RADIATION BIOLOGY 



sional potential-energy diagram of Fig. 1-2 represent a stable and an 

 unstable transition occurring when the molecule is exposed to electro- 

 magnetic radiation with frequency given by p = (Eg — Eg)/h and 

 p = (E'g — Eg)/h, respectively, h being Planck's constant. The pri- 

 mary process of photoexcitation takes place if certain selection rules 

 derivable from quantum mechanics are obeyed. The most common 

 form takes place with probabilities related to the difference in dipole 

 moments existing between the two states of the molecule and to the 

 intensity of radiation in the field. The transition probability coefficients 

 derived by Einstein are functions only of the molecule.^ For the tran- 

 sition from a ground state with wave function \pg to an excited state \pe, 

 the probability that a radiation field of unit intensity will cause a tran- 

 sition to take place is 



3/i2 



Bg-e 



\Roe\\ 



(1-2) 



\Rge\ is the matrix element of the di- 

 pole moment of all the electrons in the 

 molecule between the two states; i.e., 



j 



in which e is the charge on the elec- 

 tron, r_, is the radius vector of the ^th 

 electron, and the asterisk means a 

 complete conjugate. In molecules in 

 which dipole coupling alone occurs, 

 as here discussed, only the extra shell 

 electrons need be considered. The 

 same situation obtains for single 

 atomic species, and the equations are 

 identical. If the excitation energy 

 is not first lost by dissipation into in- 

 ternal degrees of freedom or in col- 

 lisions with other molecules, fluores- 

 cence will occur (path 3, Fig. 1-3) 

 either as a first-order process independent of the radiation field or by the 

 induced effect of this field. The corresponding transition coefficients are 



INTERNUCLEAR DISTANCE ( r) 



Fig. 1-3. Ground and excited electronic 

 states of the diatomic molecule XY. 

 D is a stable excited electronic state, C 

 an unstable excited electronic state. 



A — ^^^ '^ /? 2 



■"e-9 — o I 2 \^^o\ 



spontaneous; 

 induced. 



(1-3) 

 (1-4) 



' For a discussion of the equations in this section, see any treatise on quantum 

 mechanics, for instance, Pauling and Wilson (1935) and Eyring et al. (1944). 



