STOPPING-POWER THEORY FOR MON ATOMIC GAS 145 



(but, it is hoped, complete) survey of possible effects of the finer details 

 of electronic binding will therefore be given. This suffices to demon- 

 strate that these effects are by no means all negligible, and that some 

 are of extreme importance. 



In order to discuss the stopping-power effects more meaningfully, it 

 will first be necessarj^ to review and evaluate such aspects of contem- 

 porary knowledge and understanding of stopping powers as relate to the 

 problems under consideration. This critical evaluation will, indeed, be 

 one major objective of the present study, and should, it is hoped, prove 

 helpful quite independently of the problem of liquid water. 



III. Resume of Stopping-Power Theory for a Monatomic Gas 



The stopping power of a medium for a swiftly moving charged particle 

 of energy E is defined as the ratio of the energy lost by the particle 

 ( — AE) in penetrating a very small distance (Ax) into that medium, to 

 Ax. Thus, stopping power equals —AE/Ax, and equals —dE/dx in the 

 limit of infinitesimal penetration. (Treatment of £" as a continuously 

 decHning function of x is a valid approximation because the magnitude 

 of AE which corresponds to a Ax of atomic dimensions is of the order of 

 electronic binding energies, that is, a few electron volts, and hence is 

 extremely small compared to E for high-energy particles.) 



The stopping power is a well-defined parameter of the physical situa- 

 tion and is a compound of the probabilities of numerous possibilities 

 of energy loss. (The stopping power has in fact a probability distri- 

 bution, but only its average value will be considered in this paper.) 

 It depends in general on the nature (charge and mass) and velocity of 

 the particle, and on some of the properties of the medium. The stopping 

 power of a particular medium is often expressed (as in Section II) in 

 dimensionless form by its ratio to the corresponding stopping power of 

 air (that is, for the same particle at the same velocity, and for air at such 

 a density that the number of air "atoms" per unit volume is the same as 

 the number of molecules of the medium per unit volume). This relative 

 stopping power is simply the stopping power of a single molecule of the 

 medium divided by that of one-half of an "average" air molecule. 

 Stopping powers of air, for various particles over a wide range of ve- 

 locities, are well established, largely through the work of Bethe, and are 

 available in convenient graphical form (11, 12, 30). The relative stopping 

 power, which is denoted by s, is convenient in that it is highly insensitive 

 to the charge and mass of the penetrating particle; indeed, it is known 

 from both experiment and theory that for "fast" particles s depends 

 only on the velocity of the particle and on the nature of the medium, and 



