374 



ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 13 



be achieved in practice, it is necessary to take them into consideration and 

 make detailed corrections for each factor. Most of the corrections have 

 empirical bases because it would be difficult to make exact calculations of 

 the combined absorption and scattering effects. 



When absorbers are placed between counter and source and the counting 

 rates are plotted against absorber thickness, the well-known absorption curve 

 is obtained. Near the end of this curve at large absorption thicknesses, the 

 logarithm of the number of transmitted beta particles is, in many instances, 



5000 



4000 



tu 3000 



3 



Ul 



a. 



52 2000 - 



z 



3 

 O 



o 



1000 



EXTRAPOLATION 



■WINDOW AN0 AIR 



PATH CORRECTION 



O 12 24 36 48 60 72 



2 



MG PER CM ALUMINUM 



Fig. 104. Typical aluminum absorption curve for RaE. The units of abscissa represent 

 only the thickness of aluminum absorber. To this must be added the equivalent aluminum 

 thickness of the counter window and of the mean path of the particles in air. The extra- 

 polation shown is subject to considerable uncertainty. [Redrawn from L. R. Zitmwalt, 

 U.S. Atomic Energy Commission Report MDDC-1346, 1947.] 



proportional to the thickness. At very small absorber thicknesses this 

 relationship does not hold. In fact, theoretically one would expect the 

 absorption coefficient to be zero at very small absorber thickness because of 

 the shape of the Fermi distribution of beta-particle energies. A typical 

 absorption curve is shown in Fig. 104. Scattering plays an important role 

 in the shape of the absorption curves. Hence there is no well-defined 

 "accepted" absorption curve for any radioactive isotope since the curves 

 vary markedly with the experimental arrangement. It is customary to use 

 extrapolation procedures for correcting the effect of window absorption 

 on the observed beta-particle counting rates [16]. Starting with the counter 

 window as the only absorber additional aluminum absorbers are added in 

 steps; then assuming that the absorption curve is logarithmic, it is extra- 



