304 BELL SYSTEM TECHNICAL JOURNAL 



is somehow broken away from its interlocking with the system of 

 extra-nuclear electrons; not in the sense that it is torn out of the 

 system or that its electrostatic attraction for the electrons is sus- 

 pended, but in the sense that somehow or other the rule for the com- 

 pounding of / and / into various values of a resultant vector F is done 

 away with. The system of electrons with its angular momentum J 

 chooses among (2/ + 1) orientations with respect to the field, just as 

 if the nucleus were not there; and the nucleus chooses among (2/ -f 1) 

 orientations with respect to the field, just as if the electronic system 

 were not there. Nucleus and electrons, / and /, are said to be "de- 

 coupled" from each other; it is supposed that their angular momenta 

 precess each at its own rate separately around the direction of the 

 field.6 



This account suggests that the energy-values of the magnetic levels 

 would be given by the various values of the expression 



M,H cos dj, H + Mnll cos di, H, (14) 



where dj, h and Or, h stand for the inclinations of the angular mo- 

 menta / and / with respect to the field-direction, while M^ and M„ 

 signify the magnetic moments of the extra-nuclear electron-system 

 and of the nucleus, or, if these magnetic moments be not parallel to 

 / and / respectively, then their projections upon the directions of J 

 and /. The different groups of levels would then correspond to 

 different permitted values of cos Qj^ h, the different levels of any one 

 group to different permitted values of cos di, h- The first term, one 

 might say, would determine the (2/ -f 1) separate energy-values which 

 would occur if there were no angular momentum of the nucleus, while 

 the second term would subdivide each of these into a group of (2/ -f 1) 

 levels. 



It is found, however (as we shall later see) that the magnetic mo- 

 ments Mn of nuclei are always so very small by comparison with those 

 of extranuclear electron-systems, that the second term of (14) is 

 quite negligible. We have therefore to look for some other cause for 

 the observable subdivision. This cause is thought to be the force 

 between the moments of the nucleus and the electron-system. We 

 assumed it to be overborne by the strong field in so far as its ability to 

 control the quantized directions of the angular momenta is concerned, 



^ The analogy of / and / with L and 5 is restored when the impressed field is very 

 strong, for then L and 5 are similarly decoupled from one another—" Paschen-Back 

 effect" as distinguished from the "Zeeman effect" which we have hitherto been con- 

 sidering. Thus it is roughly correct to say that hyperfine structure reacts to a weak 

 magnetic field as fine structure does to a strong one, though this statement should 

 be carefully qualified if use were to be made of it. 



