5G Dr. L. Silberstein on the Quantum 



A glance on the form of (21) and (21*2) will suffice to see 

 that the splitting and the modification of the spectrum due 

 to the a sphericity of the nucleus are of an entirely different 

 nature from the fine structure due to the relativistic com- 

 plications, i. e. due to the variability of the electron's mass,, 

 as obtained in (the second part of) Sommerfeld's paper, cited 

 above. 



After these generalities let us return to formulae (21), etc.,, 

 with the purpose of discussing them in some detail. These 

 formulae seem to deserve some careful attention, the more so 

 as their validity is by no means limited to a nucleus consisting 

 of two isotropic centres (which would be a somewhat puerile 

 assumption) but extends to a much larger class of cases, viz.. 

 to atomic systems with any axialhj symmetrical nuclei. In 

 fact, the whole set of our formulas will continue to hold in all 

 such cases without any formal alterations whatever, the only 

 difference being that a (appearing in 7) will have a different 

 or rather a more general geometrical meaning. The exact 

 meaning to be then attributed to a, which is not difficult to> 

 guess, will be explained in Section 5. 



Thus, returning to the last set of formula?, let us first note 

 that whatever the length a characterizing an axially sym- 

 metric nucleus, it appears only through 7, (21*1), where it is> 

 divided by another, practically universal length. Let us- 

 estimate this length, L e. 



1=-^=—- so that 7 = 2/e T , 

 lick I 



k being always the number of ^-charges contained in the 

 whole nucleus. Now, in c.G.s. units, <? = 4"7.10~ 10 , c = 3.10 10 , 

 /i = 6 , 5.10~ 27 , and the Rydberg "constant," even allowing 

 for the slightly different values of m' as distinguished from 

 m \_cf. formula (2)], can safely be assumed to be always of 

 the order i? = lT0.10 5 . Thus, * 



Z = l-03.10- 8 cm., 



or almost just one A.U. If, therefore we write, for con- 

 venience, 



a = a A.U., 



the value of the coefficient in question will be 



7 = 2*«, ........ (22) 



which reads : 7 equal to twice the number of Angstrom 

 units contained in a multiplied by the total number of 

 electronic charges contained in the nucleus. 



Now, a is certainly but a fraction (and the very validity 



