238 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1953 



{rncz) — miczY = 



kT + 



(mcl) = kT + 



^^ + "^^ \ ar I (120) 



^ / SM sin^ X + 4m(l — cos x) \/l — cos xV 

 \ ar /\ ar I 



^ / 3M sin^ X + 4m(l - cos x) V l - cos x V 

 \ aT l\ ar I 



The interpretation of these formulas is implicit in the discussion of the 

 high field formulas given earlier. In particular the combination of the 

 equations (55) and (116) can be given the elegant form 



m(c') = Miff) + m(c.)' + ilf(c.)' (122) 



It states that the energy of an ion is obtained by adding the energy of a 

 gas molecule, the energy visible in the drift motion and a storage term 

 which is M/m times the energy in the drift motion; this term becomes 

 important for electrons in a gas. A low field approximation to this for- 

 mula (in which the second term on the right may be neglected) has been 

 published in the article of Kihara.^^ 



IIIB. RESULTS FOR THE POLARIZATION FORCE AND THE ISOTROPIC 

 "MAXWELLIAN" MODEL 



The polarization force between ions and molecules which predominates 

 over other forces at sufficiently low temperature satisfies the mean free 

 time requirement of the preceding section. It follows that the complete 

 theory given for those conditions applies to this force. The magnitude of 

 force was given in (4). Its potential equals 



1 eF 



F = i ^ (123) 



Classical theory is usually applicable to the scattering by the potential 

 (123) because angular momentum quantum numbers run as high as 30 

 or 50 in normal situations.^^ This classical type theory, first developed by 

 Langevin,^ follows standard elementary methods for computing the 



" Reference 27, formula 5.12. 



" Holstein, Theodore, private communication, see also Reference 11. 



" Langevin, Ann. de Chim. et do Phys., 6, p. 245, 1905. 



