THE time-rate of an accidental coincidence (resolving time t) of n Geiger counters with time rates N1, N2 . . . Nn, 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 Nntn−1, and hence the total time-rate is Rn = n N1 N2 Nn ... Nn tn–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'.
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Jánossy, L., NATURE, 153, 165 (1944).
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SCHROEDINGER, E. Rate of n-fold Accidental Coincidences. Nature 153, 592–593 (1944). https://doi.org/10.1038/153592b0
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