On the statistics of random distributions of paired events, with applications to the results obtained in the use of the interval selector with particle counters

Abstract

If a particle counter is subject to the radiation from a pure radioactive source of sensibly constant activity, it is axiomatic to suppose that the series of events constituted of the traversals of the counter by ionizing particles is a random series in relation to distribution in time. There are various reasons why the related series of events formed by the occasions on which the counter responds to these ionizing particles is not a random one—and there may also be cases in which the primary source does not, in fact, give rise to particles traversing the counter in a random sequence. The counter responses will necessarily depart from strict randomness in time because of the finite recovery time of the counter; they may also depart from strict randomness through a not uncommon counter defect, the occurrence of ‘spurious’ discharges correlated in some way with the ‘true’ discharges brought about as a result of the ionization produced by the particles. On the other hand, the original ionizing events will not have the effect of a random sequence, even with a pure radioactive source, if secondary radiations are emitted—even in a fraction of the disintegrations—with a time delay appreciable in relation to the counter resolving time, and, clearly, they may depart considerably from true randomness in time if the source is not a pure source, and, in particular, if there is produced in the source material a ‘daughter’ radioelement of lifetime comparable with this resolving time, or with the mean time between counter discharges.