THE TARGET THEORY 



109 



X-rays • 



Alpha rays- 



Low LET 



High LET 



Fig. 50. A diagrammatic presentation of the difference between radiations. 

 The densely ionizing alpha rays produce a high linear energy transfer (LET). 

 The sparsely ionizing x-rays produce a low linear energy transfer. Thus every 

 alpha ray produces many ionizations within a particle, while a particle would 

 have to be very large for x-rays to produce at least one ionization in each particle. 

 More often, the x-ray produces no more than a single ionization (if that) in a 

 particle of a size found in typical biological experiments. 



LET concept differs from the number of ionizations per unit path length 

 by the factor of the energy transferred per ionization. 



For low LET (sparsely ionizing radiations, such as very high-energy 

 charged particles, x-rays, and gamma-rays) the probability of an ioniza- 

 tion's occurring within the organism is directly proportional to its thick- 

 ness, since the thicker the organism the more likely it is that an 

 ionization will occur before the incident particle has passed entirely 

 through the organism. (See Fig. 50.) Thus we can formulate the prob- 

 ability of producing an effect by irradiation as 



P = probability that the line of flight goes through the organism 

 X the probability that an ionization will occur within the 

 organism. 



The first probability, as we have already argued, is proportional to 

 the cross-sectional area A of the organism, and the second probability is 

 proportional to its thickness t. The total probability is proportional to 

 their product, At, which equals the volume of the organism. Thus low 

 LET particles produce an effect which is proportional to the volume of 

 the organism. 



If we utilize radiation at the other extreme of high LET (densely 

 ionizing particles, such as low-energy charged particles), then, as in 

 Fig. 50, every incident particle whose line of flight goes through the 

 organism will produce an ionization and therefore the biological effect 

 being observed. This amounts to setting the second probability factor 

 equal to unity. Then the total probability of producing an effect is pro- 

 portional to the area A of the organism. 



Consequently, if we do two separate irradiations with low LET 

 particles and with high LET particles, w 7 e obtain results whose ratio is 



