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THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1953 



76°13' to the vertical, and that it can absorb a quantum hv of just the 

 right energy to turn it to the angle 118°36'. This would have led to the 

 inference that instead of absorption confined to the fieldstrength hv/2yLp 

 corresponding to the actual peak, there would be absorption at every 

 fieldstrength from hv/2yLp on upwards toward infinity. The experiment 

 frustrates this inference, and so declares for the two and the only two 

 permitted orientations. One did not have to wait for this experiment to 

 learn this fact: it has been known for thirty years, both as a consequence 

 of quantum mechanics and as a fact of experience. However this is a 

 very pretty proof of it. 



We now must generalize equation (3) so as to make it take care of 

 all nuclei and not the proton only; and in the course of this process we 

 shall meet the actor behind the scenes who determines the permitted 

 orientations. His names are spin and angular momentum. 



THE GENERAL EQUATION FOR NUCLEAR MAGNETIC RESONANCE 



We are now en route to the general equation of which (3) is the 

 special case appropriate to the proton. Our first step takes us to the 

 deuteron or nucleus of heavy hydrogen. Its magnetic moment differs 

 from that of the proton, so we must write Md instead of jxp . More sig- 

 nificant is the fact that the deuteron has three permitted orientations in 

 the big field instead of two. The orientations of proton and deuteron are 

 shown in the first and third columns of Fig. 3; beside them are horizontal 

 lines depicting their energy-values, energy being measured vertically 

 upward from an arbitrary zero. 



One guesses from the aspect of Fig. 3 that the deuteron will show 

 three peaks of magnetic resonance ; for it seems possible for the deuteron 

 to be turned from orientation a to orientation 6, from 6 to 2 and from a 

 all the way to z. But of these three conceivable "transitions" the third 



Fig. 3 — Orientations and energy -levels of protons and deuterons in a mag- 

 netic field, according to the "old" quantum-theory. 



