90 



ISOTOPIC TRACERS AND NUCLEAR RADIATIONS 



[Chap. 4 



the values of W for protons and alpha particles are 35 + 1.5 ev per ion and 36 

 ev per ion, respectively (see also Table 12). 



Table 12. Average Ionization Energy Required to Form One Ion Pair by Alpha 



Particles (7 mev) [31] 



4.10. Delta Rays. The recoil electrons produced by alpha particles, 

 observed in a Wilson cloud chamber as short, faint straggling tracks branch- 

 ing from the alpha track, are referred to as delta rays after J. J. Thomson 

 [17]. The maximum energy imparted to a recoil electron, which occurs in a 

 head-on collision, corresponds to twice the alpha-particle velocity or 



-Emax = 2mv 2 = 



Am E 



IF 



Thus, for a 10-mev alpha particle the most energetic delta ray will have an 

 energy of approximately 6,300 ev and a range in air of several millimeters. 

 The average number of ion pairs liberated by a delta particle of energy Ed 

 has been calculated to be [18] 



n 



(' + t) 



where / = ionization potential of absorber 



The number of delta rays produced and the distribution of their energy 

 depends in a complicated way on the particle velocity and on the kind of 

 absorber, and no satisfactory method for these calculations is available. 



4.11. Straggling of Charged Particles. The observed ranges of initially 

 monoenergetic particles of the same mass and charge exhibit a statistical 

 fluctuation or "straggling" about an average value. Two factors are mainly 

 responsible for straggling: (1) fluctuation in the number of ions produced per 

 unit path length, particularly near the end of the range where the charge of 

 the particle fluctuates; (2) statistical variation in the energy loss per ion pair. 

 By plotting the number of particles in a beam against distance from the 

 source, an integral range distribution or particle-range curve is obtained, as 

 shown in Fig. 19. Differentiating this curve results in a differential number- 

 range distribution curve which is the distribution of ranges about an average 

 value R . Because of the statistical nature of straggling this curve follows 

 to a close approximation a Gaussian distribution given by the following 



