44 RADIATION BIOLOGY 



theory and experiment are in agreement that energy transfer does take 

 place in this way over very long distances. Possibly further investigation 

 of the cases cited will demonstrate that these phenomena are artifacts, 

 perhaps due to molecular association. There seems no reason to doubt 

 that the coupling of electric fields is an adequate vehicle for energy migra- 

 tion over small distances, as found by Arnold and Oppenheimer (see 



Sect. 6). 



Coulson and Davies (1952) have calculated, using rather extreme 

 approximations, that the dispersion forces between conjugated molecules 

 may fall off as slowly as r-^^ at small distances of approach. Even at 

 separations greater than a few molecular diameters, the force law is pro- 

 portional to r-^ rather than to r-^ as calculated for small or nonconju- 

 gated molecules. Molecules observed to be efficient in resonance transfer 

 processes are of the conjugated type, and the new force law makes their 

 high efficiency at short distances more understandable. Unfortunately 

 the calculation sheds no light on the processes at large separation 

 distances. 



Franck and Livingston (1949) and Forster (1948) have discussed the 

 application of this type of transfer to a variety of phenomena. For 

 instance, the former authors attribute the quenching of anthracene fluo- 

 rescence in the crystalline state by naphthacene (Winterstein and Schon, 

 1934; Bowen, 1938, 1944, 1945; Bowen and Mikiewicz, 1947; and others 

 listed in Franck and Livingston, 1949) to field coupling. 



The theory of another type of direct transfer of electronic energy was 

 developed by Frenkel (1931a,b, 1936) and Peierls (1932) (see also Franck 

 and Teller, 1938). In many crystals, and especially in polar crystals, 

 the crystal elements are so closely spaced that the Heisenberg uncer- 

 tainty principle becomes an important consideration and the crystal as 

 a whole takes on some of the electronic properties of a single molecule. 

 The potential-energy structure of a single element is repeated for each 

 element of the same type but with slight perturbations that lead to the 

 familiar band structure of allowed electronic states. So close are the 

 energy levels in these bands that excitation energy can readily pass to 

 distant elements. Because little atomic displacement accompanies the 

 wandering of excitation, energy may remain for only a very short time, 

 perhaps 10"'^ sec, at any one element. Longer periods are possible when 

 weaker coupling exists. Heller and Marcus (1951) suggest that the weak 

 interactions of induced dipoles in the elements can also support "exciton 

 migration," as the process is called. Mott and Gurney (1948), who 

 employ these exciton movements in their theory of the photographic 

 process, liken the phenomenon to the simultaneous movement of an elec- 

 tron and a positive hole through the crystal lattice. Exciton movements 

 are usually associated with the presence of new spectral bands, and this 

 fact has led to the identification of excitons in the polymolecular associ- 



