164 PENETRATION PHENOMENA IN LIQUID WATER 



compared to the nuclear charge of the atom under consideration. This 

 is clearly not the case for hydrogen and must lead to an error which may 

 be serious and is as yet completely unknown. 



(c) That this assumption too has never been tested and must be in 

 error. (The calculation of the corrections is based on the use of hy- 

 drogen-like wave functions, and the L wave functions are far from hy- 

 drogen-like.) 



There being no alternative way of effecting these corrections theoret- 

 ically, and no empirical data to aid in doing so, we adopt the scheme of 

 Hirschfelder and Magee, utilizing, however, the 7l-correction function 

 of Brown. 



5. At low energies (below about 2.5 Mev for alpha particles, 0.6 Mev 

 for protons), the phenomenon of capture-and-loss of electrons by the 

 penetrating particle modifies the stopping power, both by modifying the 

 normal mode of energy loss to electrons, and by itself contributing an 

 additional energy loss. There is at present no way of estimating these 

 effects with meaningful accuracy. However, in view of deficiencies in 

 our treatment underlined under 4 above, to do so would not appreciably 

 improve the stopping-power values at low energies. We therefore ignore 

 them. 



Crenshaw (29) has given stopping-power data at low energies (cf. 

 Fig. 1). We have accordingly drawn the stopping-power curve at 

 low energies to agree with these data, and otherwise to follow the general 

 course of the calculated values. 



6. At very low energies the stopping power considered above is aug- 

 mented by an additional contribution arising from energy transfers to 

 vibrational and rotational modes of the molecule. However, very rough 

 estimate shows this contribution to the stopping power to be only 0.5 per 

 cent for 1-Mev protons and 1 per cent for 300-kev protons. It is never 

 great and is appreciable only at energies so small that our stopping- 

 power values are for other reasons grossly in error. We therefore neg- 

 lect it. 



The results of the calculations are presented as follows : 

 Figure 1 gives values of s, the stopping power of water vapor relative 

 to that of air. Values of the stopping power of air were obtained from 

 semiempirical data given by Bethe (30). For a proton of energy greater 

 than about 0.6 Mev the value of s is the same as that for an alpha par- 

 ticle of the same velocity (or energy approximately 4 times the proton 

 energy). As the energy decreases the values of s become progressively 

 less certain, and the error is different for protons and alpha particles : at 

 low energies the s curve should separate into two curves, one for protons 

 and one for alpha particles. Experimental points determined by Cren- 



