92 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 4 



strictly homogeneous because particles emitted by atoms at various depths 

 are partially absorbed and scattered in different amounts before reaching the 

 surface of the source. However, from thick, homogeneous samples and from 

 thick targets in which the production of particles is uniform throughout the 

 target, the extrapolated range obtained from the measured number-range 

 curve gives a mean range that is representative of particles coming from the 

 surface [6]. Corrections must be applied in all other cases such as "semi- 

 thick" targets and sources where the thickness is comparable to the particle's 

 range and thick targets when the radiation producing the particles does not 

 penetrate the target with uniform intensity. 



4.12. Scattering of Charged Particles. Elastic scattering of heavy charged 

 particles is quantitatively accounted for on the basis of interaction between 

 the coulomb fields of the incident particle of charge ze and the struck nucleus 

 of charge Ze. It is assumed in such collisions that the particle does not 

 approach the nucleus so closely as to be affected by the short-range nuclear 

 forces since these fields result in a different kind of scattering. For alpha 

 particles the minimum collision distance appears to be approximately 

 2.05 X 10~ 13 yl w , where A is the atomic number of the struck nucleus. 



The simplest scattering occurs in collisions of particles with very heavy 

 nuclei, for then the struck nucleus remains virtually stationary during the 

 collision and the particle is deflected with little loss of energy and momentum. 

 Rutherford's formula expressing the number of particles deflected into a unit 

 solid angle at an angle 6 with the initial direction is then 



(ehZ V 



\2mv 2 J 



jsec 4 - 



where n„ = initial number of particles per cm 2 of the beam 



N — number of atoms per cc 

 z = charge number of particle 



Z = atomic number of scatt.erer 



m = mass of particle 

 Collisions of particles with nuclei of comparable or smaller mass must 

 be corrected for the contribution of energy to the struck nucleus which recoils 

 with an appreciable fraction of the initial kinetic energy of the incident 

 particle. The general Rutherford formula for the number of particles, n, 

 scattered into a unit solid angle at an angle 9 is 



(e 2 zZ\ , „ [cot 6 + Vcosec 2 - (m/M) 2 ] 2 



I J cosec d ■ 



\niv 2 / Vcosec 2 6 - (m/M) 2 



»(0) = n N ( — 5-1 cosec 3 6 



where n = initial number of particles per cm 2 of beam 

 M = mass of nucleus 

 m = mass of particle 



