114 PRIMARY PROCESSES 



(b) A second curve presents the contribution to the stopping power of energy 

 loss to the K electrons of oxygen, and is calculated from results of Brown (2). 

 Values for the corresponding energy loss for alpha particles may be obtained 

 from those for protons by a relation similar to that given above. For extremely 

 great values of E, the energy loss to the K electrons approaches 19 per cent of 

 the total energy loss; for the energy region treated here, however, this contri- 

 bution is smaller, being 7 per cent at 3 Mev, for example. 



(c) A third curve gives the energy loss in nuclear collisions, calculated by 

 methods developed by Bohr (1). Since this treatment uses a Thomas-Fermi 

 approximation to the screening, it will be somewhat inaccurate for these light 

 atoms; however, the error should be sUght. 



(d) Finally, there are presented values of that contribution to the stopping 

 power which derives exclusively from the more violent nuclear coUisions. By a 

 "violent" coUision is meant (here) one in which the struck ("recoil") atom is 

 ejected from its molecule. For convenience in calculation, violent collisions 

 are assumed to be those in which more than 20 ev is transferred to the (H or 0) 

 recoil atom. Such a model contains the effect of chemical binding on atom 

 ejection — very crudely, to be sure. The W ev is an estimate; the conclusions, 

 however, are not very sensitive to the value of this quantity. It will be seen 

 that such violent collisions contribute about one-half of the total nuclear- 

 collision stopping power. (Although less numerous, the events involve greater 

 energy transfers.) 



Fig. 2. Fraction of Total Energy of Protons Penetrating Water Which Is Lost in 

 Ejecting K Electrons of Oxygen, and in "Violent" Nuclear Collisions 



This information is obtained by numerical integration of appropriate data 

 from Fig. 1, and is subject to the same Hmitations mentioned above. 



Fig. 3. Total Number of K Electrons Ejected from Oxygen Atoms, and of "Violent" 

 Nuclear Collisions, for Protons Penetrating Water 



(a) The cross section for ejection by a proton of a K electron from an oxygen 

 atom is computed from results of Henneberg (4). Since he calculated the effect 

 of screening for a case somewhat different from that of oxygen, values for the 

 number of K ejections computed from his cross sections and presented in Fig. 3 

 are in error, but are too low. However, they are still trustworthy approximate 

 values. A more accurate calculation could be made readily by numerical in- 

 tegration of the transition probabilities given by Bethe (6), which are valid for 

 oxygen. 



The total number of K ejections from oxygen atoms is computed by numerical 

 integration from values of the cross section for K ejection and of the total 

 stopping power of water (from Fig. 1). 



(6) The total number of violent nuclear colUsions (cf. above for definition of 

 "violent") is computed by numerical integration from the simple Rutherford 



