24 SECTIONAL ADDRESSES. 



For individual component terms : Aj=±l or 0, with ^=0 to j=0 

 forbidden. 



For systems of terms : Ar= ±2 or 0. 



Thus, according to the first rule, D terms may be combined with P or 

 F terms, but not with terms of types S or G. The second rule greatly 

 reduces the number of combinations which are arithmetically possible, 

 so that an FGr combination in the octet system, for example, does not 

 consist of 56 lines, but of 20 ; no individual term combines with more than 

 three other terms of the same set. Although more than one system of terms 

 may occur in the same spectrum, such systems are either all of odd or 

 all of even multiplicity,'^ and the third rule indicates that, in addition to the 

 ordinary combinations within the same system (Ar=0), there may be 

 inter-system combinations for which Ar=2. Thus, terms of a singlet 

 system may be found in combination with terms of a triplet system — still 

 subject to the azimuthal and inner quantum number restrictions — but 

 not with terms of a quintet system which might occur in the same 

 spectrum. 



In the more familiar spectra the components of multiple terms which 

 have the smallest j values have the highest actual values, corresponding 

 to deeper levels in the atom — i.e. 'n,.y < 'n,,. ^-.i. The more recent 

 analyses of spectra, however, have revealed the frequent occurrence of 

 ' inverted ' terms, for which the components with largest j values have 

 the largest actual values — i.e. '% > 'n,. j,-^. Such inverted terms are 

 especially numerous in the spectra of the elements of the later groups of 

 the periodic table, all the known terms of the iron arc spectrum (Fe I), 

 for example, being inverted. ' Partially inverted ' terms are also of 

 occasional occurrence. 



The general character of the regularities which appear in a group of 

 lines resulting from the combination of two multiple terms will be best 

 gathered from examples, which will at the same time illustrate applications 

 of the inner quantum rules. The examples chosen are PD and DF quartet 

 combinations from a recent analysis of the spectrum of ionised oxygen'' 

 (Table II). 



The table is almost self-explanatory, but it should be mentioned that 

 the sufSxes are inner quantum numbers, and that the numbers in brackets 

 which follow the wave-numbers representing the actual lines of the 

 spectrum denote the relative intensities on a scale of ten for the maximum. 

 The numbers printed in italics are differences of terms, or intervals 

 separating lines in the multiplets ; the slight departures from equality of 

 corresponding intervals are due to difficulties of observation. It should 

 further be noted that, while the relative values of the terms have been 

 determined with considerable accuracy, the actual values quoted above 

 are only approximate. 



Apparent exceptions to the first selection rule, A^-=Hhl, are of very 

 frequent occurrence. In the spectra of the alkaline earths there are 

 several groups of lines — some of them of great intensity — which do not 

 belong to the regular series, but are related to them through the character- 

 istic separations of the respective triplet systems, as was first recognised 



12 Neutral helium is possibly an exception. 



" A. Fowler, Roy. Soc. Proa., A, vol. 110, p. 497 (192G). 



