308 BELL SYSTEM TECHNICAL JOURNAL 



We have seen that in the absence of magnetic field, the normal state 

 is subdivided into two by the influence of the nuclear angular mo- 

 mentum / and its coupling with /. In one of these — call it A'^' — the 

 vectors / and / are nearly parallel, and their resultant, the angular 

 momentum ^Fof the atom-as-a-whole, has the quantum number (7 + /) 

 which is (/ + !); in the weak field where the coupling is not broken, 

 and the state N' maintains its identity, the number of permitted 

 orientations is {2F -f 1) which is (2/ + 2). In the other — call it 

 N" — the vectors I and / are nearly anti-parallel, and F has the quan- 

 tum number (/ — |) ; in the weak field the number of permitted 

 orientations is {2F -f 1) which is 27. Adding, we get for the total 

 number of magnetic levels the value (47 -\- 2), which is equal to 

 (27 + 1) (2/ -f 1) as I stated. In the weak field, the different 

 levels are distinguished by their values of the magnetic quantum- 

 number m, which is defined by saying that the projection F^ of the 

 angular momentum (of the atom-as-a-whole) on the field-direction is 

 equal to w(/z/27r). The permitted values of m are (7 + ^), (7 — \), 

 (7 - f) • • •, - (7 - i), - (7 + i). The first and the last of these 

 values are attached each to a single level, belonging (in the weak 

 field) to the state N' \ each of the others is attached to a pair of levels, 

 one belonging to the state N' and the other to the state N" . 



We know that each of these levels maintains its identity as the 

 field-strength is increased, even when the coupling of 7 and J into F 

 is broken down and the separate states N' and N" lose their identities. 

 We wish to know how the value of M^ for each level is varying as the 

 field increases. Leta stand for 2w/(27 -f 1) ;let6standfor theenergy- 

 difTerence between N' and N" ; let g stand for the g-f actor associated 

 with the extra-nuclear electron-system and with the angular momentum 

 /; let X stand for (glb){eH/2mc){liJ2Tr). The formulae of Breit 

 and Rabi are as follows ^ : 



^- = ± 2(1+ It + .')■'- «(^/^'-)("/2.) (16) 



For the levels characterized by the extreme values of m{viz., ± (7 + ^)) 

 and initially belonging exclusively to N', the first factor is equal to one 

 half and the two levels are distinguished by the two choices of sign, 

 and Mz is independent of field-strength. With respect to the other 

 values of m, the situation is more complex and curious. A single value 

 of m, say (7 — ^), corresponds to two different values of Mz which are 

 equal in magnitude and opposite in sign; the opposite value of m, 



* Perhaps it is not superfluous to remark that in the factor {e/2mc), the symbol ni 

 always stands for electron-mass, never for magnetic quantum-number. 



