STOPPING POWER AND RANGE IN LIQUID WATER 167 



In effect, then, the curve must be shifted up or down by an unknown 

 amount, different for the two particles. We estimate this shift as prob- 

 ably smaller than 2 microns. At high energies its role is negligible; at 

 lower energies differences in ranges for two different energies are pre- 

 dicted more accurately than either range itself. 



Only two empirical range data for water vapor have been reported: 

 a value for RaC alpha particles by Philipp (3) and one for Po alpha 

 particles by Appleyard (5). The corresponding points are indicated in 

 Fig. 2. Both agree fairly well with our calculated curve; neither is con- 

 sidered trustworthy enough to justify its use in establishing the curve (or 

 in estimating the unknown correction to the range for alpha particles). 



VII. Stopping Power and Range in Liquid Water 



The various factors to which any difference in stopping power between 

 liquid and vapor w^ater must be ascribed have been discussed quali- 

 tatively in Section V. The stopping power of the liquid must indeed 

 be greater than that of the vapor, because the dominant change will be 

 the depression of excited energy levels by the internal electrical fields 

 of adjacent molecules. That this perturbation is great for all excited 

 states of H2O (except possibly the lowest triplet state, which may be 

 strongly excited as an intercombination permitted in the external elec- 

 trical field) can be seen from a crude model in which the excited electron 

 is considered to move in a hydrogen-like orbit with effective nuclear 

 charge of roughly e. Then the lowest excited state has n = 3, and cor- 

 responds to a Bohr orbit of radius approximately equal to 9(h^/me^) = 

 4.8 A, whereas one-half the intermolecular distance (in liquid water) is 

 1.5 A. Thus the interaction is always strong and all excited states are 

 strongly perturbed. Moreover, water possesses a remarkably great pro- 

 portion of weakly bound electrons: six of the ten have ionization po- 

 tentials in the range from 12 to 17 ev! 



Even an approximate theoretical calculation of these effects and the 

 resultant change in the mean excitation energy / would be exceedingly 

 difficult and will not be attempted here. (It would require not only 

 estimation of the changes in Sn but also of those in the fn values, par- 

 ticularly the fn pattern in the continua.) We can only repeat that the 

 theoretically anticipated shift of I is of the correct sense. Whether it is 

 of the correct magnitude can be answered only by a detailed theoretical 

 analysis, and also only after the conflict in experimental results is re- 

 solved. 



It should be mentioned here that the change in I has sometimes been 

 stated to be approximately equal to the energy of vaporization — for 



