28 RADIATION BIOLOGY 



in which C and d are empirical constants, d being a characteristic bond 

 radius of about 0.35 A (Zener, 1933b), and r is the distance between 

 centers of gravity of the colUding atoms in the colUsion complex. The 

 probability that a given inelastic collision will occur can be expressed as 

 the product of factors, 



p = P0P1P2 ■ • ■ Pi • ' • Pn, (1-20) 



in which p^ includes translational aspects of the collision. It is a func- 

 tion of e, the energy that must be transferred between translational 

 degrees and vibrational degrees of freedom, and /x, the reduced mass of 

 the colliding systems. The term po increases rapidly with ix and decreases 

 more rapidly with increasing e. The function po has been tabulated for a 

 number of values of the variables. The factors pi measure the proba- 

 bility that the iih. degree of freedom will undergo a necessary change in 

 quantum number. There will be one such factor for each of the ri internal 

 degrees of freedom involved in the transfer. The pi's are approximated 



by 



V. - (™)'' (1-21) 



in which /?, measures the coupling of the struck atom with the /th vibra- 

 tional coordinate; i.e., it is the coefficient of that particular coordinate 

 when the displacement of the struck atom is expanded in terms of the 

 normal coordinates. The term Si is the matrix element of the coordinate 

 of the iih. normal mode between ground and the particular excited state v 

 involved. It may be calculated in any particular case by the method of 

 Sommerfeld (1932). Applying the procedure to deexcitation of O2 from 

 its first vibrational excited state, Zener (1935) found po == 10~^ for the 

 e of 5.3 kcal/mole, pi = 6 X 10-^ and thus p = popi = 6 X 10"^ The 

 rate constant for the process is the product of this probability times 

 the kinetic-collision frequency. The calculation is too small and can be 

 improved by choice of a better potential function, for example, that of 

 Jackson and Mott. The theory is, of course, very approximate but gives 

 fair relative agreement with the measurements of sound dispersion and 

 the transfer of thermal energy both in the bulk phase and from surfaces 

 to gases. The calculation of accommodation coefficients measuring the 

 efficiency of the latter processes has been treated by Jackson and associ- 

 ates (1932, 1933, 1935). 



An absolute-rate theory for collisions of polyatomic molecules along 

 the lines outlined in this chapter has little practical importance because 

 of the extreme complication of the potential surfaces for such molecules. 

 Similarly the Born type of scattering calculation for molecular beams 

 (Massey and Burhop, 1952) is extremely difficult to apply even to small 

 molecules. A promising attack on the problem has recently been started 

 along the lines of the Zener theory, i.e., isolation of the different types 



