compton: size and shape of electrons 3 



is supposed to be in the form of rigid spherical shell, incapable 

 of rotation, a simple calculation shows that the mass absorption 

 coefficient due to scattering is given by 



l = ^^sin^(^i^y, (2) 



p 3 m'^C' V X / V X / ^ ^ 



where a is the radius of the spherical shell and X is the wave- 

 length of the incident beam. For long waves this becomes iden- 

 tical with equation (1), but it decreases rapidly as the wave- 

 length approaches the diameter of the electron, as is shown in 

 curve I, figure 1. Such an assumption is therefore able to ex- 

 plain at least qualitatively the decrease in the absorption for 

 electromagnetic waves of very high frequency. 



It would appear more reasonable to imagine the spherical shell 

 electron to be subject to rotational as well as translational dis- 

 placements when traversed by a 7-ray. The scattering due to 

 such an electron is difficult to calculate, but an approximate 

 expression can be obtained if the electron is considered to be 

 perfectly flexible, so that each part of it can be moved inde- 

 pendently of the other parts. On this hypothesis it can be shown 

 that the intensity of the beam scattered by an electron at an 

 angle d with an unpolarized beam of 7-rays is given by the 

 expression 



If) = I — ^ < sm^ sm - / sin^ - >• (3) 



^ 2rWC* LWJ V X 2// 2j ^ ^ 



Here / is the intensity of the incident beam, r is the distance at 

 which the intensity of the scattered beam is measured, and the 

 other quantities have the same meaning as before. The mass 

 absorption coefficient due to scattering by such an electron is 

 therefore 



- = 2xAV r^smedd. (4) 



p J I 



This integral may be evaluated graphically or by expansion 

 into a series. The values of a/p in the case of aluminium, tak- 

 ing the numbers of electrons per atom to be 13, are plotted in 

 curve II, figure 1, for different values of a/X. The values for a 



