40 RADIATION BIOLOGY 



ing and hence of energy transfer can be calculated directly by means of 

 absolute-rate theory: 



Rate = [Hg*][Tl]^ ^ Ji^ e-^»/«^'. (i_36) 



When all concentrations are expressed in molecules per cubic centimeter, 

 substitution of partition functions converts Eq. (1-36) to 



Rate = [Hg*][Tl] 



(1-37) 



\ h' ) \ h' ) 



in which the primed /'s are electronic partition functions and the r's are 

 atomic radii. It is interesting to note that Eq. (1-37) reduces by cancel- 

 lation to the simple kinetic collision number Z times certain correction 

 factors: 



Rate = Zt -/4r e-^°/^^ (1-38) 



./HgVTl 



where 



Z = 2[Hg*][Tl](rH, + rxO^ h^+JI^Y (2^kTyA (1-39) 



\ niim-i / 



In calculating the value of the transmission coefficient, the crossing- 

 point formula, Eq. (1-9), must be applied twice. The probability for 

 crossing on the right-to-left trajectory is given by p. On the return 

 passage the chance for remaining in the upper curve is 



I — p = 1 — e-4'^'''/'"'l«'-*/l. (1-40) 



The order of crossing can also be reversed. Hence, neglecting restric- 

 tions on momenta, 



t = 2p(l - p). (1-41) 



Equation (1-41) has its greatest value at p - }i. The crossing formula 

 applies to states of molecules and is not strictly applicable to the cross- 

 ing between surfaces that describe the energy of two separable chemical 

 entities. It is necessary to introduce another parameter that expresses 

 the interaction potential between the entities as a function of the distance 

 of separation. For efficient crossing there must first exist a crossing 

 point, and, secondly, this point must be at a sufficiently small value of 

 the internuclear distance so that there is an interaction between the part- 

 ners involved in the exchange process. For instance, in the electronic- 

 energy-transfer process 



Hg*202 _|. JJg204 _, JJg202 _^ Hg*204^ (1_42) 



