486 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 21 



material. The useful range, however, need not correspond to the total range 

 of the particle in the substance. When a threshold energy for the reaction 

 exists, that portion of the residual range in which the particle energy is less 

 than the threshold does not contribute to the reaction and might just as well 

 lie within the copper target plate. In estimating the target thickness, 

 therefore, a length equal to the threshold range should be subtracted from the 

 total range in the material. Any scattering effects in targets, particularly of 

 heavy elements and for low energies, would tend to increase the effective 

 thickness of the target. 



The ranges for protons, deuterons, and alpha particles are given for a 

 variety of substances in Chap. 4, but for those elements for which ranges 

 are not given, a rough approximation, good enough for this purpose, can 

 be obtained by extrapolating from the range-energy data for an element 

 of nearly the same atomic number given in the graphs. If R is the known 

 range of a particle at a particular energy in an element of atomic number Z , 

 the range R in another element with atomic number Z is 



R~R M? 

 ZN 



where N = number of atoms per cc of atomic number Z 

 N = number of atoms per cc of atomic number Z 

 When the target material is a compound or mixture, it is possible in many 

 cases to use an average atomic weight for computing the range by extrapola- 

 tion; then 



R Z No 



N 



2>i 



i = \ 



where fi = fraction of atoms with atomic number Z» in substance containing 

 11 atomic species 

 21.5. Synchro -Cyclotron. Early in the development of the cyclotron it 

 was pointed out that the relativistic increase in mass of an accelerated 

 particle would place a limit on the maximum energy derivable from the 

 conventional form of cyclotron [9]. With only a few per cent increase in 

 mass this effect becomes troublesome; the rotational frequency of the particle 

 decreases, and it arrives at the gap later each successive cycle. The phase 

 of the particle with respect to the fixed-frequency electric field decreases 

 until ultimately the particle crosses the gap at zero voltage and is no longer 

 accelerated. Although high energies can be imparted to charged particles 

 despite their reduction in angular velocity and the accompanying phase 

 shift, the dee voltage required to do this becomes prohibitively great. 



i 



