On the calculation of activity concentrations and nuclide ratios from measurements of atmospheric radioactivity

Motivated by the need for consistent use of concepts central to the reporting of results from measurements of atmospheric radioactivity, we discuss some properties of the methods commonly used. Different expressions for decay correction of the activity concentration for parent–daughter decay pairs are presented, and it is suggested that this correction should be performed assuming parent–daughter ingrowth in the sample during the entire measurement process. We note that, as has already been suggested by others, activities rather than activity concentrations should be used when nuclide ratios are calculated. In addition, expressions that can be used to transform activity concentrations to activity ratios are presented. Finally we note that statistical uncertainties for nuclide ratios can be properly calculated using the exact solution to the problem of confidence intervals for a ratio of two jointly normally distributed variables, the so-called Fieller׳s theorem.