A new equation for activity calculation in pulse irradiation: derivation, simulation, and experimental validation

To calculate the radioactivity of product nuclides generated in pulse irradiation, it is generally assumed that the irradiation is approximately continuous in the entire irradiation period ($t_{\text{i}}$) and the flux of the incoming irradiation particle can be obtained by averaging their intensity in each pulse period ($T$). However, this approximation fails to acknowledge the fact that the product nuclides are not created in each pulse period ($T$) evenly: They are only produced in a very short pulse width ($t_{\text{p}}$) and then decay in a relatively long rest time ($t_{\text{r}}=T-t_{\text{p}}$). Given by the enormous number of pulses, the sum of these decays may not be negligible. To make the activity calculation in accordance with the real situation in pulse irradiation, we scrutinize the details of irradiation and decay processes in each pulse, apply the geometric series to obtain the activity superimposition of millions of pulses, and derive a novel activity equation particularly suitable for pulse irradiation. The experimental results, numerical simulations, and activity measurements from photon activation driven by a pulsed electron LINAC have confirmed the validity of this new equation. The comparison between the new and traditional equations indicates that their discrepancy could be significant under certain conditions. The limitations of the new activity equation for pulse irradiation are discussed as well.