374 ENERGY LOSS AND BIOLOGICAL EFFECTS 



For the purpose of quantitative comparisons it seems worth while to 

 assume a simple mathematical expression for the ionic 3'ields of the 

 intermediates requiring ion pairs. Exact derivation of the yield is not 

 an easy matter when ion clusters and diffusion theory are taken into 

 account. Progress is being made in this field by Landau (31) and 

 Wijsman (32). 



Lind (33) has shown that the ionic yield of H2O2 in oxygen-free pure 

 water is close to unity in a range of energies where alpha rays are used. 

 Toulis (34) has studied the yield as a function of proton energy in the 

 absence of dissolved material. Although more extensive studies are 

 desirable, the data available indicate that H2O2 yield remains low at 

 proton energies above '^6 mev ; below this it rapidly rises until a plateau 

 is reached with ionic yield of '-^3^ with low-energy alpha particles. A 

 formula was obtained for the H2O2 yield, ^2, by assuming that the 

 probability of peroxide formation in water is 1 if the distance between 

 two ion pairs formed is less than a critical distance Tq, and that the 

 probability is zero if the distance between ion pairs is greater than tq. 



1 — e-^'-o/wf 1 -^ 1 



fe = ~ (7) 



where c is the rate of energy loss, and w the energy required per ion pair. 

 This formula is admittedly poor, and there is no doubt that further 

 refinement is needed when more exact knowledge of ionic spacing 

 (clusters), cage factors, and back reactions is available. However, until 

 something better comes along, this formula may be helpful in qualitative 

 studies of the mechanism of radiation effects. When the ion spacing is 

 large, a more exact formula, derived by Wijsman and based on diffusion 

 considerations, may be used. This yields the probability for H2O2 for- 

 mation in oxygen-free water as 



■10 



1 To'e' [ ~ ~ '' 



8t 



(8) 



where 5 is the diffusion constant and t the mean life of OH radicals. 



To account for the observations of the change of RBE as a function 

 of REL in yeast cells, one assumes now that OH and HO2 radicals can 

 cause inhibition, as well as intermediates resulting from closely spaced 

 ion pairs. 



Both the organisms tested indicate that the mean action radius of an 

 H202-like product in the cells is much greater than that of the ions or 



