STOPPING POWER OF A POLYATOMIC GAS 157 



scription is not correct, however. Exchange effects in atoms other than 

 hj^drogen, or in molecules, effectively "tighten" the binding, and this 

 may be considered to have two more or less distinguishable results: the 

 ionization potential P, and the various excitation energies e^ relative to 

 P, become greater than the predictions of the hydrogen-like model; and 

 the ratio I/P is increased.* The last-mentioned effect derives in part 

 from the higher values of excitation energies (even when expressed rel- 

 ative to P), and in part from a shifting of oscillator strengths toward 

 higher excitations and especially ionizations. (In general, the total 

 fraction of oscillator strengths residing in the continuum is greater, the 

 more saturated is the character of the valence-shell binding.) It is ob- 

 viously necessary to take both effects into account. Thus, for hydrogen, 

 Pat = 13.60 ev and Pmoi = 15.43 ev. The first excited atomic level 

 (2p) has e/Pat = 0.75, but the corresponding molecular levels (2p, ^2^+ 

 and 2p, ^n„) are located at about e/Pmoi = 0.81. Similarly, higher 

 molecular levels also exceed corresponding atomic levels in their values 

 of En/P. This analysis is impeded, however, by the fact that not much 

 is known, either empirically or from theory, about the detailed dispersive 

 properties of molecular hydrogen. However, a preliminary study has 

 been reported by Mulliken and Rieke (22). Their results give a total/ 

 of 0.31 for the first excited levels (specified above), per atom, compared 

 to 0.42 for the corresponding atomic level. The second group of levels 

 also has lower / for the molecule. Thus both the effects of departure 

 from hydrogen-like binding are apparent in the case of H2. We there- 

 fore conclude that the ratio I/P should be greater for the molecule than 

 for the atom. Unfortunately, in the absence of theoretical information 

 concerning oscillator strengths for transitions to the continuum (and of 

 empirical information on the continuous absorption of H2) this analysis 

 cannot be carried much further with confidence. A crude estimate leads 

 to /bound ~ l-2Pmoi ~ 19 ev. The effects under discussion all tend to 

 make the stopping power of the molecule smaller than that of the 

 separated atoms. Thus, the above estimate suggests a decrease of about 

 5 per cent for a 5-Mev alpha particle. It would be of great interest to 

 construct an approximate but complete model for the dispersion of 

 molecular hydrogen, carry through the analysis sketched above, and 

 then compare the conclusion with accurate empirical stopping-power 

 data which will eventually become available. (Those now at hand give 

 merely //P « 1.1 ± 0.1.) 



The rather great molecular effect indicated above will not enter in the 

 application of the Bragg rule to practical cases involving hydrogen, be- 



* An extreme example is helium, for which the values of S„/P greatbj exceed hydro- 

 gen-like values, and I/P has a value of about 1.8. 



