STOPPING POWER AND RANGE IN WATER VAPOR 163 



over the energy interval from 5.1 to 2.7 Mev, to be 2.4 ± 0.4 per cent 

 smaller * than the corresponding average for an equivalent mixture of 

 hydrogen and oxygen, thus leading to an /nsoCg) greater than the 

 Bragg-law prediction by about 8 per cent, a deviation of opposite sense 

 to that suggested above. We shall not take this single measurement 

 into account, but it is obviously important that the experiment be re- 

 peated and a result established. The only other reported measurements 

 of the stopping power (in distinction to the range or to Sr) are those of 

 Crenshaw (29). However, Crenshaw's data all lie at low energy, the 

 highest being at 0. 17 Mev (protons) . At this energy the theory is so very 

 untrustworthy that the experimental data cannot be translated into a 

 value of I with any certainty whatever. 



We adopt the value: /H2o(g) = 65 ev and estimate the error as ±6 

 ev. 



3. At moderate and low energies the Bethe formula fails to account 

 properly for the contribution to the stopping power of the K electrons 

 of oxygen. However, a satisfactory method for correcting the formula 

 has been given by Livingston and Bethe (11) and more recently by 

 Brown (13). We have used the results of Brown to calculate this cor- 



'rection, which amounts to about 3 per cent of the stopping power at 2 

 Mev and 2 per cent at 4 Mev (for protons). 



4. At low energies the Bethe formula, corrected for the contribution 

 of the oxygen K shell, fails to account properly for the contributions of 

 the remaining 8 electrons. There is no satisfactory way at present to 

 correct for this failure. We therefore employ a prescription devised by 

 Hirschf elder and Magee (28), which advocates: 



(a) Assumption of the Bragg rule (that is, assumption that the cor- 

 rection is the same as that for 2 hydrogen K electrons and 6 oxygen L 

 electrons) . 



(&) Assumption that the correction for the hydrogen K electrons is 

 given by the same theory (and has the same analytic form) as that for 

 K electrons of heavier atoms. 



(c) Assumption that the contribution for the oxygen L electrons is 

 also of the same analytic form. 



The objections to this procedure are: 



(a) That the Bragg rule is certainly less vahd at low energies than at 

 high. 



(b) That the Livingston-Bethe and Brown correction is based on use 

 of the Born approximation, which for these low energies is equivalent 

 to the assumption that the charge of the passing particle is very small 



* We have corrected Forster's quoted result, 3.0 ±0.5 per cent, for a tempera- 

 ture variation that he apparently neglected. 



