Statistics and Errors of Counting

Irons can be determined by means of reactions with energy thresholds, such as (n, p) or (n, a) reactions. By application of several detectors with dilTcrcnt thresholds information about neutron spectra may be obtained. 

Radioactive decay is governed by the laws of statistics. Thus, the decay of a single atom cannot be predicted and every counting rate has a statistical error which decreases with the number of counts measured. If the counting rate of a long-lived radionuclide is measured several times under identical conditions, a distribution of the counting rates Xi about a mean value. x is observed  

The width of the distribution is characterized by the standard deviation a which is defined by 

At high values of. v (x 1) the asymmetric Poisson distribution becomes identical with the symmetric Gaussian distribution 

According to this distribution, there is a probability of 68.3% that the counting is within the standard deviation r7(. v -. x a), a probability of 95.5% that it is within 2(7 and a probability of 99.9% that it is within 3(7. 

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