Corrections for the combined effects of decay and dead time in live-timed counting of short-lived radionuclides

Studies and calibrations of short-lived radionuclides, for example 15O, are of particular interest in nuclear medicine. Yet counting experiments on such species are vulnerable to an error due to the combined effect of decay and dead time. Separate decay corrections and dead-time corrections do not account for this issue. Usually counting data are decay-corrected to the start time of the count period, or else instead of correcting the count rate, the mid-time of the measurement is used as the reference time. Correction factors are derived for both those methods, considering both extending and non-extending dead time. Series approximations are derived here and the accuracy of those approximations are discussed.