Multi-window counting of radioactivity

In counting of radioactivity, using for example gas proportional (GP) or liquid scintillation (LS) counters, one can set up two or more electronic windows, which can measure two or more radiation components. In this work, we derived general equations for n-window counting in matrix notation, including mutual crosstalk between the windows using both the ratio (not normalized) and the fraction (normalized) methods. A solution for n radiation components is presented. For the two-window measurements, we report complete statistical analysis of the results including propagation of all uncertainties. The decision-level and the detection-limit equations were derived including crosstalk correction, uncertainties of the variables, Gaussian continuity correction, interference correction, and the overdispersion correction. Numerical verifications of the two-window systems are presented, including conditions for the detection of a minor component in the presence of a major component. In addition, limited experimental verifications of the two-window systems using LS counting are reported.