32 



BEAMS OF HIGH-ENERGY PARTICLES 



but the additional multiple scattering introduced can become serious 

 very rapidly. Furthermore, the products of nuclear reactions occurring 

 in the initial stopping material can enter the tissue, thus destroying the 

 initial homogeneity of the beam. Another necessary precaution is to 

 make sure that the protons enter the tissue immediately on leaving the 

 vacuum chamber. Even a thin foil can cause an appreciable multiple 

 scattering that will diverge the beam rapidly in air. 



100 



80 



60 



40 



20 



10 



15 



Depth, cm 



Fig. 6. Comparison of depth-dose curves in water for various kinds of beam, all 

 adjusted to same maximum dosage density. 



It is interesting to consider just how the precision of a proton beam 

 depends upon the initial energy. Precision of the beam here means the 

 percentage spreading and straggling. To a first approximation, there 

 is no variation of the precision with energy or range. More accurately, 

 nuclear scattering causes the beam to spread out a bit more at high 

 energies — an effect already discussed — but this is offset, in part at least, 

 by the fact that the percentage spreading and straggling decrease very 

 slowly with initial proton energy. Thus a 150-mev proton beam has a 

 root-mean-square straggling of 0.94 per cent, while for 10 mev straggling 

 is 1.2 per cent. The percentage spreading varies similarly. 



Figure 1, showing the specific ionization of a single proton, would 

 indicate that the ratio of the ionization density at the Bragg peak to that 

 at the beginning of the range would be much greater for high energies. 

 It is true that the ion density decreases just as indicated, but the ioniza- 



