Theoretical and experimental investigations on the applicability of the Poisson and Ruark-Devol statistical density functions in the theory of radioactive decay and counting

Abstract

In radiation studies it is commonly accepted that the process of radioactive disintegration is adequately described by the Poisson statistical density function. Independence and stationarity are the fundamental properties that must be possessed by a physical process if it is to obey Poisson statistics. However for cases when λt ≳ 1, where λ is the radioactive decay constant and t the period of observation, the condition of stationarity is not satisfied. A statistical density function can be derived which describes the process of radioactive disintegration where the only fundamental property is independence. This we have called the Ruark-Devol statistical density function. An experiment, designed to test the validity of the two statistical density functions for different values of λt is described, distortions due to dead-time are avoided. On the basis of a chi-squared test it is concluded, with confidence, that the Poisson statistical density function is inadequate to describe the counting process when λt ≳ 1 and it is recommended that the Ruark-Devol function be used instead. In the limit of λt ⪡ 1 both functions are equally valid.