PRINCIPLES OF RADIOLOGICAL PHYSICS 51 



regarded as slow when the incident particle moves more slowly than 

 the atomic electron, but even a fast particle exerts a slowly variable dis- 

 turbance if it passes too far away. 



The electric force between the incident particle and each atomic elec- 

 tron tends to produce an effect basically similar to that of Rutherford 

 scattering. In fact, if the electron receives a recoil energy much larger 

 than its binding energy, it recoils just about as though it were free (see 

 Sect. 2-2), according to the law of Rutherford scattering indicated in 

 Sect. 2-2c. A collision in which the electron recoils with a large energy 

 may be called a "knock-on" collision. It implies a close approach of the 

 incident particle to the recoiling electron and therefore it occurs rather 

 infrequently. 



A high-velocity incident particle still exerts a sudden blow, which may 

 result in a fast inelastic collision, even though it passes far away from an 

 atom. The effective "radius of action" may range up to distances of the 

 order of 10~^ cm = 1000 A, i.e., a thousand times as large as the size of 

 an atom. The action of such "glancing collisions" resembles the action 

 of electromagnetic radiation because it results from an electric force 

 whose strength is fairly uniform over a whole atom but varies rapidly in 

 the course of time. 



The sudden blow received by an atomic electron in a glancing collision 

 causes the electron to start oscillating with any of its characteristic fre- 

 cjuencies. The electron may therefore land in any of its excited sta- 

 tionary states, or it may leave the atom, as in the photoelectric effect, 

 according to chance. Still, most of the atoms exposed to a glancing dis- 

 turbance remain eventually in their normal state, as is the case when they 

 are exposed to electromagnetic radiation. 



2-4b. Energy Dissipated in Inelastic Collisions. The qualitative arguments 

 just presented regarding the mechanism of inelastic collisions serve also as a basis 

 for evaluating the quantitative effect of these collisions. 



The average amount of energy dissipated by a particle in a great many col- 

 lisions is an important index of the total effectiveness of the particle. As pointed 

 out by Bohr, the total energy dissipation does not depend much on the binding of 

 the atomic electrons but can be calculated, in essence, as though the electrons 

 were free and all fast collisions were of the knock-on type. 



Accordingly, in order to calculate the energy dissipated by a particle, 

 we may start from Eq. (14) for the probabihty of colhsions which cause a 

 free particle to recoil with energy Q. The expected energy dissipation in 

 collisions in which the recoil energy ranges from Q to Q + 5Q is the 

 product of Q and of the probability P(Q) 5Q of this kind of collisions. 

 The expected energy dissipation in collisions ranging between wide 

 limits, Qmi„ and Q„^^, equals the sum, or rather the integral of QP{Q) BQ 

 over all intervals 8Q from Q„i„ to Q^^^. The result of this calculation, 

 starting from Eq. (14), is 



