Absolute radioassay of extended sources: an equivalent point-source coincidence-counting approach with application to...

A general methodology is provided for the absolute assay of radioisotopes decaying with coincident photons in an extended source. In the determination of the source activity, the method requires neither the detailed consideration of the geometric and self-attenuation processes taking place between the source component points nor a knowledge of the distribution of activity across the source. It derives from the concept of the "equivalent point source," that is a fictitious point source whose activity would equal that measured for the actual extended source. It has been developed for an arbitrary number of coincident photon types displaying an arbitrary degree of mutual correlation, and for arbitrary detection geometry. A unifying formalism is developed for both point and extended sources and for single and dual detecting systems. It is found that in all cases the various instrumental and spectroscopic uncertainties appear within a composite parameter (herein called F factor) that can be determined by standard calibration procedures; this factor is in turn only weakly dependent on its own component parameters. New expressions and relationships are obtained that provide a greater physical insight into coincidence-counting methods.