MOTION OF GASEOUS IONS IN STRONG ELECTRIC FIELDS 



177 



attractive potential shows a better way out. The potential gives rise to 

 two kinds of orbits; orbits of large angular momentum which look some- 

 what like hyperbolas, shown in Fig. 2(a), and orbits of small angular 

 momentum for which the particles are ^'sucked" toward each other in a 

 spiralling movement until a repulsive force reverses the trend, as shown in 

 Fig. 2(b).^ A calculation of Hass^^ shows that the latter type of motion 

 is much more eflScient in scattering than the former and one gets there- 

 for a picture which is semiquantitatively correct if one substitutes into 

 (5) the cross-section for spiralling collisions and assumes isotropic scat- 

 tering.^^ This cross section equals 



y m M 



Vp 



(6) 



A numerical estimate of the cross section (6) automatically leads one 

 to compare it with the short distance repulsion familiar from the kinetic 

 theory of gases. The two are of the same order, but for the usual gaseous 

 speeds (which enter into (6) through 7) and small molecules the cross 



(b) 



Fig. 2 — Sample orbits (schematic) showing the motion of a particle in the 

 polarization force field, (a) Hyperbolic orbit (large angular momentum), (b) 

 Spiralling orbit (small angular momentum) . 



8 There are quantum mechanical analogues to these classical ideas; they should 

 lead to practically identical answers unless the angular momentum quantum 

 number is small. 



9 Hass^, H. R., Phil. Mag., 1, p. 139, 1926. 



1° This will be discussed more fully in Section IIIB. 



