298 BELL SYSTEM TECHNICAL JOURNAL 



electrons, their orbital momenta l\, h ■ ■ ■ are likely* so to orient them- 

 selves as to form a fixed resultant L, and their spin-momenta S\, 

 S2 • • • are likely to orient themselves so as to form a fixed resultant S\ 

 then L and 6' are likely so to orient themselves as to form a fixed 

 resultant J, following in so doing the rule of page 295. Considered as 

 quantum-numbers, / and 5 may have half-integer values only (1/2, 

 3/2 • • • ) or full-integer values only (0, 1, 2 • • • ) according as the number 

 of valence-electrons is odd or even, while L for any atom may have full- 

 integer values only. The three resultants are vectors of magnitudes 

 V/(/ + 1), V5(i -f 1) and VL(L + 1). The g-factor associated 

 with L is unity and the ^-factor associated with S is two, and the 

 value of g for the atom-as-a-whole is given by (12) with capital letters 

 replacing the small ones; so that the g-formula is verifiable with atoms 

 of all kinds, as I intimated before. A final point: one might expect 

 the conplexity to go on increasing tremendously from one end to the 

 other of the Periodic Table, but there is a counteraction. In all 

 atoms excepting the lightest, most of the electrons hav^e oriented their 

 orbits and their spins in such a way that they have interlocked them- 

 selves into groups or "closed shells" for which L is zero and 5 is zero 

 and / is zero and the magnetic moment is zero, as have the ten elec- 

 trons of the "cage" of the sodium atom to which I alluded. The so- 

 called valence-electrons are those few which have not been locked 

 into any such a cage. It is this quality which makes the Periodic 

 Table periodic; but this must be left for some other place. 



We arrive at last at the nuclear moment. 



Suppose that even with these spins and these orbital motions of all 

 the extra-nuclear electrons, we have not yet exhausted the internal 

 angular momenta of the atom, and that the nucleus itself possesses 

 one. Suppose, to be specific, that the nucleus has an angular momen- 

 tum with a quantum-number / and a magnitude •\'/(/ + l)(/?/27r), and 

 a propensity for orienting itself in distinct permitted directions with 

 respect to the other angular momenta of the atom. How shall we 

 detect this, and how shall we determine /? 



It is practically necessary to be yet more specific. One could 

 probably not tell a priori whether the nuclear angular momentum 

 would tend to orient itself with special respect to individual electron- 

 momenta, or with special respect to some resultant or in particular to 

 that grand resultant of all electron-momenta which we have denoted 

 by /. However, in the cases which have been successfully analyzed, it 



* This is the description of what is known as "Russell-Saunders coupling" or 

 " LS coupling"; in certain states of certain atoms, the mutual orientations of the 

 vectors conform to different schemes. 



