Refractivity and Atomic Interaction. 109 



where g> s , co a are as before. If their form (14) is used, then 



fl ,= 3(« 1 + « 2 )+3 i_ 4ft)lft)2 / W , • (24) 



and if the form (16) is used, in which the natural frequencies 

 are brought into evidence, then 



o)_2/JB j _ B, \ 1/ B' B" \ /9K . 



^"3l7i-7 72-7 1 3l 7 '-7 /-t'' * ( } 



where 5', i?" and 7', 7" are as in (17) and (18). Thus the 

 dispersion curve of an isotropic diatomic substance has four 

 singularities (to which as many absorption bands will corre- 

 spond), two inherent in the atoms, 7^ 7 2 , and two more, 

 7', 7", due to their interaction. In general, therefore, the 

 dispersion curve will be profoundly modified by the atomic 

 interaction. 



Subcase: Equal Atoms. — In this case we have7 1 =y 2 = 7 , 

 B 1 = B 2 — B, and B' = 2B, B" = 0, as has been shown before, 

 so that (24) becomes 



a >=| w o+| 1 _J o <> / gj R s, • • • (24 a) 



and (25). 



- »B(-?- + - T ^) ! 



vc 5 \7o — 7 7 —7/ 

 7' = 7 -2B/R 3 . 



i 



(25 a) 



The molecular refractivity, JY=^AIcoJd, of such a sub- 

 stance will have two singularities : one at 7=70 belonging 

 to each of the atoms, and another at 7 = 7', which is always 

 <7o and is due to the mutual action of the atoms. 



Notice that the denominator in (24 a) vanishes (a> becomes 

 infinite and iT imaginary) for 9f?R 3 = 2o) , that is, by (12), for 

 R 3 = 2B/(7 — 7), i.e. precisely for 7 = 7'. Thus, keeping the 

 incident frequency V7 constant and varying R *, we shall 

 have to remember that approaching the particular distance 



?'-(£)* (26) 



means that V7 is approaching the natural frequency vV 

 of the molecule, when the omitted " friction " terms must be 

 taken into account. In short, for that singular distance we 



* As in an example to be given in the next Section. 



