324 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 10 



is given by Volz [41] and Schiff [39] as 



n = Ne~ TN cpm 



It is derived on the assumption that the occurrence of an event while the 

 device is recovering from previous count is not counted but has the effect 

 of prolonging the recovery as though it had been counted. It is evident 

 from this that as the true activity increases without limit the recorded 

 counting rate goes to zero; the device becomes blocked and no counts are 

 passed. At low counting rates, however, the difference between this and the 

 preceding formula is negligible and either one can be validly used. 



It is tacitly assumed in applying these formulas that the resolving time 

 of the counter tube is longer than that of all components of the circuits 

 which follow, including that of the register divided by the scaling factor. 

 If this were not true, the formulas above would not be valid since the resolving 

 time of such components would also influence the amount of the correction. 

 Fortunately this requirement is met in modern counting circuits, for the 

 exact calculations in this case prove to be impracticable. 



Nevertheless, at very high counting rates the correction formulas above 

 are not sufficiently accurate to give reliable values for the true counting rate. 

 Consequently it is often necessary to construct a calibration curve with the 

 requisite accuracy extending to very high counting-rate levels. This can 

 be done analytically with any prescribed accuracy by expressing the true 

 counting rate in terms of a power series in n, the recorded rate, of the form 



N = n + rn 2 + vn 3 + ju^ 4 H~ * ' * cpm 



An arbitrary number of terms may be used, depending upon the desired 

 accuracy, but the labor involved in computing the coefficients of terms beyond 

 the fourth usually makes the inclusion of higher order terms impracticable. 

 The coefficient of the first term is unity because at very low counting rates 

 N c^n. The second coefficient is the counter resolving time. The physical 

 significance of higher order coefficients is less clear other than that they are 

 coefficients of higher order moments which take into account variations from 

 the simple quadratic curve due to second-order effects that influence the 

 counting rate. 



Kohman [33] has presented in detail a method for evaluating the coeffi- 

 cients from a least-squares solution of measurements on paired sources. 

 Each set of measurements includes the recorded counting rates n\ of source 

 I, »2 of source II, which is approximately equal in activity to I, their com- 

 bined rate n^, and the background count % (see preceding section for 

 experimental procedure). For the greatest accuracy, many sets of measure- 

 ments should be made with paired sources covering the entire counting range. 



