How pileup rejection affects the precision of loss-free counting

The mechanism behind the particularly high count scatter observed with loss-free counting (LFC) on spectrometers with pileup rejection is scrutinised. It is shown theoretically and experimentally that, contrary to other loss mechanisms, pileup rejection does not preserve Poisson statistics during the system live-time. Consequently, the statistical uncertainty obtained with loss-free counting increases proportionally to the broadening of the count-yield distribution per live-time inspection period. A new theoretical formula for the LFC uncertainty is presented and predicted values are compared with experimental data obtained on a gamma-ray spectrometer and data from computer simulations of nuclear counting. Additionally, the statistical effect of using floating-point values instead of integers for the LFC correction factors is investigated; the LFC uncertainty shows little change.