STOPPING-POWER THEORY FOR MON ATOMIC GAS 149 



the mean excitation energy for all the atomic electrons. Unfortunately, 

 it has not yet been possible, except for Z = 1, 2, 3, or 4, to calculate / 

 on the basis of theory alone, because of inadequacy of present knowledge 

 of the dispersive properties of the atoms, and this constant must be de- 

 termined for each value of Z from experimental stopping-power data.* 

 Once / is so established for any atomic medium, the stopping power can 

 be computed at once for any sufficiently swift particle by Eq. 4.t 



The restriction of the stopping-power formula to particle velocities 

 great compared to Zvq robs it of much of its potential usefulness by re- 

 moving from its domain of applicability the majority of cases heretofore 

 of practical interest. (Work with particles in the 20- to 1000-Mev en- 

 ergy region is only just beginning.) Thus, even for a medium composed 

 of oxygen atoms, the formula is not valid for any natural alpha particles. 

 Fortunately, it is possible to deduce from theory the necessary correction 

 to the formula, at least in some instances. For intermediate and heavy 

 atoms this is a highly complicated problem which has not yet been very 

 much developed. For light atoms, for which, in the case of all but very 

 slow particles, only the K electrons do not satisfy the velocity criterion, 

 the correction for the modified contribution to the stopping power of the 

 K electrons when v is not great compared to Zvq has been calculated 

 quantitatively by Bethe (11) and by Brown (13). This means that the 

 stopping power so corrected is valid for particle velocities great com- 

 pared to the orbital velocity of L electrons in an atom of the medium, 

 and this is a very much less stringent restriction, so that the formula 

 thus corrected covers a much broader region of applicability. 



The above considerations apply strictly only to media which are 

 monatomic gases. Experimentally, this entails limitation to the noble 

 gases He, Ne, A, etc. Metal vapors, ivhen monatomic — for example, Hg 

 or Na — would be interesting cases, but their stopping powers have not 



* It is possible, on the basis of the Thomas-Fermi model for the atomic frequen- 

 cies, to deduce from theory an expression giving I of any atom, complete except 

 for a single constant (which is calculable in principle but must at present be obtained 

 empirically). The usefulness of this result has been limited by the fact that the 

 Thomas-Fermi model is trustworthy only for heavier atoms, for which, at familiar 

 particle energies, the Bethe formula does not apply because of the velocity restric- 

 tion. 



t It must be stated that the proof of Eq. 4 has been accomplished only for the 

 special model in which all atomic electrons are assumed to be hydrogen-like. This 

 fact, together with the absence of a purely theoretical calculation of / for a complex 

 atom, has in a sense reduced the formula, which is of the greatest fundamental im- 

 portance and which must be very accurate for atomic hydrogen, to the status of a 

 semiempirical formula. As such it has been extremely valuable in practice, but it 

 cannot be said to have been rigorously tested as yet by accurate experimental data 

 for a single particle and medium over a broad energy region. 



