326 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 10 



this case only for accidental coincidence counts. Such counts may be 

 produced by the simultaneous arrival of several related particles as in cosmic- 

 ray showers or by the chance arrival of two independent particles in a time 

 of the order It due to a high radiation level such as exists near high-energy 

 accelerators. The number of accidental counts per minute to be expected 

 from a twofold coincidence arrangement is 



m = IfxiUiT cpm 



where »i, Th = average counts per minute independently from counters 1 

 and 2 

 r = resolving time of counters, min 

 For an r-fold coincidence arrangement, assuming the resolving times to be 

 equal, the accidental counting rate is 



m = rr r_1 (wiW2 • • • n r ) cpm 



If the resolving time of each of the counters in an r-fold coincidence set 

 is different, the accidental counting rate is [22] 



V"l To T r / 



m = 71)112 ■ • ■ n T TiT2 • • T r \ 1 h ' ■ ■ i — I cpm 



V"l To T r / 



If the radiation density is not high, the accidental rate can be determined 

 by dispersing the counters and counting the coincidences. Alternatively, 

 the accidental rate can be made negligibly small by increasing the multiplicity 

 of the system and by reducing the counter resolving time. Accidentals may 

 be further reduced by the proper use of anticoincidence counters; however, 

 their use decreases the counting efficiency because of the over-all increase in 

 resolving time of the set. 



10.19. Counter Efficiency. Aside from the counting loss due to the finite 

 resolving time, not all particles traversing a counter will produce discharges. 

 The efficiency with which a counter responds to incident particles can be 

 determined with a three- or higher fold coincident arrangement by counting 

 coincidences with and without the counter as a part of the system. The 

 absolute counter efficiency is then given by 



n r — m r 



n r -\ — m r -\ 



where n r = total counts in time / (or counting rate) of r-fold coincidence 

 arrangement, i.e., with tested counter included 

 w r _! = same but with tested counter removed 

 m r = accidental counts in time / (or counting rate) for r-fold coin- 

 cidence arrangement, i.e., with tested counter included 

 w r _i = accidental counts without tested counter 



