168 PENETRATION PHENOMENA IN LIQUID WATER 



water, about 0.4 ev. This is a fallacy. The ground state is shifted by 

 this amount, but the shifts in excited levels are virtually unrelated to it. 

 The rather close agreement between the older range determinations 

 by Michl and by Philipp and the recent stopping-power measurement 

 by Appleyard has already been stressed. This is important (to the ex- 

 tent that any credence can be granted to the old experiments) because 

 of the weakness in the theoretical basis for the calculation of the ab- 

 solute range: the phenomena at low energy — for example, capture-and- 

 loss of electrons — are not in the least understood quantitatively. It is 

 interesting to note that the difference in ranges of Po and RaC alpha 

 particles, calculated from the measurements of Michl and of Philipp 

 (27.5 n), agrees much more closely with the result of de Carvalho and 

 Yagoda (29.1 m) than do the absolute measurements, suggesting the pos- 

 sibility that at least part of the disparity lies at the end of the range, 

 where the experiments may measure something different from what is 

 claimed. Some disagreement for the high-energy portion of the range 

 remains, however. We may summarize the experimental results by 

 presenting values of /h2o(1) calculated, respectively, from the Po, RaC 

 range differences determined by Michl and by Philipp, from the same 

 range differences determined by de Carvalho and Yagoda, and from the 

 stopping power determined by Appleyard. These results are presented 

 in Table 2. In addition to /h2o(1) is given the corresponding value of 



TABLE 2 

 Summary of Values for the Mean Excitation Energy of Water 



/h2o(1), 



/', the contribution to /h2o(1) of the eight outer electrons of water, cal- 

 culated from the formula 



T/ (T lOr — 1.89\!-iii 



-/ = UH2O ^K ) 



where Ik is the effective excitation energy of the K shell (31) . Analogous 

 quantities for the vapor are included to facilitate comparison. The 

 data for F show at once the unsatisfactory state of affairs. This has a 

 two-fold basis: not only are the experiments with the liquid in disagree- 

 ment, but the uncertainties in the deviation from the Bragg rule and in 

 the adopted values of /h and 7o preclude a trustworthy comparison of 



