150 PENETRATION PHENOMENA IN LIQUID WATER 



yet been studied. To this list might be added atomic hydrogen, which 

 can be treated very accurately by theory but which is not amenable to 

 experimental observation. To summarize, for all monatomic gases we 

 have an accurate, simple formula for the stopping power, involving one 

 empirical constant for each gas, which is, however, applicable to a suc- 

 cessively smaller domain of velocities, the larger is Z. For light mon- 

 atomic gases there are available numerical values of the stopping power, 

 again requiring an empirically determined constant, which span prac- 

 tically the entire useful range of velocities. For atomic hydrogen and 

 helium we have an exact, purely theoretical formula of very wide ap- 

 plicability. Empirically, however, we possess only a moderate amount 

 of information about the stopping powers of He and A, and rather less 

 about Ne, Kr, and Xe. 



IV. Stopping Power of a Polyatomic Gas 



No detailed theoretical treatment of the stopping power of a diatomic 

 or polyatomic gas has yet been achieved. There is available, however, a 

 wealth of experimental data on diatomic gases (notably H2, N2, O2, and 

 air) and also some information on a few polyatomic gases. 



It must be stated at once that the binding of atoms in molecules does 

 not alter their stopping powers to any great extent. Little is known 

 about the changes that do occur. The problem has not been one of great 

 interest as far as collision theory is concerned — it is at least as much a 

 problem involving the electronic structure of molecules — and since the 

 advance of our understanding of penetration phenomena has, histori- 

 cally, stemmed largely from the practical needs of nuclear physics, the 

 topic has been a neglected one. Yet it surely is important. Not only 

 have such small alterations an intrinsic practical consequence for ac- 

 curate work; they also may afford valuable clues to far greater effects 

 of molecular structure on other aspects of penetration phenomena; and 

 they are in themselves of much fundamental interest. In this section 

 we shall first appraise the present status of the empirical information 

 and then analyze the molecular problem theoretically. 



To illustrate the effect of chemical binding on the stopping power we 

 need only consider the case of hydrogen; here we have experimental data 

 for H2 and trustworthy theory for H. The empirical data can be fitted 

 to formula 4, with the quantity N interpreted as the number of molecules 

 per unit volume and Z as the number of electrons per molecule (that is, 

 2). The data are not at all certain enough to determine the value of I 

 as accurately as one might wish, but values ii^ the neighborhood of 18 ev 

 are usually obtained. However, the theoretical value for isolated hy- 



