162 PENETRATION PHENOMENA IN LIQUID WATER 



VI. Stopping Power and Range in Water Vapor 



The object of this section is the assembly of data on stopping-power 

 and range relations for water vapor, with as great accuracy as may at 

 present be achieved, using both experimental and theoretical informa- 

 tion. The difficulties which this comparatively simple problem presents, 

 and the unsatisfactory and inaccurate way in which many of these diffi- 

 culties must be met, vividly underscore some of the quantitative short- 

 comings in contemporary understanding of energy-loss problems. The 

 results which are obtained, uncertain as they are, are nevertheless useful 

 as a basis for discussion of the phenomena for the liquid state and will 

 doubtless prove helpful in the future as a starting point for more accurate 

 experimental or theoretical work. 



The Bethe stopping-power formula 4 and a modified application of the 

 Bragg rule compose the basis for the calculations. Of course, Eq. 4 

 gives the stopping power directly, in the energy region in which it is 

 valid, once the mean excitation energy for isolated water molecules, 

 /jj2o(g), is known. In the extensive energy region in which it is not 

 valid, resort must be made to approximations, some moderately satis- 

 factory, others highly unsatisfactory. The various complications, and 

 the manner in which they are met, are now itemized and explained. 



ac- 



1. The Bragg rule predicts that lu^g) = (^h /q ) • Verj 

 curate values of /h and 7o are not available, however, and there is sen- 

 sible disagreement between various "adopted" values in the literature. 

 Thus, data given by Livingston and Bethe (11, Table XLIX, p. 272) 

 lead to /h = 14; JoHot-Curie et al. (27, p. 19) give In = 16.0, Iq = 

 100; from Sr values adopted by Gray (10) we calculate /h = 18, Iq = 

 95; Hirschf elder and Magee (28) give 7h = 17.93, /o = 98.9. (All 

 values of I are in electron volts.) 



We adopt the values: In = 18, Iq = 94. From these values the 

 Bragg rule predicts that Ik^oii) = 68 ev. We estimate the correspond- 

 ing uncertainty as ±3 ev. 



2. The actual value of /H2o(g) must depart to some extent from the 

 prediction of the Bragg rule. This departure is not known and cannot 

 even be estimated with any confidence. Considered very crudely, the 

 binding is "looser" in H2O than in (2H2 + O2), as evidenced, for ex- 

 ample, by the low ionization potential, and one might suppose /H2o(g) 

 to be slightly smaller than the Bragg-rule prediction. However, the 

 possible influence of the permanent electric dipole moment of H2O on 

 the ultraviolet dispersion, and hence on /H2o(g), is not known, so that 

 very little weight should be given to this reasoning. Also, Forster (16) 

 found the stopping power of water vapor for alpha particles, averaged 



