PHOTONS AND ELECTRONS 39 



the "virtual P state " must be supposed to have energy superior to that of 

 the D state, though in the previous paragraph the real P state is supposed 

 intermediate between S and Z), as is usually the case.) 



I must remove the impression possibly left by my phrasing, that an 

 atom or molecule has only three states with these peculiar interrelations. 

 As a matter of fact, there is a great number of S states, a great number of 

 P states, a great number of D states, and various other categories; tran- 

 sitions can occur between any P state and any >S or D state, but they 

 cannot occur between any S state and any D state, or between any two 

 states distinguished by the same letter. The art of analyzing spectra 

 consists largely in classifying states according to their relations of per- 

 mitted or forbidden transitions with other states. The rules of the 

 classification are called "selection principles" and in many cases are 

 admirably explained by the contemporary atom models. 



SCATTERING OF X-RAYS WITH CHANGE OF FREQUENCY: COMPTON 



EFFECT 



We have already become acquainted with two of the interactions 

 between X-rays and matter: true absorption in atoms, and scattering 

 without change of frequency. A third and important interaction has 

 features in common with the former, and also with the Raman effect 

 which we have just been considering. Like true absorption, it involves 

 the ejection of high-speed electrons from the matter; but these are 

 originally the most loosely bound of the electrons in the atoms, or perhaps 

 some of them are actually the "free" electrons roaming in the substance 

 (there is no sharp distinction between these two classes), while true 

 absorption often involves the ejection of tightly bound electrons such as 

 the K electrons. As in the Raman effect, the photons themselves are not 

 totally absorbed but reappear with lessened energy and lessened frequency. 



This Compton effect may be interpreted as an elastic impact between 

 corpuscles of matter and corpuscles of light, and as such it is the most 

 beautiful example of a phenomenon amenable to an extreme corpuscular 

 explanation and the most beautiful demonstration of equations {1) and {2) 

 as applied to Hght. I now develop the equations of elastic impact 

 between electrons and photons, employing the expressions for energy and 

 momentum of material particles (such as electrons) which are used in 

 relativistic mechanics, ^^ and assuming the electrons to be initially 

 stationary and free. The symbols v, X refer to the incident X-rays 

 (photons before impact); v' , X' to the scattered X-rays (photons after 



" As many a physicist must have found out for himself, the attempt to make the 

 equations look simpler and be more easily solvable by using ordinary mechanics has 

 precisely the opposite effect from that desired. The theory of the Compton effect 

 affords one of the cases where the wisest policy is also the easiest. 



