PRINCIPLES OF RADIOLOGICAL PHYSICS 



117 



To calculate the distribution of energy transfers from neutrons to heavy 

 charged particles, we must proceed, in essence, as we did for the X rays in Eqs. 

 (44) and (45). One must multiply the probability of collision per unit length of 

 path by the average kinetic energy T imparted to heavy charged particles in each 

 collision. To calculate T, one should break down the value of n into components 

 jia, /Xfc, . . . , corresponding to the various possible types of collision, a,b,c, . . . , 

 then evaluate T for each type of collision separately, and finally add again: 



IjlT = fiaTa + flbTb + fx/fc + 



(47) 



Data for this detailed analysis are often inadequate, and we must resort to crude 

 estimates. In the simple case of collisions with the nuclei of ordinary hydrogen 

 (protons), T equals one-half the energy of the incident neutrons. 



The rate of energy transfer to heavy charged particles per unit volume and per 

 unit time equals the product of ju'T and of the neutron flux at the point of interest: 



nTN(x) 



(48) 



Since fi. and T depend on the energy of the neutrons, the fluxes of neutrons of 

 different energies must be considered separately. The contributions of the cor- 

 responding energy transfers are then added. The result expresses the energy 

 transfer per unit volume or per unit mass of material, depending on whether ^ 

 represents the linear or the mass absorp- 

 tion coefficient. 



A considerable amount of y radiation 

 originates from the nuclei of a material 

 as a result of neutron collisions. The 

 eventual capture of a neutron by a nu- 

 cleus of medium or high atomic weight 

 takes usually the form of an {n,y) reac- 

 tion. The (n,7) capture is normal in 

 hydrogen and yields a photon of 2.23 

 Mev. Gamma rays also follow the in- 

 elastic {n,n) processes. 



Detailed data on the intensity and the 

 spectrum of these 7 rays are still quite 

 scarce. Figure 1-76 gives some data on 

 this subject. 



The 7 rays produced by neutron cap- 

 ture are, as a rule, as penetrating as, or 

 more penetrating than, the neutrons 

 themselves. Therefore the distribution 



in space of the energy dissipated by these 7 rays does not parallel closely the dis- 

 tribution of the nuclei from which the 7 rays originate. This can be done in 

 the same way as the calculation of the neutron production of heavy charged 

 particles. Then the 7-ray penetration away from the 7-ray source is treated 

 as an entirely separate problem, by the methods discussed under the heading 

 of X-ray penetration. 



The (8 rays emitted by the radioactive nuclei which result from neutron col- 

 lisions have energies of the order of 1 Mev. Therefore the /3 rays travel much 



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ENERGY, Mev 

 Fig. 1-76. Sketch of the energy spectra 

 of the 7 rays emitted from aluminum 

 and iron following the captvire of a 

 neutron. {Hamermesh, 1950.) 



