On the detection of rare,and moderately rare,nuclear events

Some of the more important developments in science and practical demands in commerce have been linked to attempts to detect rare events and rare contaminants, ranging from the early “counting” of solar neutrinos to the occurrence of dodder seeds in clover. For moderately rare events (≈5 to 50 counts) we consider limitations of the Poisson-normal approximation, together with the apparent problem of excessive false positives when a common expression is (mis-)used for detection decisions. For very rare events, rigorous approaches published more than half a century ago are applicable to such current problems as trace actinide contamination and nuclear treaty monitoring.