30 BEAMS OF HIGH-ENERGY PARTICLES 



its rest mass (934 mev). Also, because of its large mass, the proton does 

 not radiate secondary x-rays; consequently the straggling in range is 

 much less than for an electron. Similarly, multiple scattering is small 

 for protons. Thus a 150-mev proton has a range of 16 cm in tissue, the 

 mean range straggling is about 0.3 cm, and the mean lateral spreading is 

 about 0.6 cm^. Accordingly, it should be possible with 150-mev protons 

 to give a spherical volume of 1-cm diameter located 16 cm deep in tissue 

 several times the dosage of any of the neighboring tissue. It is a radio- 

 logical problem whether the much higher specific ionization at the end of 

 the proton tracks is advantageous or not. It should be emphasized that 

 at the peak of the ionization curve the protons have a broad energy dis- 

 tribution, the mean energy being about 20 mev. The specific ionization 

 of such protons is only several times that of fast electrons. Thus one 

 should not compare the radiological effects to those of recoil protons 

 produced by neutrons, for such protons have very much smaller energies, 

 less than 1 mev. 



Nuclear effects become pronounced at these energies. The proton 

 has a considerable chance of impinging on a nucleus of one of the atoms 

 of the tissue before coming to rest (about 30 per cent chance in going 

 15 cm). In that case it may go right on through, for nuclei are partially 

 transparent at these energies; it may exchange its charge with a neutron 

 and so become a neutron of the same energy and direction as the proton 

 before the collision; it may be scattered; or it may be absorbed. The 

 proton, in going past a nucleus, may also be diffracted or scattered 

 through a small angle. Quantum mechanically, the motion of a proton 

 is described by an associated wave, and the diffraction of this wave is 

 is exactly like that of sound or light around an obstacle. At these energies 

 the w^ave length of the proton is small compared to the size of the 

 nucleus and the scattering is predominantly forward. 



The nuclear effects all tend to flatten the sharp maximum in ionization 

 density that would obtain if only atomic straggling w^ere effective. Thus 

 the protons absorbed along the way excite the nuclei to such a high state 

 of energy that several short-ranged particles may come off, and these 

 will add to the ionization density at the point of disintegration. If the 

 proton exchanges into a neutron, that neutron may exchange back into 

 a proton farther on in the tissue and so contribute ionization beyond the 

 sharp cut-off — a small effect at energies near 150 mev. Large-angle 

 scattering of the proton is not too important; an occasional proton 

 leaving the beam cannot contribute much ionization elsewhere; but its 

 absence at the end of the range decreases the Bragg peak there. Dif- 

 fraction scattering can be the most important of the nuclear effects if 

 one is interested in confining a dose to the smallest volume possible. 



