STOPPING POWER OF A POLYATOMIC GAS 155 



ligible unless the molecule possesses a permanent electric dipole mo- 

 ment. * The stopping power arising from these two types of energy loss 

 has not been calculated.! However, we may easily deduce the following 

 approximate expressions which must be correct, at least in order of mag- 

 nitude, and which suffice for the present discussion: 



-SL-"^fe'lrr;-)in— (5) 



\ rf.r/rot \me /2h / \h /me/ i«rot 



Here ifvib and Wtot are the energies of the first molecular vibrational and 

 rotational levels, respectively. Note that this contribution to the stop- 

 ping power is not of order of magnitude kN\ the great magnitude of 

 atomic relative to electronic mass enters through the small value of w 

 (in atomic units). The equations show at once that these contributions 

 are small compared to the electronic stopping power for fast particles, 

 being roughly 10"^ and 10"^ of the total, respectively: the small factor 

 w'/(me^/2h^) dominates the greater logarithmic factor. In the language 

 of the method of impact parameters, the energy loss is smaller because 

 of the greater mass (atomic rather than electronic) which must be set 

 in motion, although this is partly compensated by the greater p„,a,x — 

 greater because the dynamic screening is less stringent and permits en- 

 ergy transfer to greater distances. In the language of the Williams- 

 Weizsacker method, the energy transfer by emission and absorption of 

 virtual, infrared quanta is smaller, although the smaller energy in such 

 quanta is partly compensated by their greater abundance in the Fourier 

 spectrum. 



The magnitude of these two additional contributions to the stopping 

 power, relative to the total, is not, however, independent of the energy 



* There is always a small probability of vibrational excitation arising from col- 

 lisions in which the particle actually passes through the molecule. This probability 

 is small compared to that for "indirect" excitation in the case of polar molecules, 

 and for fast particles is always insignificant in its contribution to the total stopping 

 power. For extremely slow particles (for example, electrons of a few-electron-volt 

 energy) it is known to be appreciable, even for homopolar molecules, but this case 

 does not concern us in the present study. 



t Massey (20) has derived an expression for the cross section for rotational ex- 

 citation which leads at once to our expression (Eq. 6) for the stopping power, but 

 which is valid only if the dipole moment ijl is small compared to one-half of an atomic 

 unit (h^/me). However, Eq. 6 is still approximately correct for greater values of n, 

 a fact worth noting because n is comparable to h^/me for many molecules of practical 

 importance. Cf. also Wu (21). 



