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THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1953 



the older theory up to now, but conscience obliges me to introduce the 

 new one. 



In the old theory, / is the nuclear angular momentum in terms of the 

 unit V2ir. Two of the permitted orientations, which I will call the 

 "extreme" ones, are straight along and straight against the field- 

 direction. For these, the projections of the angular momentum upon the 

 field-direction are -\-Ih/2Tr and —Ih/2Tr. For 'the proton / = M, and 

 the two extreme orientations are the only ones. 



In the new theory, the nuclear angular momentum in terms of the 

 unit h/2ir is \//(/ + !)• For the two extreme orientations, the pro- 

 jections of the angular momentum on the field-direction are +//i/27r 

 and —Ih/2ir, just as they were in the old theory. But now these orienta- 

 tions are no longer straight along and straight against the field-direction. 

 They must be inclined, one to the up direction and the other to the 

 down direction, at the angle of which the cosine is I/^s/I/{I -\- 1). 



Thus I has partly changed its meaning: it is still the maximum 

 permissible projection, upon the field-direction, of the nuclear angular 

 momentum in terms of the unit V^tt, and this is what it was before; 

 but it is no longer the magnitude of the nuclear angular momentum. 

 So also has /i changed a part of its meaning. It is the maximum per- 

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

 of the nucleus, and this it was before ; but it is not the magnitude of the 

 nuclear magnetic moment. The language of this subject has not been 

 well adjusted to this change. Fortunately I is called the "spin," which 

 does not necessarily convey the impression that it is quite the same 

 thing as angular momentum; but ^ is still called the "magnetic moment," 

 and in the new quantum mechanics this is a mistake. 



Fig. 4 is Fig. 3 redrawn in the spirit of quantum mechanics. The 

 arrows now represent angular momentum and magnetic moment jointly. 



PROTON 



2//pH 



Fig. 4 — Oriontutions and energy-levels of protons and dcuterons in a mag- 

 netic field, according to quantum mechanics. 



