362 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 13 



emission and disintegration rates of different radioactive isotopes will there- 

 fore depend to a considerable extent on the decay scheme of each isotope. 

 When one radioactive isotope has been satisfactorily standardized, generally 

 it cannot be used to serve as a standard for measurement of other radioactive 

 isotopes with different level schemes and different beta-particle and gamma- 

 ray energies. 



13.5. Standardization by Coincidence Measurements. By means of an 

 electronic circuit first developed by Rossi [7], it is possible to record simul- 

 taneous occurrence of pulses generated in Geiger counters with a resolution 

 of 10~ 7 sec. Coincidence counting was originally used as one method for the 

 study of the level schemes of radioactive isotopes. However, in radioactive 

 isotopes where the level scheme is completely known, this method may be 

 used to determine the absolute disintegration rate of such isotopes as well 

 as the efficiency of the beta and gamma counters. A review of the early 

 literature is given by Dunworth [9]; more recently various investigators 

 used the coincidence method for standardization, for example, M. Wieden- 

 beck [10]. 



A number of radioactive substances emit beta particles that are followed in 

 less than 10 -7 sec by one or more gamma-ray quanta. In some radioactive 

 substances the direction taken by the beta particle with respect to the gamma 

 ray that follows is isotropic; in others, as shown by Brady and Deutsch [8], 

 there may be a slight dependence on the angle. For the purpose of coin- 

 cidence standardization, however, the distribution should be isotropic. 



To derive the simple relationships necessary for this method, consider a 

 radioactive isotope emitting a single beta particle followed by a single gamma 

 ray. Denote the disintegration rate of the radioactive isotope by R, and 

 assume a beta counter counts at the rate B, a gamma counter at rate G, and a 

 coincidence device records beta-gamma coincidences at the rate C. Let us 

 further assume that the over-all efficiency of a beta counter is e$ and that of 

 the gamma counter e y . For the moment neglect the various corrections, 

 background, etc., and write the self-evident expressions for B, G, and C as 

 follows 



B = Re$ G = Re y and C = Re y e$ 



These relationships assume that there is no correlation between the direction 

 of each beta particle and the following gamma quantum and that only one 

 gamma ray follows the beta particle and is not internally converted. Solving 

 for ep, e y , and R, 



C C „ BG 



e " = G €y = B R = ~C 



In an actual experiment the quantities B, G, and C are obtained by taking into 



