  To calculate the radioactivity of product nuclides generated in pulse
irradiation, it is generally assumed that the irradiation is approximately
continues in the entire irradiation period ($t_i$) and the flux of 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 ($t_p$) and then decay in a
relative long rest time ($t_r=T-t_p$). 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, applies the geometric
series to obtain the activity superimposition of millions of pulses, and
derives 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.
