STOPPING POWER OF A SOLID OR LIQUID 161 



and measurement of its stopping power (which could readily be ac- 

 complished, for example, using the extremely fast particles provided by 

 the new accelerators), and a parallel theoretical study based on its known 

 optical properties, would appear to be equally feasible and straight- 

 forward, and a promising subject for investigation. 



It deserves mention that stopping-power and range data for several 

 solid organic substances and for mica have been accumulated, and — in 

 those cases in which the data have been "interpreted" — the Bragg rule 

 apparently confirmed. It would appear, however, that the uncertainties 

 in the component atomic stopping powers as well as in the experimental 

 data do not permit a clear analysis of the quantitative extent of the 

 agreement. 



A qualitative analysis of the difference in stopping powers of a molec- 

 ular sohd or liquid and its vapor can be given readily. In the condensed 

 state the intermolecular fields alter the excitation levels in two ways 

 which can be distinguished formally: the levels are broadened and may 

 be split into a number of components. The latter effect results essen- 

 tially in lower energies of excitation for a given electron. (This shifts 

 an absorption line ''toward the red," an effect often observed, and is to 

 be understood as a consequence of the fact that an excited electron is 

 always attracted in the internal field of a neighboring molecule.) Such 

 an alteration results in an increased stopping power; this can be seen 

 directly from formula 3, in which / has been decreased, or more physi- 

 cally from the Williams- Weizsacker view in terms of the increase in num- 

 ber of virtual radiation quanta for the greater wave length. The mag- 

 nitude of this shift will be greater, the higher the level of excitation. 

 (This statement can be understood simply as following from the greater 

 size of the orbit of a more highly excited electron, with greater con- 

 sequent penetration of neighboring molecules.) The continuum will, 

 indeed, be more radically altered. But the broadening of the energy 

 levels by the strong fields present will also have an effect on the stopping 

 power; even a symmetrical broadening will lower the stopping power 

 slightly (cf. again Eq. 3). It is concluded that the stopping power of 

 the condensed state must always be greater than that of the vapor. 

 These effects will be discussed again in Section VII with specific reference 

 to liquid water. It would be a valuable advance if a general, semi- 

 quantitative theory for them could be developed, based upon a simple 

 model. 



