enough for engineering purposes. A discussion of the numerical precision of the result for the particular case are discussed.