Sec. 3.6] BETA PARTICLES 55 



subsequent ionization by the primary ions and that produced by Brems- 

 strahlung or x-rays emitted from the initial particle. In general, the range of 

 the secondary ions is a fraction of a millimeter so that the majority of ions lie 

 close to the path of the beta particle. The total ionization, however, usually 

 amounts to at least several times the primary ionization produced directly by 

 the initial particle. Differentiation between primary and secondary ion- 

 ization is possible only in the Wilson cloud chamber with properly controlled 

 expansion. When expansion takes place just before the electron traverses 

 the chamber, the number of drops formed per unit length of path corresponds 

 to the specific primary ionization. Under this condition secondary ions 

 cannot diffuse sufficiently far to form separate drops but rather coalesce into 

 a single drop containing the primary ion. If, on the other hand, expansion is 

 delayed, the ions can diffuse far enough from one another to form separate 

 drops and thus indicate quantitatively the total specific ionization. 



The intensity of ionization is greatest (50 to 200 ion pairs per centimeter 

 path in air) at very low beta particle velocities and decreases with greater 

 velocity until a minimum value is reached when the energy is in the order of 1 

 mev. For energies greater than 1 mev, the specific ionization increases 

 very slowly, roughly as log E, but for practical purposes, in the energy range 

 1 to 10 mev, it remains essentially constant at approximately 25 ion pairs 

 per centimeter path in air at normal temperature and pressure. 



The average energy absorbed from a beta particle in the formation of an ion 

 pair has been shown to be independent of velocity for energies greater than 

 0.01 mev. The value for air has been carefully measured, and its best value 

 is given as 32.5 ev [22,23]. The energy absorbed per ion pair at low velocities 

 is somewhat larger. For the energy range 300 to 60,000 ev Gerbes [24] gives 

 the following formula for the value of W in air: 



S 27 

 W = 31.62 + ^- ev 



E — I 



where E = beta-particle energy, kev 



I = ionization potential (1.7 X 10 -2 kev) 

 3.6. Relative Stopping Power. The relative stopping power 5 is defined 

 as the ratio of the rate of energy loss in one substance to that in another sub- 

 stance, usually air. It is seen from the stopping formula for ionization energy 

 loss that 5 should be relatively independent of velocity but strongly dependent 

 upon the electronic density and to some extent on the average excitation 

 potential of the medium. Considering only the stopping power per electron, 

 the value of S e in the range from hydrogen to copper decreases about 20 per 

 cent [22] while, for any one substance, the variation with velocity is approx- 

 imately 8 per cent in the energy range 0.1 to 2.0 mev [22]. 



