312 BELL SYSTEM TECHNICAL JOURNAL 



U = AI{pe/mrh) co s di, j 



= Mie/mc)(r-^)^|J(J -\- \)hl2ir cos Oi, j, ^ ' 



and using expressions based on equation (13) for the cosine. Finally 

 we should form the differences between the right-hand members of these 

 equations, and equate them to the observed energy-differences between 

 the states of the cluster, and solve for M. 



Even this formula, when applied to the data, gives values of M of the 

 same order of magnitude as do the more elaborate ones; otherv\^ise 

 there would be no point in quoting it. There is, however, very much 

 to be done to improve it. There is the magnetic field produced at the 

 nucleus by the spin of the electron. There is the alteration required 

 by relativity. There is the task of applying quantum-mechanical 

 rather than quasi-classical reasoning to the postulates. The pro- 

 cedure is strongly supported by the fact that it is copied from the 

 argument which, in the theory of the interaction between the spin and 

 the orbital angular momentum of the valence-electron, leads to a 

 wonderful explanation of the fine-structure of the hydrogen spectrum. 

 It is, however, certainly not perfect, since when applied to different 

 states of a particular kind of atom it is likely to lead to different 

 values of the nuclear magnetic moment, a result which either shows 

 some of the mathematical methods of approximation to be faulty or 

 else is a reductio ad absurdum of one or more of the postulates. The 

 problem is in fact one of the great unmastered problems of atomic 

 physics, and some believe that it is wrong to postulate that the nucleus 

 can be regarded, in its interactions with the extra-nuclear electrons, 

 as nothing but a simple magnet attached to a body having mass and 

 charge. I shall therefore say nothing further about it, except for 

 quoting the formula oftenest used in cases such as those of sodium and 

 hydrogen, where the energy-difference b in question (to follow the 

 notation of page 308) is that between the two members of a pair of 

 states for both of which L = and 7 = 5"= 1/2, while for one of 

 them F = I — J and for the other F = 1 -\- J: 



b = (87r/3) I ^1+J \ M(e//./47rwr)S^H0), (18) 



the last symbol standing for the square of the value which the Schroed- 

 inger wave-function has at the nucleus, which is known exactly for 

 hydrogen and approximately for other one- valence-electron atoms; 

 the formula is due to Fermi. Applying this formula to the values of b 

 for light and heavy hydrogen which they had ascertained by the 

 magnetic-defiection method (page 310), Rabi Kellogg and Zacharias 



