PRINCIPLES OF RADIOLOGICAL PHYSICS 



87 



4-1. HEAVY CHARGED PARTICLES 



Rutherford's basic experiment described in Fig. 1-32 shows that sharp 

 deflections of heavy charged particles are quite rare. Hence it may be 

 assumed, as a first approximation, that these particles travel through 

 matter along straight tracks. 



Heavy charged particles dissipate their energy progressively along 

 their tracks in the course of a very large 

 number of inelastic collisions. Since 

 heavy particles with a kinetic energy of 

 the order of a few million electron volts 

 are not extremely fast, they experience 

 rather frequent energy losses. As men- 

 tioned before, the average distance be- 

 tween successive inelastic collisions is of 

 the order of 10 A in a material hke 

 water and 1000 times larger in air. 



As a particle dissipates its energy and 

 slows down, its rate of energy dissipa- 

 tion, i.e., the "stopping power" of the 

 material for that particle, varies as indicated in Fig. 1-37. When the 

 total energy dissipation by a beam of particles in successive layers of the 

 material is plotted against the depth of the layer from the surface, there 

 results a curve of the type shown in Fig. 1-52. This curve is called a 

 ''Bragg curve." As the depth of penetration increases, the curve of Fig. 

 1-52 is followed from left to right, the curve of Fig. 1-37 from right to 

 left. The "specific ionization" along the track of particles in a gas, i.e., 



Fig. 1-52. Rate of energy dissi- 

 pation ("Bragg curve") and mean 

 residual energy of an a particle 

 along its path in air. 



in 



o - 



o o 



O Q 



O O 



o 

 b 



o 



d 



ro 



RANGE IN WATER, cm 

 19^ PROTON ENERGY, Mev 

 RANGE IN AIR, cm 

 0.10 1.0 10 10^ 10^ 10"* 10^ 2x10^ 



Fig. 1-53. Range of protons of different energies in water and in air. (Courtesy 

 M. Lewis.) For extensive data on the ranges of heavy particles see Aron et al. (1949), 

 Bethe (1949), and Bakker and Segre (1951). 



the number of ion pairs produced per unit distance, is proportional to the 

 stopping power at a rate of approximately 30,000 ion pairs produced 

 per million electron volts of energy dissipated. Figure 1-52 also shows 

 the progressive average decrease of the particle energy in the course of 

 penetration. 



Figure 1-52 shows a dotted straight-line extension of the steepest por- 

 tion of the Bragg curve. The intercept of this dotted line on the abscissa 

 is generally taken as the value of the effective "range" of the particles, as 



