APPENDIX. EXPLANATION OF THE FIGURES 113 



APPENDIX. EXPLANATION OF THE FIGURES 



Fig. 1. Various Modes of Energy Loss of Protons in Water 



(a) The total electronic energy loss (stopping power), newly recalculated, is 

 plotted as a function of proton energy. For more suggestive reference in inter- 

 pretations of radiation chemistry and biology, the stopping power is expressed 

 in units of electron volts of energy loss per angstrom of distance traversed, for 

 water of density 1.00. (The distance between nearest neighbor molecules in 

 water is about 3 A.) 



The basis for the calculation of these values of the stopping power is discussed 

 in detail in reference 7. Briefly, it is: 



1. The stopping power of water is assumed to be equal to the sum of the 

 stopping powers of its constituent atoms. 



2. The Born approximation is presumed to be valid, and the theory of Bethe 

 (6) is therefore applied. 



3. The simple Bethe stopping-power formula is, however, corrected for its 

 premise that the orbital velocities of the various atomic electrons are negligibly 

 small compared to the proton velocity: for the K electrons of oxygen, by the 

 accurate method developed by Bethe (6) and recently modified (2), and for the 

 electron of hydrogen, and the L electrons of oxygen, by a prescription of yet 

 unestablished validity proposed by Hirschf elder and Magee (5). 



4. The empirical constants representing the mean excitation potentials of 

 hydrogen and oxygen atoms are redetermined from data on the stopping powers 

 of the elements and some of their compounds. 



5. At low energies — specifically, for proton energies less than about 0.3 Mev— 

 no competent theory exists. The stopping power in this region is therefore 

 estimated as well as possible, using experimental data on water vapor obtained 

 by Crenshaw (3). 



The results cannot be considered trustworthy in this region. Because of some 

 of the approximations used, and the absence of adequate experimental infor- 

 mation on the stopping power of water itself, the data are presented with no 

 assurance that they are more than a qualitative guide (7). 



Values of the stopping power of water for alpha particles can be obtained from 

 those for protons by use of the famihar relation: 



— ■ ) (for alpha of energy E') 



^^ ' (dE\ 



= 4 ( — ) (for proton of energy E = 0.2517^') \E' > 1 Mev] 

 \dx/ 



For proton energies greater than about 3 Mev (but not so great that relativ- 

 istic corrections are demanded) the energy loss may be computed directly from 

 the formula: 



\ dx) 



^^ (1.525 + logio E) ev/A [E in Mev] 

 E 



