388 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1953 



sible projection upon the field-direction, of the magnetic moment of 

 the nucleus. But since these phrases are intolerably long, one avoids 

 them by saying that / is the spin and ju the magnetic moment of the 

 nucleus. In this sense, which to the users of quantum mechanics is a 

 distorted one, the words "magnetic moment" shall be used hereafter. 



The spin of the proton is 1/2, and so is the spin of the electron. Equa- 

 tion (4) degenerates into (3) for the electron and into (2) for the proton. 

 These we had already; what was then the point of introducing here the 

 general case? 



Well, the point is that two, or three, or several electrons may col- 

 laborate in what is known as "parallel coupling," though in the new 

 quantum theory it is not quite parallel. They behave as though they 

 formed a rigid unit, of which the spin is the sum of their spins and the 

 magnetic moment is the sum of their magnetic moments. Thus if there 

 are N of these electrons welded together (metaphorically speaking) it 

 comes to the same as though there were a single particle of spin A^ times 

 1/2 and magnetic moment N times Me • On putting these values of / and 

 /u into equation (4) we find ourselves right back at equation (3), which 

 is that for the individual electron. There is a single peak of magnetic 

 resonance composed of N coinciding peaks, and it is just where the 

 peak for a single electron would be. Thus in the ideal case, N electrons 

 coupled parallel behave just like one electron by itself. 



Such a conclusion may seem hardly worth the trouble of arriving at 

 it; but note the stipulation "in the ideal case." This refers to what has 

 been tacitly but obviously assumed till now, to wit, that no force acts 

 upon the electronic magnet except the big field H. But there are also 

 what I will call "local forces," forces due to fields within the sample 

 arising from other particles in the sample. These forces may, and they 

 often do, separate the N peaks which in the ideal case coincide. Often 

 one finds a flock of resonance lines where, or near where, there should be 

 only one; and if this is the explanation (which is not always the case, 

 for there are other causes of "splitting") then the number of lines in the 

 flock is the number of electrons coupled parallel. 



This illustrates one of the great contrasts between the electronic 

 resonance and the nuclear. Nuclear resonance is a "textbook phenom- 

 enon." The ideal case and the actual case are close together; the devia- 

 tions due to the local fields are neither trivial nor useless, but they are 

 not large enough to distort the simple laws, and it is quite permissible 

 to leave them out of a first presentation. But the phenomenon of elec- 

 tronic resonance is liable to be distorted almost beyond recognition; and 

 if one were to present only the cases in which the local fields are ncgli- 



