Rate of n-fold Accidental Coincidences

Abstract

THE time-rate of an accidental coincidence (resolving time t) of n Geiger counters with time rates N₁, N₂ . . . N_n, is most easily obtained by classifying the coincidences according to the counter which goes off first. The time rate of each class is obviously N₁, N₂ N_ntⁿ⁻¹, and hence the total time-rate is R_n = n N₁ N₂ N_n ... N_n t^n–1as indicated by Jánossy¹. The present derivation shows that the formula is exact on the understanding that any two groups fulfilling the requirements are counted separately, even when they differ only by one of the n constituent pulses. But physical counting will as a rule distinguish at best such coincidences as differ with regard to all n constituents. That is how the terms of higher order in t mentioned by Jánossy come in. They are sort of a 'correction for overlapping'.