Counting statistics of short-lived nuclides

The well-known Poisson formula for counting statistics is generalized to the situation where the radioactive source studied, with mean lifetime 1/λ, decays apprecialy during the total time of observation T. A general expression is given for the modified probability_λP(k) of observing k events in a short time interval t_o=T/n, where the results are averaged over the period of observation T. This corresponds to the experimental distribution which is obtained by pooling together all the n≫1 individual measurements of k made with a given source. The deviation from the simple Poisson law, which neglects decay, depends essentially on the quantity ν=λ·T. If ν is of the order of unity, the deformation is strong enough that it can serve as the basis of a new method for measuring the half-life of the nuclide involved. Invited paper.