(updated for 2013)

In Ion-Neutral reactions, the neutral atom is polarized by the electric field of the ion, so that interaction potential is

,

where* * is the electric field due to the charged particle, is the induced dipole moment in the neutral particle (determined by quantum mechanics), and is the polarizability, which defines for a neutral atom in a uniform static electric field. See Draine, section 2.4 for more details.

This interaction can take **strong** or **weak **forms. We distinguish between the two cases by considering b, the impact parameter. Recall that the reduced mass of a 2-body system is In the weak regime, the interaction energy is much smaller than the kinetic energy of the reduced mass:

.

In the strong regime, the opposite holds:

.

The spatial scale which separates these two regimes corresponds to , the critical impact parameter. Setting the two sides equal, we see that

The effective cross section for ion-neutral interactions is

Deriving an interaction rate is tricker than for neutral-neutral collisions because in general. So, let’s leave out an explicit *n* and calculate a **rate coefficient** *k *instead, in .

(although really , so k is largely independent of v). Combining with the equation above, we get the ion-neutral scattering rate coefficient

As an example, for interactions we get . This is about the rate for most ion-neutral exothermic reactions. This gives us

.

So, if , the average time between collisions is **16 years**. Recall that, for neutral-neutral collisions in the diffuse ISM, we had years. Ion-neutral collisions are **much** more frequent in most parts of the ISM due to the larger interaction cross section.