Sec. 13.10] STANDARDIZATION OF RADIOACTIVE SAMPLES 373 



readily obtained. However, since the method is not entirely foolproof, 

 it may be useful to consider some of the factors that influence the counting 

 rate, and some of the methods whereby simple and fairly reliable standardiza- 

 tion may be achieved for almost any radioactive isotope. 



Theoretical considerations as well as actual tests carried out with coin- 

 cidence counters make it fairly certain that each beta particle that passes 

 through the sensitive volume of a counter will be counted. The gas pressure 

 in most counters is made high enough to make certain that each beta particle 

 will make at least one ion pair. Similarly, a gamma ray will be counted if at 

 least one of its secondary particles passes through the sensitive volume. 



It is generally assumed that the sensitive volume is a well-defined space 

 within the counter. However, this is not strictly true. Measurements of 

 counter efficiency indicate that the apparent sensitive volume changes with 

 beta-particle energy in bell-jar counters [40]. Furthermore, these counters 

 are less sensitive in the region near the end by the window and in the region 

 close to the surface of the cathode (cylindrical electrode) than they are near 

 the anode (wire electrode). In order to avoid using the insensitive regions 

 of the counter a circular aperture about one-half the diameter of the counter 

 is placed in front of the counter window, as shown in Fig. 103. All beta 

 particles within the cone subtended by the aperture from a point source are 

 counted, provided that they have enough energy, penetrate the counter 

 window, and reach the sensitive volume. The aperture may be made in a 

 piece of brass plate thick enough to stop all beta particles. From Fig. 103 

 it is seen that the solid angle subtended by the aperture at the source is 



<E> = 0.5(1 — cos a) 



where tan a = - 

 a 



The value of <$ is more generally referred to as the geometrical efficiency. 



In performing measurements on beta particles it is important to keep in 

 mind the effects of multiple scattering. The importance of scattering on beta 

 particles may be emphasized by observing the tracks left by these particles in 

 a cloud chamber. They are observed to be deflected many times, often 

 through large angles. A complete study of the scattering process is not 

 available, but it is known that the beta particles are scattered both by nuclei 

 (Rutherford scattering) and by the atomic electrons. Sometimes the 

 scattering is inelastic, giving rise to x-rays (Bremsstrahlung). The scattering 

 and absorption phenomena are usually superimposed and together modify 

 the distribution and intensity of beta particles. 



The above "geometrical-efficiency" formula would be correct if the sample 

 were a point source and of negligible mass and if there were no air, window 

 and self-absorption, or scattering by supports. Since these conditions cannot 



