Sec. 2.3] GAMMA RAYS 37 



by considering the interaction as a classical two-body collision, derived the 

 following relation between the scattering angle and change in wavelength 

 (see Fig. 3): 



h 



V - X = — (1 — cos 4>) = 0.0242(1 - cos 0) angstrom 



m c ° 



where X', X = initial and scattered wavelengths, angstroms 



<j> = scattering angle 

 The factor h/m c = 0.0242 angstrom, known as the Compton wavelength, is 

 the shift in wavelength for any gamma ray scattered through an angle of 90 deg. 

 The scattering angle may take any value from to tt. Furthermore it is 



INCIDENT PHOTON / RECOIL ELECTRON 



RECOIL 

 PHOTON 



Fig. 3. Compton effect. A gamma photon is scattered by electrons as though it were a 

 particle. The scattered photon consequently leaves with less energy (longer wavelength) 

 and at a definite angle as required for conservation of energy and momentum in elastic, 

 two-body collisions. 



apparent that on the average after one or two collisions, high-energy gamma 

 rays are degraded to wavelengths in the order of a Compton wavelength. 

 Further scattering then has lessmarked effect, and the photon is more likely- 

 to be absorbed subsequently by the photoelectric effect. 



For gamma-ray energies corresponding to the soft x-ray region, Compton 

 scattering is negligible compared with the photoelectric effect, but at higher 

 energies, approximately 0.5 to 5 mev, it is the most important process in 

 gamma-ray absorption. For energies greater than this the scattering coeffi- 

 cient decreases slowly with energy and is rapidly superseded in importance 

 by pair production. Furthermore, since the electronic cross section is 

 independent of the atomic number of the absorber, scattering is relatively 

 more important in light than in heavy elements as compared with the photo- 

 electric effect and pair production, both of which exhibit strong dependence 

 on Z. 



