The accidental $n$-fold coincidences ($n>\mathrm{}2\mathrm{}$), are of various kinds. The first kind involves $n$ events that accidentally occur nearly simultaneously. The second kind involves two events that are causally simultaneous, and $n-2\mathrm{}$ events that are accidentally nearly simultaneous; etc. For theoretical purposes, it is sufficient to treat only accidentals of the first kind, since the theory of the other kinds is very similar. It is also possible, for theoretical purposes, to replace each of the various coincidence circuits in actual use by the same schematic circuit. This consists of three parts: the counting, relay, and recording circuits. For $n$-fold coincidences, the relay circuit will contain $n$ relays (e.g. type 57 tubes). It is shown that the time constants (${\tau }_i$) of these relays determine the accidental counting rates. The time constants of the counting and recording circuits are not important in this connection. It is shown experimentally that each of the relays ordinarily has a different time constant, ${\tau }_i$, even though it is constructed of commercially identical parts. By the use of these results, it is shown that when $N_i$ particles per second traverse the $i\mathrm{th}$ counter, the rate at which accidentals of the first kind occur is given by $\{A_{1,2,\cdots n},=BC,\}\{B,=N_1{\tau }_1·N_2{\tau }_2·N_n{\tau }_n,\}\{C,=\frac{1}{{\tau }_1}+\frac{1}{{\tau }_2}+\cdots +\frac{1}{{\tau }_n}.\}$ The rates of occurrence of the other kinds of accidentals are readily deduced from this result by slight modifications. This formula is verified by experiment.

Close

PrevNext

View figure in article