154 PENETRATION PHENOMENA IN LIQUID WATER 



difference between molecular and atomic binding of the electron is cer- 

 tainly insignificant. But of approximately equal importance for the 

 total stopping power are those collisions in which the energy transfer is 

 of the same order of magnitude as the ionization potential. For such col- 

 lisions the penetrating particle has an effect equivalent to electromag- 

 netic radiation, the frequency distribution of which corresponds to a 

 Fourier analysis of the impulsive field of the passing particle. The en- 

 ergy transfers are thus closely related to the optical absorption spectrum, 

 both discrete and continuous. (This relation was encountered, in the 

 discussion above, as the dependence of I on the dispersion.) Now molec- 

 ular binding has a decisive effect on the discrete spectrum and would 

 without doubt be known to have as great an influence on the continuous 

 absorption in the vicinity of the absorption edge, were our knowledge of 

 the continuous absorption in the case of molecules sufficiently advanced. 

 We must thus anticipate a pronounced alteration by molecular binding 

 of the details of energy loss in these "lighter" collisions, a somewhat 

 smaller influence on the over-all energy loss, and a still smaller but never- 

 theless appreciable influence on the stopping power, which, as may be 

 recognized by inspection of formula 4, depends chiefly on 2kNZ and less 

 sensitively on details of the binding of the electrons. 



Molecular binding will also influence, to some extent, the oscillator 

 strengths, but not appreciably the binding energies, of inner electrons. 

 This is related to the fact that the osciUator strength of an inner electron 

 is smaller than unity, because its transitions to occupied discrete states 

 are not possible. For a molecule there is, in crude terms, a fuller occu- 

 pancy of the lowest discrete states, thus decreasing the total oscillator 

 strength of an inner electron. This decrease must be compensated by an 

 augmentation of oscillator strengths of outer electrons, so that one might 

 expect / in molecules to be decreased and the stopping power therefore 

 increased by this effect. However, the character and positions of the 

 energy levels are so altered in the molecule that it is not certain whether 

 this conclusion has any validity. 



The second and third factors listed above are simply additional modes 

 of energy loss, and must be added to the energy loss to electrons in order 

 to obtain the total stopping power. Some energy transfer to vibrational 

 modes will in general accompany electronic excitation, of course; this 

 follows from the Franck-Condon principle and the fact that bond dis- 

 tances in excited states usually differ from those in the ground state. 

 However, energy transfer to vibrational and rotational modes can occur 

 independently of electronic excitation, as is seen at once by considering 

 the equivalent radiation field of the particle. This view also shows that, 

 as in the corresponding optical effects, the energy transfer will be neg- 



