Effect of Long Decay Chains on the Counting Statistics in the Analysis of Radium224 and Radon222

Abstract

In the counting of long decay chains, it is often necessary to use counting intervals that are long with respect to the half‐life of the individual members of the series. With modern instrumentation the geometrical and detection efficiencies may be very nearly 4π and 100%, respectively. Consequently, the approximations normally used for estimating the statistical counting error are not valid. A method has been presented by which the variance of the observed count can be easily calculated for any long decay chain. The effects of the counting interval, the geometrical efficiency, and the delay of start of counting relative to the time of separation of Ra²²⁴ and Rn²²² from their respective daughters have been determined. The counting interval and the geometrical efficiency were found to produce the most significant effect for both the Ra²²⁴ and Rn²²² series. A simple and convenient method has been presented to correct for this effect by the use of a quantity J which can be calculated for a given experimental condition.