216 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1953 



-3.0 -2.5 -2.0 -\.5 -1.0 -0.5 0.5 1.0 1.5 2.0 2.5 3.0 



Wx 



Fig. 13 — Velocity distribution function of ions moving through the parent 

 gas in a high field; contours constructed from the Monte Carlo results of Fig. 12. 



A simple physical proof of this statement goes as follows. Suppose an 

 ion and a molecule make a collision which is almost central, but has a 

 small impact parameter h. The collision will bring the ion almost to rest 

 because the atom was originally at rest by hypothesis. Because the col- 

 lision was not quite central, however, the ion will have a small residual 

 velocity C/ at right angles to its original velocity c,- . For any reasonable 

 law of scattering this quantity C/ will be proportional to d and to h. 



Cf oc cr6 

 The probability for a value of b between h and b + db is proportional 



