CONTEMPORARY ADVANCES IN PHYSICS, XXIX 301 



We now consider briefly the methods of determining the quantum- 

 number / of the nuclear angular momentum. 



{a) The ideal method is the one already described: investigate line- 

 clusters connecting state-clusters of as many different values of J 

 as there are; ascertain thus the number N of states per cluster; verify 

 that N is equal to (2 J + 1) whenever / is less than or equal to some 

 particular value Jm (say), and that it is equal to {2Jm + 1) whenever 

 / is equal to or greater than /,„• All this being verified, the value of / 

 must be Jm- 



One seldom if ever finds such a programme as this worked out very 

 fully. The difficulties seem to be that, at best, it is a lot of work to 

 analyze the hyperfine-structure of even one line, let alone a great 

 number; while at worst, lines connected with states of certain /-values, 

 high ones especially, may be quite unobservable; also there is the 

 striking fact that in a given spectrum a very few lines or even one 

 alone may have their hyperfine-structures spread out so much more 

 broadly than all the rest, that research is practically concentrated on 

 them alone. (One hears so much about 4722 of bismuth as almost to 

 have it blotted from mind that bismuth has other lines!) But of 

 course if one is willing to accept without test the rule for compounding 

 the vectors / and /, then it suffices to discover and analyze a state- 

 cluster for which N is less than (2/ +1). 



{b) The intervals between the members of a state-duster may give a clue 

 to tlie value of /. These intervals are of course energy-differences, and 

 the fact that they exist shows that there are forces between the spin- 

 ning nucleus and the system of revolving and spinning electrons which 

 surrounds it. If these forces are magnetic, then they may reasonably 

 be expected to vary as the sine of the angle di, j between the angular 

 momenta of nucleus and extranuclear electron system; for either the 

 magnetic moments of these two will be parallel to the respective angu- 

 lar momenta, or else (by the reasoning of page 297) their non-parallel 

 components will presumably change so rapidly as to be ineflFective, 

 leaving only the parallel components to be detectable. Comparing 

 the different orientations of / and J which correspond to the several 

 values of F and thus to the states of the cluster, one sees that their 

 energies — or rather, the parts Wp thereof which are due to the inter- 

 action — should then vary as cos 6i, j: putting for which the formula 

 based on (10) 



F{F+i) - 1(1 + I) - J(J+ 1) . 



