14 RADIATION BIOLOGY 



upper- and lower-lying potential-energy surfaces independent of the elec- 

 tronic state. 



According to Landau (1932) and Zener (1932), the probability of the 

 change from one potential-energy surface of a diatomic molecule to 

 another at a crossing point is given by the expression 



in which 2e is the smallest potential-energy difference existing between 

 upper and lower curves; v represents the relative velocities of the nuclei 

 as they pass through the crossing point, i.e., dR/df{0), if R is the inter- 

 nuclear distance and refers to the crossing-point value of R; and 

 \Si — Sf\ is the absolute value of the difference between the quantities 

 dEi(Ro)/dR and dEf{Ro)/dR if Ei and Ef are the potential energies on 

 the initial and final surfaces. Teller (1937) has extended the treatment 

 to polyatomic molecules (see also Kramers, 1940; Neumann and Wigner, 

 1929; and Wigner, 1927). When 2e is large, as it is when the states are 

 very similar and thus interact strongly to give a large resonance energy, 

 Eq. (1-9) ceases to apply. However, it does indicate correctly that p 

 will be exceedingly small. When the states change at the osculating 

 point (Fig. 1-7) in spin quantum number or in symmetry or angular- 

 momentum quantum number, or, indeed, if an electron is transferred 

 from one atom or ion to another, crossing may occur with the probability 

 given by Eq. (1-9). Only when quantum numbers do not change, or 

 change in the ways required by optical selection rules, will the inter- 

 action e be large and crossing a poorly probable process. Thus, in 

 general, systems of colliding molecules will demonstrate the same total 

 values of each quantum number before and after collision. It is apparent 

 that these rules will manifest themselves in a general predilection for the 

 system to retain its original quantum numbers at crossing points. Such 

 behavior has been especially predicted for the spin-angular-momentum 

 quantum number and is called the Wigner (1927) spin-conversion rule. 



Van Vleck (1932) and Zener (1933a) have proposed that external fields 

 will increase the probability of crossing favoring the recoupling of nuclear 

 spins. Turner (1930) observed a decrease of 1 2 fluorescences in a mag- 

 netic field. The presence of paramagnetic ions, for example, Fe++, Co++, 

 and Fe^'*", may act in a similar manner in quenching, since these ions are 

 frequently very eflficient quenching agents and are known to favor the 

 interconversion of ortho- and parahydrogen. In Sect. 4-3 an alternative 

 mechanism involving oxidation and reduction of the ions (Weiss, 1939b) 

 is proposed as an explanation of their effectiveness in quenching. The 

 theory of Zener predicts that electric fields will increase the probability of 

 crossing between states of the same multiplicity. Field-intensity require- 

 ments are apparently too high to allow observation of the phenomenon. 



Substances causing either type of induced internal conversion will not 



