Statistical properties of gamma-ray spectra obtained with loss-free or zero-dead-time counting, and ORTEC’S “variance spectrum”

In the “dual spectrum” approach to non-Poisson counting statistics of gamma-ray spectra obtained with loss-free or zero-dead-time (ZDT) counting, an uncorrected spectrum acquired in parallel is employed to obtain the uncertainties in the dead-time-corrected spectrum. In this paper, it is mathematically proved that this approach can only yield correct results under very special conditions. It is also proved that a variance spectrum acquired by adding the squares of the increments added to the dead-time-corrected spectrum do provide the correct variances in a loss-free or ZDT spectrum.