The I-Integral Representation

With the specifications from above and with the choices va = (va,tp, p), vn = (vm o, 0) we can write for the Maxwellian average gA 

Here u = yj2Ta/ ma, the thermal velocity, uroi va — vn is the relative velocity, ip was chosen as the angle between the velocity of the charged particle a and the neutral particle labelled n.  

We are considering collision processes with azimuthal symmetry only hence dtp - = 2n  

After substitution va = vroi + vn, and with v y sin ip dva dip = v elsinip dvieidip the integration over the resulting angular co-ordinate ip can be carried out, and one obtains  

For v A = 1 this is the ordinary rate coefficient for an interaction of a mono-energetic beam with a Maxwellian host medium (e.g., [20]). Since any 

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