PRINCIPLES OF RADIOLOGICAL PHYSICS 57 



The electrons which escape with an amount of energy E much larger than their 

 binding energy I should be regarded as resulting from knock-on collisions. 

 Therefore , the expected number of these electrons must be given directly by Eq. 

 (14). The numl/er of knock-on electrons which receive an energy between 

 Q ^ E + Ii and Q + 8Q = E -\- h -\- 5E \s given by 



[91i(E)]ko 8E = Nt ?^ Tp^^, (24) 



Comparison of Eqs. (23) and (24) indicates the following relation: 



''^^^^%wh^^ whenS»7> (25) 



The value of the riglit-hand side of Eq. (25) is indicated by the dotted line in 

 Fig. 1-38. 



The excess of lower energy electrons, over the number expected on the basis of 

 knock-on processes only, may be loosely regarded as the result of glancing col- 

 lisions. This excess is very large because the total number of glancing collisions 

 is much larger than the number of knock-on collisions (roughly in a ratio of B to 

 1). Glancing colhsions are unlikely to result in the ejection of electrons with 

 energies E ^ I, for the same reason as that which makes the ejection of high- 

 energy photoelectrons unlikely (see Sect. 2-3). 



The maximum energy of the ejected electrons is set by the conditions of con- 

 servation of momentum and energy in a knock-on collision. If the incident 

 particle is heavy (proton, a particle, etc.), it can impart to an atomic electron up 

 to twice its own speed, and therefore only a small fraction of its own kinetic 

 energy. Thus, for example, if the incident proton has an energy of 1 Mev, the 

 maximum energy of ejected electrons equals 2200 ev. 



On the other hand, if the incident particle is itself an electron, it may share any 

 fraction of its energy with an atomic electron in the course of a collision. When 

 the two energies are comparable after the collision, the faster of the two electrons 

 is usually called "primary" and the slower one, "secondary"; this convention 

 amounts to fixing the upper limit to the energy of the ejected electrons at one- 

 half the energy of the primary. 



The ejected electrons constitute a new, "secondary," corpuscular radiation 

 and therefore receive the name of "secondary electrons." The aggregate energy 

 of this radiation amounts approximately to two-thirds of the energy dissipated 

 by the incident, or "primary," radiation. This fraction is a little lower than two- 

 thirds when the dissipation takes place in the lightest elements, which have no 

 internal electrons, and amounts to about one-half in hydrogen. 



2-4d. Excitation of Atomic Nuclei. We consider here the effect of the impact of 

 fast electrons upon atomic nuclei, and also the effect of the impact of protons 

 and other heavy particles if they remain outside the range of attraction of nuclear 

 forces. Electrons cannot impart a strong recoil to individual nuclear particles 

 because of their low mass; protons cannot either unless they come close to the 

 nucleus. Therefore the collisions we are dealing with can be treated as glancing 

 collisions. 



The probability of these glancing colhsions can be estimated utilizing data on 



