Discrete Counting of Short Lived Isotopes with Low Background Detectors

We consider radiation counting experiments used to measure quantities of materials that are short-lived with respect to the count durations. The HPS 13.31 statistical analysis seriously overestimates the uncertainty when the quantity and background are very low. We consider the case in which the objective is to quantify the number of atoms, n, that were present in a sample when it was drawn. Mathews and Gerts [JRNC, 2008] analyzed this case and developed formulas for the probability distribution of n, in order to develop experiment design processes that minimize the smallest detectable quantity of material, thus maximizing sensitivity for the detection problem. We extend their effort to the quantification problem: designing such experiments to find the count duration that yields the lowest possible minimum quantifiable quantity, given the other measurement parameters. A value of n is quantifiable if the precision of the measurement, defined as the width of the confidence interval for n divided by the mean value of It is sufficiently likely to be better than a specified precision tolerance. Our analysis and methods are confirmed by Monte Carlo simulation.