54 



RADIATION BIOLOGY 



Since B depends upon the binding of the atomic electrons, we should more 

 properly introduce a separate value B\, B2, Bz, . . . , Bz ior each of the Z 

 electrons. The sum of these values can then be entered in Eq. (17) or (18) in 

 place of the factors Z and B. (The symbol B actually represents the mean of 

 the values of B for all electrons.) Therefore we write 



W _ .J 2TZ^e' 



t 



= A' 



mv^ 



(Bi + B, + B,+ 



+ B2) 



(19) 



Values of B for various conditions are not so readily available as we might wish. 

 Most of the effort has been devoted to the preparation of data of greater tech- 

 nical interest, namely, range-energy relations (see Sects. 4-1 and 4-2g). Figure 

 1-36 shows some illustrative data with special regard to the variation of £ as a 

 function of the energy of the incident particle. The value of B vanishes when the 

 incident particle is much slower than the atomic electron and the collisions are 

 all elastic. Thereafter B increases steadily because inelastic collisions can occur 

 under an increasing variety of conditions. The increase is rapid at first, then 

 slows down; it follows approximately a straight line if the energy is plotted on a 

 logarithmic scale. 



The variation of the stopping power as a function of the energy of the incident 

 particle results from the combined variations of the factor 2-KzH^lmv'^ and of the 

 stopping numbers B for the different electrons. The stopping numbers increase 

 monotonically as the energy increases, beginning at zero and then leveling off 

 gradually. The factor 2'KzH^lmv'^ decreases at first in inverse ratio to the energy, 

 since it is inversely proportional to v^, but then it stops decreasing as the velocity 

 V approaches the speed of light. The increase of B predominates at very low 

 energies, where B tends to vanish, and at very high energies, where l-KzH^lmv^ 

 becomes constant; the decrease of 2Trz^e* / mv"^ causes a characteristic decrease of 

 the stopping power at intermediate energies. Figure 1-37 gives illustrative data. 



(J) 



V) 



o 



>- 



U 



U. 



o 



UJ 



I- 



ev 



A 

 10 



2 



1 

 0.5 



0.2 



0.1 



0.05 



0.02 

 0.01 



Mev 



micron 



0.10 



0.05 



0.02 

 0.01 

 0.005 



0.002 

 0.001 

 0.0005 



0.0002 



100 I 10 100 I 10 100 I 10 



ev kev Mev bev 



ENERGY OF PENETRATING PARTICLE 



0.0001 



Fig. 1-37. Stopping power of water (rate of energy loss by inelastic collisions) for 

 electrons and protons of different energies. {Courtesy M. Lewis.) 



